researchseminars.org

Nicholas Wilkins (Bristol)
2020-04-17 13:15 - 14:45 UTC
Title: Equivariant quantum operations and relations between them (https://master.researchseminars.org/talk/SympZoominar/1/)
by Nicholas Wilkins (Bristol) as part of Symplectic zoominar

Abstract
There is growing interest in looking at operations on quantum cohomology that take into account symmetries in the holomorphic spheres (such as the quantum Steenrod powers, using a Z/p-symmetry). In order to prove relations between them, one needs to generalise this to include equivariant operations with more marked points, varying domains and different symmetry groups. We will look at the general method of construction of these operations, as well as two distinct examples of relations between them.

Lisa Traynor (Bryn Mawr)
2020-04-24 13:15 - 14:45
Title: The geography of immersed Lagrangian fillings of Legendrian submanifolds (https://master.researchseminars.org/talk/SympZoominar/2/)
by Lisa Traynor (Bryn Mawr) as part of Symplectic zoominar

Abstract
Given a smooth knot K in the 3-sphere, a classic question in knot theory is: What surfaces in the 4-ball have boundary equal to K? One can also consider immersed surfaces and ask a “geography” question: What combinations of genus and double points can be realized by surfaces with boundary equal to K? I will discuss symplectic analogues of these questions: Given a Legendrian knot, what Lagrangian surfaces can it bound? What immersed Lagrangian surfaces can it bound? These Lagrangian surfaces are commonly called Lagrangian fillings of the Legendrian knot and are more rigid than their topological counterpart. In particular, while any smooth knot bounds an infinite number of topologically distinct surfaces, there are classical and non-classical obstructions to the existence of Lagrangian fillings of Legendrian knots. Specifically, a polynomial associated to the Legendrian boundary through the technique of generating families can show that there is no compatible embedded Lagrangian filling. Immersed Lagrangian fillings are more flexible, and I will describe how this polynomial associated to the Legendrian boundary forbids particular combinations of genus and double points in immersed Lagrangian fillings. In addition, I will describe some constructions of immersed fillings that allow us to completely answer the Lagrangian geography question for some Legendrian knots. This is joint work with Samantha Pezzimenti.

Alberto Abbondandolo (Bochum)
2020-05-01 13:15 - 14:45
Title: Zoll contact forms are local maximisers of the systolic ratio (https://master.researchseminars.org/talk/SympZoominar/3/)
by Alberto Abbondandolo (Bochum) as part of Symplectic zoominar

Abstract
A central question from systolic geometry is to find upper bounds for the systolic ratio of a Riemannian metric on a closed $n$-dimensional manifold, i.e. the ratio of the $n$-th power of the shortest length of closed geodesics by the volume. This question can be naturally extended to Reeb flows, a class of dynamical systems including geodesic flows and induced by a contact form on a closed manifold. The aim of this talk is to discuss a recent result obtained in collaboration with Gabriele Benedetti: Zoll contact forms, i.e. forms such that all the orbits of the induced Reeb flow are periodic with the same period, are local maximisers of the systolic ratio. Consequences of this result are: (i) sharp systolic inequalities for Riemannian and Finsler metrics close to Zoll ones, (ii) the perturbative case of a conjecture of Viterbo on the symplectic capacity of convex bodies, (iii) a generalization of Gromov's non-squeezing theorem in the intermediate dimensions for symplectomorphisms that are close to linear ones.

Marco Mazzucchelli (ENS- Lyon)
2020-05-08 13:15 - 14:45
Title: Spectral characterizations of Besse and Zoll Reeb flows (https://master.researchseminars.org/talk/SympZoominar/4/)
by Marco Mazzucchelli (ENS- Lyon) as part of Symplectic zoominar

Abstract
In this talk, I will address a geometric inverse problem from contact geometry: is it possible to recognize whether all orbits of a given Reeb flow are closed from the knowledge of the action spectrum? Borrowing the terminology from Riemannian geometry, Reeb flows all of whose orbits are closed are sometimes called Besse, and Besse Reeb flows all of whose orbits have the same minimal period are sometimes called Zoll. In the talk I will summarize recent results on this inverse problem in a few settings: geodesic flows (joint work with Stefan Suhr), closed contact 3-manifolds (joint work with Daniel Cristofaro-Gardiner), convex contact spheres and, more generally, restricted contact type hypersurfaces of symplectic vector spaces (joint work with Viktor Ginzburg and Basak Gürel). I will also mention a few conjectures and open problems.

Jo Nelson (Rice)
2020-05-15 13:15 - 14:45
Title: Reflections on cylindrical contact homology (https://master.researchseminars.org/talk/SympZoominar/5/)
by Jo Nelson (Rice) as part of Symplectic zoominar

Abstract
This talk beings with a light introduction, including some historical anecdotes to motivate the development of this Floer theoretic machinery for contact manifolds some 25 years ago. I will discuss joint work with Hutchings which constructs nonequivariant and a family Floer equivariant version of contact homology. Both theories are generated by two copies of each Reeb orbit over Z and capture interesting torsion information. I will explain the need for an obstruction bundle gluing correction term in the expression of the differential in the presence of contractible Reeb orbits, which is essential even in the simple example of an ellipsoid. I will then explain how one can recover the original cylindrical theory proposed by Eliashberg-Givental-Hofer via our constructions.

Denis Auroux (Harvard)
2020-05-22 13:15 - 14:45
Title: Mirrors of curves and their Fukaya categories (https://master.researchseminars.org/talk/SympZoominar/6/)
by Denis Auroux (Harvard) as part of Symplectic zoominar

Abstract
Homological mirror symmetry predicts that the derived category of coherent sheaves on a curve has a symplectic counterpart as the Fukaya category of a mirror space. However, with the exception of elliptic curves, this mirror is usually a symplectic Landau-Ginzburg model, i.e. a non-compact manifold equipped with the extra data of a "stop" in its boundary at infinity. Most of the talk will focus on a family of Landau-Ginzburg models which provide mirrors to curves in (C*)^2 or in toric surfaces (or more generally to hypersurfaces in toric varieties), and their fiberwise wrapped Fukaya categories (joint work with Mohammed Abouzaid). I will then discuss more a speculative way of constructing mirrors of curves without Landau-Ginzburg models, involving a new flavor of Lagrangian Floer theory in trivalent configurations of Riemann surfaces (joint work with Alexander Efimov and Ludmil Katzarkov).

Alex Oancea (Paris)
2020-05-29 13:15 - 14:45
Title: Duality for Rabinowitz-Floer homology (https://master.researchseminars.org/talk/SympZoominar/7/)
by Alex Oancea (Paris) as part of Symplectic zoominar

Abstract
I will explain a duality theorem with products in Rabinowitz-Floer homology. This has a bearing on string topology and explains a number of dualities that have been observed in that setting. Joint work in progress with Kai Cieliebak and Nancy Hingston.

Leonid Polterovich (Tel Aviv)
2020-04-10 13:15 - 14:45
Title: Geometry of Quantum Uncertainty (https://master.researchseminars.org/talk/SympZoominar/8/)
by Leonid Polterovich (Tel Aviv) as part of Symplectic zoominar

Abstract: TBA

Daniel Cristofaro-Gardiner (IAS)
2020-04-03 13:15 - 14:45
Title: The Simplicity Conjecture (https://master.researchseminars.org/talk/SympZoominar/9/)
by Daniel Cristofaro-Gardiner (IAS) as part of Symplectic zoominar

Abstract: TBA

Octav Cornea (Montreal)
2020-03-27 13:15 - 14:45
Title: Fragmentation pseudo-metrics and Lagrangian submanifolds (https://master.researchseminars.org/talk/SympZoominar/10/)
by Octav Cornea (Montreal) as part of Symplectic zoominar

Abstract: TBA

Mark Mclean (SUNY, Stony Brook)
2020-06-12 13:15 - 14:45
Title: Floer Cohomology and Arc Spaces. (https://master.researchseminars.org/talk/SympZoominar/11/)
by Mark Mclean (SUNY, Stony Brook) as part of Symplectic zoominar

Abstract
Let f be a polynomial over the complex numbers with an isolated singular point at the origin and let d be a positive integer. To such a polynomial we can assign a variety called the dth contact locus of f. Morally, this corresponds to the space of d-jets of holomorphic disks in complex affine space whose boundary `wraps' around the singularity d times. We show that Floer cohomology of the dth power of the Milnor monodromy map is isomorphic to compactly supported cohomology of the dth contact locus. This answers a question of Paul Seidel and it also proves a conjecture of Nero Budur, Javier Fernández de Bobadilla, Quy Thuong Lê and Hong Duc Nguyen. The key idea of the proof is to use a jet space version of the PSS map together with a filtration argument.

Morgan Weiler, Joé Brendel, Abror Pirnapasov
2020-06-05 13:15 - 14:45
Title: Three 20 minutes research talks by young researchers. (https://master.researchseminars.org/talk/SympZoominar/12/)
by Morgan Weiler, Joé Brendel, Abror Pirnapasov as part of Symplectic zoominar

Abstract
Morgan Weiler (Rice):Infinite staircases of symplectic embeddings of ellipsoids into Hirzebruch surfaces

Joé Brendel (Neuchatel): Real Lagrangian Tori in toric symplectic manifolds

Abror Pirnapasov (Bochum): Reeb orbits that force topological entropy

See the external web page for full abstracts.

Igor Uljarevic (Belgrade)
2020-06-19 13:15 - 14:45
Title: Exotic symplectomorphisms and contact circle action (https://master.researchseminars.org/talk/SympZoominar/13/)
by Igor Uljarevic (Belgrade) as part of Symplectic zoominar

Abstract
An exotic symplectomorphism is a symplectomorphism that is not isotopic to the identity through compactly supported symplectomorphisms.Using Floer-theoretic methods, we prove that the non-existence of an exotic symplectomorphism on the standard symplectic ball, $\mathbb{B}^{2n},$ implies a rather strict topological condition on the free contact circle actions on the standard contact sphere, $\mathbb{S}^{2n-1}.$ We also prove an analogue for a Liouville domain and contact circle actions on its boundary. Applications include results on the symplectic mapping class group, the fundamental group of the group of contactomorphisms, and exotic contact structures on $\mathbb{S}^3.$ The talk is based on joint work with Dusan Drobnjak.

Ailsa Keating (Cambridge)
2020-06-26 13:15 - 14:45
Title: Distinguishing monotone Lagrangians via holomorphic annuli (https://master.researchseminars.org/talk/SympZoominar/14/)
by Ailsa Keating (Cambridge) as part of Symplectic zoominar

Abstract
We present techniques for constructing families of compact, monotone (including exact) Lagrangians in certain affine varieties, starting with Brieskorn-Pham hypersurfaces. We will focus on dimensions 2 and 3. In particular, we'll explain how to set up well-defined counts of holomorphic annuli for a range of these families. Time allowing, we will give a number of applications.

Ana Rita Pires (Edinburgh)
2020-07-03 13:15 - 14:45
Title: Infinite staircases and reflexive polygons (part of Ellipsoid day joint with Western Hemisphere Virtual Symplectic Seminar) (https://master.researchseminars.org/talk/SympZoominar/15/)
by Ana Rita Pires (Edinburgh) as part of Symplectic zoominar

Abstract
A classic result, due to McDuff and Schlenk, asserts that the function that encodes when a four-dimensional symplectic ellipsoid can be embedded into a four-dimensional ball has a remarkable structure: the function has infinitely many corners, determined by the odd-index Fibonacci numbers, that fit together to form an infinite staircase. The work of McDuff and Schlenk has recently led to considerable interest in understanding when the ellipsoid embedding function for other symplectic 4-manifolds is partly described by an infinite staircase. In this talk we will discuss a general framework for analyzing this question for a large family of targets, and in particular give an obstruction to the existence of an infinite staircase that experimentally seems strong. We will then look at the special case of rational convex toric domains / closed symplectic toric manifolds, for which we prove the existence of six families of targets with infinite staircases that are distinguished by the fact that their moment polygon is reflexive. The proof uses, among other tools, almost toric fibrations -- see also the second of the ellipsoid day talks. Finally, we conjecture that these six families constitute a complete answer to the question of existence of infinite staircase. This conjecture has been verified in the case when the target is an ellipsoid -- see the third of the ellipsoid day talks. This is based on joint work of Dan Cristofaro-Gardiner, Tara Holm, Alessia Mandini, and Ana Rita Pires.

Peter Ozsvath (Princeton)
2020-07-10 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/16/
Title: Knot Floer homology and bordered algebras (https://master.researchseminars.org/talk/SympZoominar/16/)
by Peter Ozsvath (Princeton) as part of Symplectic zoominar

Abstract
Knot Floer homology is an invariant for knots in three-space, defined as a Lagrangian Floer homology in a symmetric product. It has the form of a bigraded vector space, encoding topological information about the knot. I will discuss an algebraic approach to computing knot Floer homology, and a corresponding version for links, based on decomposing knot diagrams. This is joint work with Zoltan Szabo, building on earlier joint work (bordered Heegaard Floer homology) with Robert Lipshitz and Dylan Thurston.

Yusuke Kawamoto (Ecole Normale Supérieure), Shira Tanny (Tel-Aviv University), and Javier Martínez-Aguinaga (Universidad Complutense Madrid)
2020-07-17 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/17/
Title: Three 20 minutes research talks by young researchers. (https://master.researchseminars.org/talk/SympZoominar/17/)
by Yusuke Kawamoto (Ecole Normale Supérieure), Shira Tanny (Tel-Aviv University), and Javier Martínez-Aguinaga (Universidad Complutense Madrid) as part of Symplectic zoominar

Abstract
Kawamoto: Homogeneous quasimorphism, C^0-topology and Lagrangian intersection

Tanny: Floer theory of disjointly supported Hamiltonians

Martínez-Aguinaga: Madrid Formal Legendrian and horizontal embeddings

John Pardon (Princeton)
2020-07-24 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/18/
Title: Pontryagin--Thom for orbifold bordism (https://master.researchseminars.org/talk/SympZoominar/18/)
by John Pardon (Princeton) as part of Symplectic zoominar

Abstract
The classical Pontryagin–Thom isomorphism equates manifold bordism groups with corresponding stable homotopy groups. This construction moreover generalizes to the equivariant context. I will discuss work which establishes a Pontryagin--Thom isomorphism for orbispaces (an orbispace is a "space" which is locally modelled on Y/G for Y a space and G a finite group; examples of orbispaces include orbifolds and moduli spaces of pseudo-holomorphic curves). This involves defining a category of orbispectra and an involution of this category extending Spanier--Whitehead duality. Global homotopy theory also plays a key role.

Georgios Dimitroglou Rizell (Uppsala)
2020-09-04 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/19/
Title: Hamiltonian classification and unlinkedness of fibres in cotangent bundles of Riemann surfaces (https://master.researchseminars.org/talk/SympZoominar/19/)
by Georgios Dimitroglou Rizell (Uppsala) as part of Symplectic zoominar

Abstract
In a joint work with Laurent Côté we show the following
result. Any Lagrangian plane in the cotangent bundle of an open Riemann surface which coincides with a cotangent fibre outside of some compact subset, is compactly supported Hamiltonian isotopic to that fibre. This result implies Hamiltonian unlinkedness for Lagrangian links in the cotangent bundle of a (possibly closed Riemann surface whose components are Hamiltonian isotopic to fibres.

Vincent Colin (Nantes)
2020-09-11 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/20/
Title: Reeb dynamics in dimension 3 and broken book decompositions (https://master.researchseminars.org/talk/SympZoominar/20/)
by Vincent Colin (Nantes) as part of Symplectic zoominar

Abstract
In a joint work with Pierre Dehornoy and Ana Rechtman, we prove that on a closed 3-manifold, every nondegenerate Reeb vector field is supported by a broken book decomposition. From this property, we deduce that in dimension 3 every nondegenerate Reeb vector field has either 2 or infinitely periodic orbits and that on a closed 3-manifold that is not graphed, every nondegenerate Reeb vector field has positive topological entropy.

Cheol-Hyun Cho (Seoul)
2020-09-18 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/21/
Title: Fukaya category for Landau-Ginzburg orbifolds and Berglund-H\"ubsch homological mirror symmetry for curve singularities. (https://master.researchseminars.org/talk/SympZoominar/21/)
by Cheol-Hyun Cho (Seoul) as part of Symplectic zoominar

Abstract
For a weighted homogeneous polynomial and a choice of a diagonal symmetry group, we define a new Fukaya category based on wrapped Fukaya category of its Milnor fiber together with monodromy
information. It is analogous to the variation operator in singularity theory. As an application, we formulate a complete version of Berglund-H\"ubsch homological mirror symmetry and prove it for two variable cases. Namely, given one of the polynomials $f= x^p+y^q, x^p+xy^q,x^py+xy^q$ and a symmetry group $G$, we use Floer theoretic construction to obtain the transpose polynomial $f^t$ with the transpose symmetry group $G^t$ as well as an explicit A-infinity equivalence between the new Fukaya category of $(f,G)$ to the matrix factorization category of $(f^t, G^t)$. In this case, monodromy is mirror to the restriction of LG model to a hypersurface. For ADE singularities, Auslander-Reiten quiver for indecomposable matrix factorizations were known from 80's, and we find the corresponding Lagrangians as well as surgery exact sequences. This is a joint work with Dongwook Choa and Wonbo Jung.

Lev Buhovsky (Tel Aviv)
2020-10-09 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/22/
Title: The Arnold conjecture, spectral invariants and C^0 symplectic topology (https://master.researchseminars.org/talk/SympZoominar/22/)
by Lev Buhovsky (Tel Aviv) as part of Symplectic zoominar

Abstract
The Arnold conjecture about fixed points of Hamiltonian diffeomorphisms was partly motivated by the celebrated Poincare-Birkhoff fixed point
theorem for an area-preserving homeomorphism of an annulus in the plane. Despite the fact that the Arnold conjecture was formulated in he smooth setting, several attempts to return to the continuous setting of homeomorphisms and to study the conjecture in this setting has been made afterwards. In this talk I will describe some old and more recent results on the subject. Based on a joint work with V. Humiliere and S. Seyfaddini.

Jun Zhang (Montreal)
2020-09-25 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/23/
Title: Triangulated persistence categories (https://master.researchseminars.org/talk/SympZoominar/23/)
by Jun Zhang (Montreal) as part of Symplectic zoominar

Abstract
This talk will discuss a new algebraic structure called triangulated persistence category (TPC). It combines the triangulated category structure with the persistence module structure. This algebraic structure can be used to associate a metric topology on the object-set of a triangulated category, which leads to various dynamical questions on a pure algebraic set-up. Many examples are naturally endowed with the TPC structure, for instance, derived Fukaya category, Tamarkin category, etc. In this talk, we will illustrate one algebraic example in depth via extending the Bondal-Kapranov’s classical pre-triangulated dg-category to a filtered version. This talk is based on an in-progress project joint with Paul Biran and Octav Cornea.

Dusa McDuff (Columbia)
2020-10-02 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/24/
Title: Embedding ellipsoids into the one-point blowup of $\C P^2$ (https://master.researchseminars.org/talk/SympZoominar/24/)
by Dusa McDuff (Columbia) as part of Symplectic zoominar

Abstract
This talk reports on joint work with Maria Bertozzi, Tara Holm, Emily Maw, Grace Mwakyoma, Ana Rita Pires, and Morgan Weiler on a WiSCon project to investigate the embedding capacity function of the one-point blow up of $\C P^2$. We found three new families of staircases, that are related by symmetries and have other interesting structural features. This talk will explain our findings and our conjectures.

Michael Hutchings (Berkeley)
2020-10-23 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/25/
Title: Examples related to Viterbo's conjectures (https://master.researchseminars.org/talk/SympZoominar/25/)
by Michael Hutchings (Berkeley) as part of Symplectic zoominar

Abstract
Viterbo conjectured that a normalized symplectic capacity, on convex domains of a given volume, is maximized for the ball. A stronger version of this conjecture asserts that all normalized symplectic capacities agree on convex domains. Since convexity is not symplectomorphism invariant, one can also ask to what extent these statements still hold for nonconvex domains. We survey some special cases and examples around these questions, including recent joint works with Julian Chaidez and Jean Gutt + Vinicius Ramos.

Umut Varolgunes (Stanford)
2020-10-16 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/26/
Title: Mirror symmetry for chain type polynomials (https://master.researchseminars.org/talk/SympZoominar/26/)
by Umut Varolgunes (Stanford) as part of Symplectic zoominar

Abstract
I will start by explaining Takahashi's homological mirror symmetry (HMS) conjecture regarding invertible polynomials, which is an open string reinterpretation of Berglund-Hubsch-Henningson mirror symmetry. In joint work with A. Polishchuk, we resolved this HMS conjecture in the chain type case up to rigorous proofs of general statements about Fukaya-Seidel categories. Our proof goes by showing that the categories in both sides are obtained from the category Vect(k) by applying a recursion. I will explain this recursion categorically and sketch the argument for why it is satisfied on the A-side assuming the aforementioned foundational results. If time permits, I will also mention what goes into the proof in the B-side.

Eva Miranda (UPC)
2020-12-04 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/27/
Title: The singular Weinstein conjecture and the Contact/Beltrami mirror (https://master.researchseminars.org/talk/SympZoominar/27/)
by Eva Miranda (UPC) as part of Symplectic zoominar

Abstract
In this talk, I will address the (singular) Weinstein conjecture about the existence of (singular) periodic orbits of Reeb vector fields on compact manifolds endowed with singular contact forms. Our motivating examples come from Celestial mechanics (restricted three-body problem) where contact topology techniques were already successful in determining the existence of periodic orbits (Albers-Frauenfelder-Van Koert-Paternain). With the aim of completing this understanding, we deal with the restricted three body example by adding the so-called "infinity set" (via a McGehee regularization). This induces a singularity on the contact structure which permeates the geometry and topology of the problem.

Hofer's fine techniques to prove the Weinstein conjecture for overtwisted 3-dimensional contact manifolds can be adapted in this singular set-up under some symmetry assumptions close to the singular set (which also work for the non-compact case). We prove the existence of infinite smooth Reeb periodic orbits on the (compact) critical set of the contact form. This critical set can often be identified with the collision set or set at infinity in the motivating examples from Celestial mechanics. In those examples, escape trajectories can be often compactified as singular periodic orbits.

Time permitting, we will end up this talk proving the existence of escape orbits and generalized singular periodic orbits for 3-dimensional singular contact manifolds under some mild assumptions. Our theory benefits in a great manner from the existence of a correspondence (up to reparametrization) between Reeb and Beltrami vector fields (Etnyre and Ghrist) which can be exported to this singular set-up. In particular, Uhlenbeck's genericity results for the eigenfunctions of the Laplacian is a key point of the proof.

The contents of this talk are based on joint works with Cédric Oms and Daniel Peralta-Salas.

Zhengyi Zhou (IAS, Princeton)
2020-12-11 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/28/
Title: Hierarchies of contact manifolds via rational SFT (https://master.researchseminars.org/talk/SympZoominar/28/)
by Zhengyi Zhou (IAS, Princeton) as part of Symplectic zoominar

Abstract
I will explain the construction of a functor from the exact symplectic cobordism category to a totally ordered set, which measures the complexity of the contact structure. Those invariants are derived from a bi-Lie infinity formalism of the rational SFT and a partial construction of the rational SFT. In this talk, I will focus on the construction and properties of the functor. Time permitting, I will explain applications, computations, and relations to the involutive bi-Lie infinity formalism of the full SFT. This is joint work with Agustin Moreno.

Kai Cieliebak (Augsburg)
2020-11-06 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/29/
Title: Secondary coproducts in Morse and Floer homology (https://master.researchseminars.org/talk/SympZoominar/29/)
by Kai Cieliebak (Augsburg) as part of Symplectic zoominar

Abstract
This talk is about joint work with Nancy Hingston and Alexandru Oancea. We describe various secondary coproducts on the Floer homology of a cotangent bundle and show that, under Viterbo's isomorphism, they all correspond to the Goresky-Hingston coproduct on loop space homology. The proof uses compactified moduli spaces of punctured holomorphic annuli.

Yu-Wei Fan (Berkeley); Surena Hozoori (Georgia Tech); Marcelo Atallah (Montreal)
2020-11-27 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/30/
Title: Three short research talks of 20 min each. (https://master.researchseminars.org/talk/SympZoominar/30/)
by Yu-Wei Fan (Berkeley); Surena Hozoori (Georgia Tech); Marcelo Atallah (Montreal) as part of Symplectic zoominar

Abstract
Yu-Wei Fan: Shifting numbers in triangulated categories.

Abstract: One can consider endofunctors of triangulated categories as categorical dynamical systems, and study their long term behaviors under large iterations. There are (at least) three natural invariants that one can associate to endofunctors from the dynamical perspective: categorical entropy, and upper/lower shifting numbers. We will recall some background on categorical dynamical systems and categorical entropy, and introduce the notion of shifting numbers, which measure the asymptotic amount by which an endofunctor of a triangulated category translates inside the category. The shifting numbers are analogous to Poincare translation numbers. We additionally establish that in some examples the shifting numbers provide a quasimorphism on the group of autoequivalences. Joint work with Simion Filip.

Surena Hozoori: Symplectic Geometry of Anosov Flows in Dimension 3 and Bi-Contact Topology.

Abstract: We give a purely contact and symplectic geometric characterization of Anosov flows in dimension 3 and set up a framework to use tools from contact and symplectic geometry and topology in the study of questions about Anosov dynamics. If time permits, we will discuss some uniqueness results for the underlying (bi-) contact structure for an Anosov flow, and/or a characterization of Anosovity based on Reeb flows.

Marcelo Atallah: Hamiltonian no-torsion

Abstract: In 2002 Polterovich notably showed that Hamiltonian diffeomorphisms of finite order, which we call Hamiltonian torsion, must be trivial on closed symplectically aspherical manifolds. We study the existence of Hamiltonian torsion and its metric rigidity properties in more general situations. First, we extend Polterovich's result to closed symplectically Calabi-Yau and closed negative monotone manifolds. Second, going beyond topological constraints, we describe how Hamiltonian torsion is related to the existence of pseudo-holomorphic spheres and answer a close variant of Problem 24 from the introductory monograph of McDuff-Salamon. Finally, we prove an analogue of Newman’s 1931 theorem for Hofer’s metric and Viterbo’s spectral metric on the Hamiltonian group of monotone symplecitc manifolds: a sufficiently small ball around the identity contains no torsion. During the talk, I shall discuss the results above and some of the key ingredients of their proofs. This talk is based on joint work with Egor Shelukhin.

Simon Allais (ENS Lyon); Orsola Capovilla-Searle (Duke); Julian Chaidez (UCB)
2020-10-30 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/31/
Title: Three short research talks of 20 min each. (https://master.researchseminars.org/talk/SympZoominar/31/)
by Simon Allais (ENS Lyon); Orsola Capovilla-Searle (Duke); Julian Chaidez (UCB) as part of Symplectic zoominar

Abstract
Simon Allais (ENS Lyon): Generating functions in Hamiltonian dynamics and symplectic-contact rigidity

Abstract: Generating functions of Hamiltonian diffeomorphisms are maps that can be seen as finite dimensional versions of the action functional. In various situations, classical Morse theory applied to them can retrieve the same information as the Floer theory. In this talk, I will introduce this tool and expose some old and new results of Hamiltonian dynamics and symplectic rigidity that can be retrieved and sometimes extended using elementary Morse theory and generating functions; among others, the recent theorem of Shelukhin about the Hofer-Zehnder conjecture in the special case of CP^d and a contact generalization of the symplectic camel theorem.

Orsola Capovilla-Searle (Duke University): Weinstein handle decompositions of complements of toric divisors in toric 4 manifolds

Abstract: We consider toric 4 manifolds with certain toric divisors that have normal crossing singularities. The normal crossing singularities can be smoothed, changing the topology of the complement. In specific cases this complement has a Weinstein structure, and we develop an algorithm to construct a Weinstein handlebody diagram of the complement of the smoothed toric divisor. The algorithm we construct more generally gives a Weinstein handlebody diagram for Weinstein 4-manifolds constructed by attaching 2 handles to T*S for any surface S, where the 2 handles are attached along the conormal lift of curves on S. Joint work with Bahar Acu, Agnes Gadbled, Aleksandra Marinkovic, Emmy Murphy, Laura Starkston and Angela Wu.

Julian Chaidez (UC Berkeley): ECH Embedding Obstructions For Rational Surfaces

Abstract: Is the Gromov width on toric varieties monotonic with respect to inclusions of moment polytopes? In this talk, I will prove a generalization in dimension 4: the "width" associated to a concave toric domain is monotonic with inclusion of momenty polygons. This is an application of some new algebro-geometric obstructions for embeddings of star-shaped domains into rational surfaces. This work is joint with Ben Wormleighton.

Nick Sheridan (Edinburgh)
2020-11-13 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/32/
Title: Quantum cohomology as a deformation of symplectic cohomology (https://master.researchseminars.org/talk/SympZoominar/32/)
by Nick Sheridan (Edinburgh) as part of Symplectic zoominar

Abstract
Let X be a compact symplectic manifold, and D a normal crossings symplectic divisor in X. We give a criterion under which the quantum cohomology of X is the cohomology of a natural deformation of the symplectic cochain complex of X \ D. The criterion can be thought of in terms of the Kodaira dimension of X (which should be non-positive), and the log Kodaira dimension of X \ D (which should be non-negative). The crucial tool is Varolgunes' relative symplectic cohomology. This is joint work with Strom Borman and Umut Varolgunes.

Paul Biran (ETH Zurich)
2020-11-20 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/33/
Title: Persistence and Triangulation in Lagrangian Topology. (https://master.researchseminars.org/talk/SympZoominar/33/)
by Paul Biran (ETH Zurich) as part of Symplectic zoominar

Abstract
Triangulated categories play an important role in symplectic topology. The aim of this talk is to explain how to combine triangulated structures with persistence module theory in a geometrically meaningful way. The guiding principle comes from the theory of Lagrangian cobordism. The talk is based on ongoing joint work with Octav Cornea and Jun Zhang.

Lisa Jeffrey (University of Toronto)
2021-01-15 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/34/
Title: Symplectic implosion (https://master.researchseminars.org/talk/SympZoominar/34/)
by Lisa Jeffrey (University of Toronto) as part of Symplectic zoominar

Abstract
Symplectic implosion was developed to solve the problem that the
symplectic cross-section of a Hamiltonian K-space is usually not
symplectic, when K is a compact Lie group.

The symplectic implosion is a stratified symplectic space, introduced in
a 2002 paper of the speaker with Guillemin and Sjamaar. I survey some examples showing how symplectic implosion has been used.
I describe the universal imploded cross-section, which is the
imploded cross-section of the cotangent bundle of a compact Lie group.

Imploded cross-sections are normally not smooth manifolds.
We describe some invariants (for example intersection homology)
which replace homology for singular stratified spaces.

(Joint work with Sina Zabanfahm)

Basak Gurel (UCF)
2021-01-22 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/35/
Title: Pseudo-rotations vs. rotations (https://master.researchseminars.org/talk/SympZoominar/35/)
by Basak Gurel (UCF) as part of Symplectic zoominar

Abstract
The talk will focus on the question of whether existing symplectic methods can distinguish pseudo-rotations from rotations (i.e., elements of Hamiltonian circle actions). For the projective plane, in many instances, but not always, the answer is negative. Namely, for virtually every pseudo-rotation there exists a unique rotation with precisely the same fixed-point data. However, the hypothetical exceptions — ghost pseudo-rotations — suggest that the relation between the two classes of maps might be much weaker than previously thought, possibly leading to some unexpected consequences. This is based on joint work with Viktor Ginzburg.

Three 20 min research talks: Alexandre Jannaud (Sorbonne); Tim Large (MIT); Oliver Edtmair (Berkeley)
2021-01-29 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/36/
by Three 20 min research talks: Alexandre Jannaud (Sorbonne); Tim Large (MIT); Oliver Edtmair (Berkeley) as part of Symplectic zoominar

Abstract
Alexandre Jannaud (University of Neuchatel), Dehn-Seidel twist, C^0 symplectic geometry and barcodes

Abstract. In this talk I will present my work initiating the study of the $C^0$ symplectic mapping class group, i.e. the group of isotopy classes of symplectic homeomorphisms, and briefly present the proofs of the first results regarding the topology of the group of symplectic homeomorphisms. For that purpose, we will introduce a method coming from Floer theory and barcodes theory. Applying this strategy to the Dehn-Seidel twist, a symplectomorphism of particular interest when studying the symplectic mapping class group, we will generalize to $C^0$ settings a result of Seidel concerning the non-triviality of the mapping class of this symplectomorphism. We will indeed prove that the generalized Dehn twist is not in the connected component of the identity in the group of symplectic homeomorphisms. Doing so, we prove the non-triviality of the $C^0$ symplectic mapping class group of some Liouville domains.

Tim Large (MIT), Floer K-theory and exotic Liouville manifolds

Abstract: In this short talk, I will explain how to construct Liouville manifolds which have zero traditional symplectic cohomology but interesting symplectic K-theory. In particular, we construct an exotic symplectic structure on Euclidean space which is not distinguished by traditional Floer homology invariants. Instead, it is detected by a module spectrum for complex K-theory, built as a variant of Cohen-Jones-Segal’s Floer homotopy type. The proof involves passage through (wrapped) Fukaya categories with coefficients in a ring spectrum, rather than an ordinary ring.

Oliver Edtmair (Berkeley), 3D convex contact forms and the Ruelle invariant

Abstract. Is every dynamically convex contact form on the three sphere convex? In this talk I will explain why the answer to this question is no. The strategy is to derive a lower bound on the Ruelle invariant of convex contact forms and construct dynamically convex contact forms violating this lower bound. This is based on joint work with Julian Chaidez.

Yusuf Baris Kartal (Princeton)
2021-02-05 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/37/
Title: Algebraic torus actions on Fukaya categories and tameness of change in Floer homology under symplectic isotopies. (https://master.researchseminars.org/talk/SympZoominar/37/)
by Yusuf Baris Kartal (Princeton) as part of Symplectic zoominar

Abstract
The purpose of this talk is to explore how Lagrangian Floer homology groups change under (non-Hamiltonian) symplectic isotopies on a (negatively) monotone symplectic manifold $(M,\omega)$ satisfying a strong non-degeneracy condition. More precisely, given two Lagrangian branes $L,L'$, consider family of Floer homology groups $HF(\phi_v(L),L')$, where $v\in H^1(M,\mathbb R)$ and $\phi_v$ is the time-1 map of a symplectic isotopy with flux $v$. We show how to fit this collection into an algebraic sheaf over the algebraic torus $H^1(M,\mathbb G_m)$. The main tool is the construction of an "algebraic action" of $H^1(M,\mathbb G_m)$ on the Fukaya category. As an application, we deduce the change in Floer homology groups satisfy various tameness properties, for instance, the dimension is constant outside an algebraic subset of $H^1(M,\mathbb G_m)$. Similarly, given closed $1$-form $\alpha$, which generates a symplectic isotopy denoted by $\phi_\alpha^t$, the Floer homology groups $HF(\phi_\alpha^t(L),L')$ have rank that is constant in $t$, with finitely many possible exceptions.

Cheuk Yu Mak (Edinburgh)
2021-02-12 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/38/
Title: Non-displaceable Lagrangian links in four-manifolds (https://master.researchseminars.org/talk/SympZoominar/38/)
by Cheuk Yu Mak (Edinburgh) as part of Symplectic zoominar

Abstract
One of the earliest fundamental applications of Lagrangian Floer theory is detecting the non-displaceablity of a Lagrangian submanifold. Many progress and generalisations have been made since then but little is known when the Lagrangian submanifold is disconnected. In this talk, we describe a new idea to address this problem. Subsequently, we explain how to use Fukaya-Oh-Ohta-Ono and Cho-Poddar theory to show that for every S^2 \times S^2 with a non-monotone product symplectic form, there is a continuum of disconnected, non-displaceable Lagrangian submanifolds such that each connected component is displaceable. This is a joint work with Ivan Smith.

Daniel Pomerleano (Boston)
2021-02-19 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/39/
Title: Intrinsic mirror symmetry and categorical crepant resolutions (https://master.researchseminars.org/talk/SympZoominar/39/)
by Daniel Pomerleano (Boston) as part of Symplectic zoominar

Abstract
Gross and Siebert have recently proposed an "intrinsic" programme for studying mirror symmetry. In this talk, we will discuss a symplectic interpretation of some of their ideas in the setting of affine log Calabi-Yau varieties. Namely, we describe work in progress which shows that, under suitable assumptions, the wrapped Fukaya category of such a variety X gives an intrinsic "categorical crepant resolution" of Spec(SH0(X)). No background in mirror symmetry will be assumed for the talk.

Sylvain Courte (Université Grenoble Alpes)
2021-02-26 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/40/
Title: Twisted generating functions and the nearby Lagrangian conjecture (Part of the Generating Functions Day joint with Western Hemisphere Virtual Symplectic Seminar) (https://master.researchseminars.org/talk/SympZoominar/40/)
by Sylvain Courte (Université Grenoble Alpes) as part of Symplectic zoominar

Abstract
I will explain the notion of twisted generating function and show that a closed exact Lagrangian submanifold L in the cotangent bundle of M admits such a thing. The type of function arising in our construction is related to Waldhausen's tube space from his manifold approach to algebraic K-theory of spaces. Using the rational equivalence of this space with BO, as proved by Bökstedt, we conclude that the stable Lagrangian Gauss map of L vanishes on all homotopy groups. In particular when M is a homotopy sphere, we obtain the triviality of the stable Lagrangian Gauss map and a genuine generating function for L. This is a joint work with M. Abouzaid, S. Guillermou and T. Kragh.

Sobhan Seyfaddini (IMJ-PRG)
2021-03-05 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/41/
Title: Periodic Floer homology and the large-scale geometry of Hofer's metric on the sphere (https://master.researchseminars.org/talk/SympZoominar/41/)
by Sobhan Seyfaddini (IMJ-PRG) as part of Symplectic zoominar

Abstract
The large-scale geometry of Hofer's has been studied since the 90s and has seen much progress for a large class of symplectic manifolds. However, the case of the two-sphere has remained very mysterious, especially in comparison to other surfaces. For example, a well-known conjecture of Kapovich and Polterovich, from 2006, states that, on the two-sphere, Hofer's metric is not quasi-isometric to the real line. I will explain how invariants from periodic Floer homology can be used to answer this question. Time permitting we will also discuss connections to continuous symplectic topology. This is based on joint work with Dan Cristofaro-Gardiner and Vincent Humilière.

Oleg Lazarev (Harvard)
2021-03-12 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/42/
Title: Inverting primes in Weinstein geometry (https://master.researchseminars.org/talk/SympZoominar/42/)
by Oleg Lazarev (Harvard) as part of Symplectic zoominar

Abstract
A classical construction in topology associates to a space $X$ and prime $p$, a new "localized" space $X_p$ whose homotopy and homology groups are obtained from those of $X$ by inverting $p$. In this talk, I will discuss a symplectic analog of this construction, extending work of Abouzaid-Seidel and Cieliebak-Eliashberg on flexible Weinstein structures. Concretely, I will produce prime-localized Weinstein subdomains of high-dimensional Weinstein domains and also show that any Weinstein subdomain of a cotangent bundle agrees Fukaya-categorically with one of these special subdomains. The key will be to classify which objects of the Fukaya category of $T^{\ast} M$ – twisted complexes of Lagrangians – are quasi-isomorphic to actual Lagrangians. This talk is based on joint work with Z. Sylvan.

Egor Shelukhin (UdeM)
2021-03-19 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/43/
Title: Lagrangian configurations and Hamiltonian maps (https://master.researchseminars.org/talk/SympZoominar/43/)
by Egor Shelukhin (UdeM) as part of Symplectic zoominar

Abstract
We study configurations of disjoint Lagrangian submanifolds in certain low-dimensional symplectic manifolds from the perspective of the geometry of Hamiltonian maps. We detect infinite-dimensional flats in the Hamiltonian group of the two-sphere equipped with Hofer's metric, showing in particular that this group is not quasi-isometric to a line. This answers a well-known question of Kapovich-Polterovich from 2006. We show that these flats in $Ham(S^2)$ stabilize to certain product four-manifolds, prove constraints on Lagrangian packing, and find new instances of Lagrangian Poincare recurrence. The technology involves Lagrangian spectral invariants with Hamiltonian term in symmetric product orbifolds. This is joint work with Leonid Polterovich.

Jesse Huang(UIUC)/Shaoyun Bai(Princeton)/Thomas Melistas(UGA)
2021-03-26 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/44/
Title: Three short research talks of 20 min each. (https://master.researchseminars.org/talk/SympZoominar/44/)
by Jesse Huang(UIUC)/Shaoyun Bai(Princeton)/Thomas Melistas(UGA) as part of Symplectic zoominar

Abstract
Jesse Huang(UIUC), Variation of FLTZ skeleta.

In this short talk, I will discuss an interpolation of FLTZ skeleta mirror to derived equivalent toric varieties. This is joint work with Peng Zhou.

Shaoyun Bai(Princeton), $SU(n)$–Casson invariants and symplectic geometry.

In 1985, Casson introduced an invariant of integer homology 3-spheres by counting $SU(2)$-representations of the fundamental groups. The generalization of Casson invariant by considering Lie groups $SU(n)$ has been long expected, but the original construction of Casson encounters some difficulties. I will present a solution to this problem, highlighting the equivariant symplectic geometry and Atiyah-Floer type result entering the construction.

Thomas Melistas(UGA), The Large-Scale Geometry of Overtwisted Contact Forms.

Inspired by the symplectic Banach-Mazur distance, proposed by Ostrover and Polterovich in the setting of non-degenerate starshaped domains of Liouville manifolds, we define a distance on the space of contact forms supporting a given contact structure on a closed contact manifold and we use it to bi-Lipschitz embed part of the 2-dimensional Euclidean space into the space of overtwisted contact forms supporting a given contact structure on a smooth closed manifold.

Sheel Ganatra (USC)
2021-04-02 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/45/
Title: Categorical non-properness in wrapped Floer theory (https://master.researchseminars.org/talk/SympZoominar/45/)
by Sheel Ganatra (USC) as part of Symplectic zoominar

Abstract
In all known explicit computations on Weinstein manifolds, the self-wrapped Floer homology of non-compact exact Lagrangian is always either infinite-dimensional or zero. We will explain why a global variant of this observed phenomenon holds in broad generality: the wrapped Fukaya category of any Weinstein (or non-degenerate Liouville) manifold is always either non-proper or zero, as is any quotient thereof. Moreover any non-compact connected exact Lagrangian is always either a "non-proper object" or zero in such a wrapped Fukaya category, as is any idempotent summand thereof. We will also examine where the argument could break if one drops exactness, which is consistent with known computations of non-exact wrapped Fukaya categories which are smooth, proper, and non-vanishing (e.g., work of Ritter-Smith).

Sara Tukachinsky (IAS)
2021-04-09 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/46/
Title: Relative quantum cohomology and other stories (https://master.researchseminars.org/talk/SympZoominar/46/)
by Sara Tukachinsky (IAS) as part of Symplectic zoominar

Abstract
We define a quantum product on the cohomology of a symplectic manifold relative to a Lagrangian submanifold, with coefficients in a Novikov ring. The associativity of this product is equivalent to an open version of the WDVV equations for an appropriate disk superpotential. Both structures — the quantum product and the WDVV equations — are consequences of a more general structure we call the tensor potential, which will be the main focus of this talk. This is joint work with Jake Solomon.

Maxim Jeffs/Côme Dattin/Bingyu Zhang (Harvard/Nantes/Université Grenoble Alpes)
2021-04-16 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/47/
Title: Three 20min research talks (https://master.researchseminars.org/talk/SympZoominar/47/)
by Maxim Jeffs/Côme Dattin/Bingyu Zhang (Harvard/Nantes/Université Grenoble Alpes) as part of Symplectic zoominar

Abstract
Mirror symmetry and Fukaya categories of singular varieties (Maxim Jeffs)

In this talk I will explain Auroux' definition of the Fukaya category of a singular hypersurface and two results about this definition, illustrated with some examples. The first result is that Auroux' category is equivalent to the Fukaya-Seidel category of a Landau-Ginzburg model on a smooth variety; the second result is a homological mirror symmetry equivalence at certain large complex structure limits. I will also discuss ongoing work on generalizations.

Wrapped sutured Legendrian homology and the conormal of braids (Côme Dattin)

In this talk we will discuss invariants of sutured Legendrians. A sutured contact manifold can be seen as either generalizing the contactisation of a Liouville domain, or as a presentation of a contact manifold with convex boundary. Using the first point of view, we define the wrapped sutured homology of Legendrians with boundary, employing ideas coming from Floer theory. To illustrate the second aspect, we apply the unit conormal construction to braids with two strands, which yields a sutured Legendrian. We will show that, if the conormals of two 2-braids are Legendrian isotopic, then the braids are equivalent.

Capacities from the Chiu-Tamarkin complex (Bingyu Zhang)

In this talk, we will discuss the Chiu-Tamarkin complex. It is a symplectic/contact invariant that comes from the microlocal sheaf theory. I will explain how to define some capacities using the Chiu-Tamarkin complex in both symplectic and contact situations. The main result is the structure theorem of the Chiu-Tamarkin complex of convex toric domains. Consequently, we can compute the capacities of convex toric domains.

Laura Starkston (UC Davis)
2021-05-07 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/48/
Title: Unexpected fillings, singularities, and plane curve arrangements (https://master.researchseminars.org/talk/SympZoominar/48/)
by Laura Starkston (UC Davis) as part of Symplectic zoominar

Abstract
I will discuss joint work with Olga Plamenevskaya studying symplectic fillings of links of certain complex surface singularities, and comparing symplectic fillings with complex smoothings. We develop characterizations of the symplectic fillings using planar Lefschetz fibrations and singular braided surfaces. This provides an analogue of de Jong and van Straten's work which characterizes the complex smoothings in terms of decorated complex plane curves. We find differences between symplectic fillings and complex smoothings that had not previously been found in rational complex surface singularities.

Daniel Álvarez-Gavela (MIT)
2021-05-14 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/49/
Title: Caustics of Lagrangian homotopy spheres with stably trivial Gauss map (https://master.researchseminars.org/talk/SympZoominar/49/)
by Daniel Álvarez-Gavela (MIT) as part of Symplectic zoominar

Abstract
The h-principle for the simplification of caustics (i.e. Lagrangian tangencies) reduces a geometric problem to a homotopical problem. In this talk I will explain the solution to this homotopical problem in the case of spheres. More precisely, I will show that the stably trivial elements of the nth homotopy group of the Lagrangian Grassmannian $U_n/O_n$
, which lies in the metastable range, admit representatives with only fold type tangencies. By the h-principle, it follows that if $D$ is a Lagrangian distribution defined along a Lagrangian homotopy sphere $L$, then there exists a Hamiltonian isotopy which simplifies the tangencies between $L$ and $D$ to consist only of folds if and only if $D$ is stably trivial. I will give two applications of this result, one to the arborealization program and another to the study of nearby Lagrangian homotopy spheres. Joint work with David Darrow (in the form of an undergraduate research project).

Oğuz Şavk/Irene Seifert/Hang Yuan (Boğaziçi University/Heidelberg/Stony Brook)
2021-05-28 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/50/
Title: Three short research talks of 20 min each. (https://master.researchseminars.org/talk/SympZoominar/50/)
by Oğuz Şavk/Irene Seifert/Hang Yuan (Boğaziçi University/Heidelberg/Stony Brook) as part of Symplectic zoominar

Abstract
(Oğuz Şavk) Classical and new plumbings bounding contractible manifolds and homology balls

A central problem in low-dimensional topology asks which homology 3-spheres bound contractible 4-manifolds and homology 4-balls. In this talk, we address this problem for plumbed 3-manifolds and we present the classical and new results together. Along the way, we touch symplectic geometry by using the classical results of Eliashberg and Gompf. Our approach is based on Mazur’s famous argument which provides a unification of all results.

(Irene Seifert) Periodic delay orbits and the polyfold IFT

Differential delay equations arise very naturally, but they are much more complicated than ordinary differential equations. Polyfold theory, originally developed for the study of moduli spaces of pseudoholomorphic curves, can help to understand solutions of certain delay equations. In my talk, I will show an existence result about periodic delay orbits with small delay. If time permits, we can discuss possible further applications of polyfold theory to the differential delay equations. This is joint work with Peter Albers.

(Hang Yuan) Disk counting via family Floer theory

Given a family of Lagrangian tori with full quantum corrections, the non-archimedean SYZ mirror construction uses the family Floer theory to construct a non-archimedean analytic space with a global superpotential. In this talk, we will first briefly review the construction. Then, we will apply it to the Gross’s fibrations. As an application, we can compute all the non-trivial open GW invariants for a Chekanov-type torus in $\mathbb{CP}^n$ or $\mathbb{CP}^r\times \mathbb{CP}^{n-r}$. When $n=2$, $r=1$, we retrieve the previous results of Auroux and Chekanov-Schlenk without finding the disks explicitly. It is also compatible with the Pascaleff-Tonkonog’s work on Lagrangian mutations.

Simion Filip (Chicago)
2021-06-04 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/51/
Title: Degenerations of Kahler forms on K3 surfaces, and some dynamics (https://master.researchseminars.org/talk/SympZoominar/51/)
by Simion Filip (Chicago) as part of Symplectic zoominar

Abstract
K3 surfaces have a rich geometry and admit interesting holomorphic automorphisms. As examples of Calabi-Yau manifolds, they admit Ricci-flat Kähler metrics, and a lot of attention has been devoted to how these metrics degenerate as the Kähler class approaches natural boundaries. I will discuss how to use the full automorphism group to analyze the degenerations and obtain certain canonical objects (closed positive currents) on the boundary. While most of the previous work was devoted to degenerating the metric along an elliptic fibration (motivated by the SYZ picture of mirror symmetry) I will discuss how to analyze all the other points. Time permitting, I will also describe the construction of canonical heights on K3 surfaces (in the sense of number theory), generalizing constructions due to Silverman and Tate.
Joint work with Valentino Tosatti.

Francisco Presas (ICMAT)
2021-06-11 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/52/
Title: The homotopy type of the space of tight contact structures and the overtwisted mirage (https://master.researchseminars.org/talk/SympZoominar/52/)
by Francisco Presas (ICMAT) as part of Symplectic zoominar

Abstract: TBA

Agustin Moreno (Uppsala)
2021-06-18 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/53/
Title: On the spatial restricted three-body problem (https://master.researchseminars.org/talk/SympZoominar/53/)
by Agustin Moreno (Uppsala) as part of Symplectic zoominar

Abstract
In his search for closed orbits in the planar restricted three-body problem, Poincaré’s approach roughly reduces to:

(1) Finding a global surface of section;
(2) Proving a fixed-point theorem for the resulting return map.

This is the setting for the celebrated Poincaré-Birkhoff theorem. In this talk, I will discuss a generalization of this program to the spatial problem.

For the first step, we obtain the existence of global hypersurfaces of section for which the return maps are Hamiltonian, valid for energies below the first critical value and all mass ratios. For the second, we prove a higher-dimensional version of the Poincaré-Birkhoff theorem, which gives infinitely many orbits of arbitrary large period, provided a suitable twist condition is satisfied. Time permitting, we also discuss a construction that associates a Reeb dynamics on a moduli space of holomorphic curves (a copy of the three-sphere), to the given dynamics, and its properties.

This is based on joint work with Otto van Koert.

Laurent Côté (IAS/Harvard)
2021-07-09 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/54/
Title: Action filtrations associated to smooth categorical compactifications (https://master.researchseminars.org/talk/SympZoominar/54/)
by Laurent Côté (IAS/Harvard) as part of Symplectic zoominar

Abstract
There is notion of a smooth categorical compactification of dg/A-infinity categories: for example, a smooth compactification of algebraic varieties induces a smooth categorical compactification of the associated bounded dg categories of coherent sheaves. In symplectic topology, wrapped Fukaya categories of Weinstein manifolds admit smooth compactifications by partially wrapped Fukaya categories. The goal of this talk is to explain how to associate an "action filtration" to a smooth categorical compactifications, which is invariant (up to appropriate equivalence) under zig-zags of smooth compactifications. I will then discuss applications to symplectic topology and categorical dynamics. This talk reports on joint work with Y. Baris Kartal.

Helmut Hofer (IAS)
2021-07-16 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/55/
Title: The Floer Jungle: 35 years of Floer Theory (https://master.researchseminars.org/talk/SympZoominar/55/)
by Helmut Hofer (IAS) as part of Symplectic zoominar

Abstract
An exceptionally gifted mathematician and an extremely complex person, Floer exhibited, as one friend put it, a "radical individuality." He viewed the world around him with a singularly critical way of thinking and a quintessential disregard for convention. Indeed, his revolutionary mathematical ideas, contradicting conventional wisdom, could only be inspired by such impetus, and can only be understood in this context.

Poincaré's research on the Three Body Problem laid the foundations for the fields of dynamical systems and symplectic geometry. From whence the ancestral trail follows Marston Morse and Morse theory, Vladimir Arnold and the Arnold conjectures, through to breakthroughs by Yasha Eliashberg. Likewise, Charles Conley and Eduard Zehnder on the Arnold conjectures, Mikhail Gromov's theory of pseudoholomorphic curves, providing a new and powerful tool to study symplectic geometry, and Edward Witten's fresh perspective on Morse theory. And finally, Andreas Floer, who counter-intuitively combined all of this, hitting the "jackpot" with what is now called Floer theory.

Mohan Swaminathan/Ben Wormleighton/Jonathan Zung (Princeton/WashU/Princeton)
2021-06-25 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/56/
Title: Three short research talks of 20 min each (https://master.researchseminars.org/talk/SympZoominar/56/)
by Mohan Swaminathan/Ben Wormleighton/Jonathan Zung (Princeton/WashU/Princeton) as part of Symplectic zoominar

Abstract
Talk 1: Super-rigidity and bifurcations of embedded curves in
Calabi-Yau 3-folds

Abstract: I will describe my recent work, joint with Shaoyun Bai,
which studies a class of bifurcations of moduli spaces of embedded
pseudo-holomorphic curves in symplectic Calabi-Yau 3-folds and their
associated obstruction bundles. As an application, we are able to give
a direct definition of the Gopakumar-Vafa invariant in a special case.

Talk 2: Lattice formulas for rational SFT capacities of toric domain

Abstract: Siegel has recently defined ‘higher’ symplectic capacities using rational SFT that obstruct symplectic embeddings and behave well with respect to stabilisation. I will report on joint work with Julian Chaidez that relates these capacities to algebro-geometric invariants, which leads to computable, combinatorial formulas for many convex toric domains.

Talk 3: Reeb flows transverse to foliations

Abstract: Eliashberg and Thurston showed that $C^2$ taut foliations on 3-manifolds can be approximated by tight contact structures. I will explain a new approach to this theorem which allows one to control the resulting Reeb flow and hence produce many hypertight contact structures. Along the way, I will explain how harmonic transverse measures may be used to understand the holonomy of foliations.

Felix Schlenk (UniNE)
2021-07-02 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/57/
Title: Symplectically knotted cubes (https://master.researchseminars.org/talk/SympZoominar/57/)
by Felix Schlenk (UniNE) as part of Symplectic zoominar

Abstract
While by a result of McDuff the space of symplectic embeddings of a closed 4-ball into an open 4-ball is connected, the situation for embeddings of cubes $C^4=D^2 \times D^2$ is very different. For instance, for the open ball $B^4$ of capacity 1, there exists an explicit decreasing sequence $c_1,c_2,\ldots \to 1/3$ such that for $c < c_k$ there are at least k symplectic embeddings of the closed cube $C^4(c)$ of capacity c into $B^4$ that are not isotopic. Furthermore, there are infinitely many non-isotopic symplectic embeddings of $C^4(1/3)$ into $B^4$.

A similar result holds for several other targets, like the open 4-cube, the complex projective plane, the product of two equal 2-spheres, or a monotone product of such manifolds and any closed monotone toric symplectic manifold.

The proof uses exotic Lagrangian tori.

This is joint work with Joé Brendel and Grisha Mikhalkin.

Jean-Philippe Chassé (UdeM)/ Leo Digiosia (Rice)/ Rima Chatterjee (Cologne)
2021-10-08 13:15 - 14:45
Title: Three 20 min research talks (https://master.researchseminars.org/talk/SympZoominar/58/)
by Jean-Philippe Chassé (UdeM)/ Leo Digiosia (Rice)/ Rima Chatterjee (Cologne) as part of Symplectic zoominar

Abstract
Jean-Philippe Chassé (UdeM)

Title: Convergence and Riemannian bounds on Lagrangian submanifolds

Abstract: Recent years have seen the appearance of a plethora of possible metrics on spaces of Lagrangian submanifolds. Indeed, on top of the better-known Lagrangian Hofer metric and spectral norm, Biran, Cornea, and Shelukhin have constructed families of so-called weighted fragmentation metrics on these spaces. I will explain how — under the presence of bounds coming from Riemannian geometry — all these metrics behave well with respect to the set-theoretic Hausdorff metric.

Leo Digiosia (Rice)

Title: Cylindrical contact homology of links of simple singularities
Abstract: In this talk we consider the links of simple singularities, which are contactomoprhic to $S^3/G$ for finite subgroups $G$ of $SU(2,\mathbb C)$. We explain how to compute the cylindrical contact homology of $S^3/G$ by means of perturbing the canonical contact form by a Morse function that is invariant under the corresponding rotation subgroup. We prove that the ranks are given in terms of the number of conjugacy classes of $G$, demonstrating a form of the McKay correspondence. We also explain how our computation realizes the Seifert fiber structure of these links.

Rima Chatterjee (Cologne)

Title: Cabling of knots in overtwisted contact manifolds
Abstract: Knots associated to overtwisted manifolds are less explored. There are two types of knots in an overtwisted manifold – loose and non-loose. Non-loose knots are knots with tight complements whereas loose knots have overtwisted complements. While we understand loose knots, non-loose knots remain a mystery. The classification and structure problems of these knots vary greatly compared to the knots in tight manifolds. Especially we are interested in how satellite operations on a knot in overtwisted manifold changes the geometric property of the knot. In this talk, I will discuss under what conditions cabling operation on a non-loose knot preserves non-looseness. This is a joint work with Etnyre, Min and Mukherjee.

Umberto Hryniewicz (RWTH Aachen)
2021-10-15 13:15 - 14:45
Title: Results on abundance of global surfaces of section (https://master.researchseminars.org/talk/SympZoominar/59/)
by Umberto Hryniewicz (RWTH Aachen) as part of Symplectic zoominar

Abstract
One might ask if global surfaces of section (GSS) for Reeb flows in dimension 3 are abundant in two different senses. One might ask if GSS are abundant for a given Reeb flow, or if Reeb flows carrying some GSS are abundant in the set of all Reeb flows. In this talk, answers to these two questions in specific contexts will be presented. First, I would like to discuss a result, obtained in collaboration with Florio, stating that there are explicit sets of Reeb flows on $S^3$ which are right-handed in the sense of Ghys; in particular, for such a flow all finite (non-empty) collections of periodic orbits span a GSS. Then, I would like to discuss genericity results, obtained in collaboration with Colin, Dehornoy and Rechtman, for Reeb flows carrying a GSS; as a particular case of such results, we prove that a $C^\infty$-generic Reeb flow on the tight 3-sphere carries a GSS.

Yakov Eliashberg (Standford)
2021-10-22 13:15 - 14:45
by Yakov Eliashberg (Standford) as part of Symplectic zoominar

Abstract: TBA

Yaniv Ganor (Technion)
2021-10-29 13:15 - 14:45
Title: Big fiber theorems and ideal-valued measures in symplectic topology (https://master.researchseminars.org/talk/SympZoominar/61/)
by Yaniv Ganor (Technion) as part of Symplectic zoominar

Abstract
In various areas of mathematics there exist "big fiber theorems", these are theorems of the following type: "For any map in a certain class, there exists a 'big' fiber", where the class of maps and the notion of size changes from case to case.

We will discuss three examples of such theorems, coming from combinatorics, topology and symplectic topology from a unified viewpoint provided by Gromov's notion of ideal-valued measures.

We adapt the latter notion to the realm of symplectic topology, using an enhancement of Varolgunes’ relative symplectic cohomology to include cohomology of pairs. This allows us to prove symplectic analogues for the first two theorems, yielding new symplectic rigidity results.

Necessary preliminaries will be explained.

Rohil Prasad (Princeton)/ Alex Pieloch (Columbia)/ Chi Hong Chow (CUHK)
2021-11-05 13:15 - 14:45
Title: Three 20 min research talks (https://master.researchseminars.org/talk/SympZoominar/62/)
by Rohil Prasad (Princeton)/ Alex Pieloch (Columbia)/ Chi Hong Chow (CUHK) as part of Symplectic zoominar

Abstract: TBA

Fabio Gironella (HU Berlin)
2021-11-19 14:15 - 15:45
Title: Exact orbifold fillings of contact manifolds (https://master.researchseminars.org/talk/SympZoominar/63/)
by Fabio Gironella (HU Berlin) as part of Symplectic zoominar

Abstract
The topic of the talk will be Floer theories on exact symplectic orbifolds with smooth contact boundary. More precisely, I will first describe the construction, which only uses classical transversality techniques, of a symplectic cohomology group on such symplectic orbifolds. Then, I will give some geometrical applications, such as restrictions on possible singularities of exact symplectic fillings of some particular contact manifolds, and the existence, in any odd dimension at least 5, of a pair of contact manifolds with no exact symplectic (smooth) cobordisms in either direction. This is joint work with Zhengyi Zhou.

Urs Frauenfelder (Augsburg)
2021-12-10 14:15 - 15:45
Title: GIT quotients and Symplectic data analysis (https://master.researchseminars.org/talk/SympZoominar/64/)
by Urs Frauenfelder (Augsburg) as part of Symplectic zoominar

Abstract
This is joint work with Agustin Moreno and Dayung Koh. The restricted three-body problem is invariant under various antisymplectic involutions. These real structures give rise to the notion of symmetric periodic orbits which simultaneously have a closed string interpretation namely as a
periodic orbit as well as an open string interpretation as Hamiltonian chords. This makes the bifurcation analysis of symmetric periodic orbits very intriguing since under bifurcations two local Floer homologies are invariant, the periodic one as well as the Lagrangian one. In this talk we explain how methods from symmetric space theory can help to extract efficiently datas from reduced monodromy matrices of periodic orbits helping to analyse the possible bifurcation patterns.

Mohammed Abouzaid (Columbia)
2021-11-26 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/65/
Title: Complex cobordism and Hamiltonian fibrations (https://master.researchseminars.org/talk/SympZoominar/65/)
by Mohammed Abouzaid (Columbia) as part of Symplectic zoominar

Abstract
I will discuss joint work with McLean and Smith, lifting the results of Seidel, Lalonde, McDuff, and Polterovich concerning the topology of Hamiltonian fibrations over the 2-sphere from rational cohomology to complex cobordism. In addition to the use of Morava K-theory (as in the recent work with Blumberg on the Arnold Conjecture), the essential new ingredient is the construction of global Kuranishi charts for genus 0 pseudo-holomorphic curves; i.e. their realisation as quotients of zero loci of sections of equivariant vector bundles on manifolds.

three short research talks. (Wenyuan Li (Northwestern)/Jakob Hedicke (Bochum)/Johan Asplund (Uppsala))
2021-12-17 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/66/
by three short research talks. (Wenyuan Li (Northwestern)/Jakob Hedicke (Bochum)/Johan Asplund (Uppsala)) as part of Symplectic zoominar

Abstract
Wenyuan Li (Northwestern)
Title: Estimating Reeb chords using microlocal sheaf theory

Abstract: We show that, for closed Legendrians in 1-jet bundles, when there is a sheaf with singular support on the Legendrian, then (1) its self Reeb chords are bounded from below by half the sum of Betti numbers, and (2) the Reeb chords between itself and its Hamiltonian push off is bounded from below by Betti numbers when the C^0-norm of the Hamiltonian is small. I will show how to visualize Reeb chords/Lagrangian intersections in sheaf theory, and then explain the duality exact triangle and the persistence structure used in the proof. If time permits, I will state a conjecture on the relative Calabi-Yau structure that arises from the duality exact triangle.

Jakob Hedicke (Bochum)
Title: Lorentzian distance functions on the group of contactomorphisms

Abstract: The notion of positive (non-negative) contact isotopy, defined by Eliashberg and Polterovich, leads to two relations on the group of contactomorphisms. These relations resemble the causal relations of a Lorentzian manifold. In this talk we will introduce a class of Lorentzian distance functions on the group of contactomorphisms, that are compatible with these relations.
The Lorentzian distance functions turn out to be continuous with respect to the Hofer-norm of a contactomorphism defined by Shelukhin.

Johan Asplund (Uppsala)
Title: Simplicial descent for Chekanov-Eliashberg dg-algebras

Abstract: In this talk we introduce a type of surgery decomposition of Weinstein manifolds we call simplicial decompositions. We will discuss the result that the Chekanov-Eliashberg dg-algebra of the attaching spheres of a Weinstein manifold satisfies a descent (cosheaf) property with respect to a simplicial decomposition. Simplicial decompositions generalize the notion of Weinstein connected sum and there is in fact a one-to-one correspondence (up to Weinstein homotopy) between simplicial decompositions and so-called good sectorial covers. The motivation behind these results is the sectorial descent result for wrapped Fukaya categories by Ganatra-Pardon-Shende.

Michael Sullivan (UMass Amherst)
2022-01-14 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/67/
Title: Quantitative Legendrian geometry (https://master.researchseminars.org/talk/SympZoominar/67/)
by Michael Sullivan (UMass Amherst) as part of Symplectic zoominar

Abstract
I will discuss some quantitative aspects for Legendrians in a (more or less) general contact manifold. These include lower bounds on the number of Reeb chords between a Legendrian and its contact Hamiltonian image, the non-degeneracy of the Chekanov/Hofer/Shelukhin Legendrian metric, and some 3-dimensional non-squeezing results. The main tool is the barcode of a relative Rabinowitz Floer theory. This is joint work with Georgios Dimitroglou Rizell.

Ely Kerman (UIUC)
2022-02-11 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/68/
Title: On symplectic capacities and their blind spots (https://master.researchseminars.org/talk/SympZoominar/68/)
by Ely Kerman (UIUC) as part of Symplectic zoominar

Abstract
In this talk I will discuss a joint project with Yuanpu Liang in which we establish several properties of the sequence of symplectic capacities defined by Gutt and Hutchings for star-shaped domains using $S^1$-equivariant symplectic homology. Among the results discussed will be the fact that, unlike the first of these capacities, the others all fail to satisfy the symplectic version of the Brunn Minkowski established by Artstein-Avidan and Ostrover. We also show that the Gutt-Hutchings capacities, together with the volume, do not constitute a complete set of symplectic invariants even for convex bodies with smooth boundary. The examples constructed to prove these results are not exotic. They are convex and concave toric domains. The main new tool used is a significant simplification of the formulae of Gutt and Hutchings for the capacities of such domains, that holds under an additional symmetry assumption. This allows us to compute the capacities in new examples and to identify and exploit blind spots that they sometimes share.

Dustin Connery-Grigg (UdeM)/Pazit Haim-Kislev (Tel Aviv)/ Thibaut Mazuir (Paris)
2022-01-28 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/69/
Title: Three 20 min research talks (https://master.researchseminars.org/talk/SympZoominar/69/)
by Dustin Connery-Grigg (UdeM)/Pazit Haim-Kislev (Tel Aviv)/ Thibaut Mazuir (Paris) as part of Symplectic zoominar

Abstract
$\textbf{Dustin Connery-Grigg (UdeM)}$

Title: Geometry and topology of Hamiltonian Floer complexes in low-dimension

In this talk, I will present two results relating the qualitative dynamics of non-degenerate Hamiltonian isotopies on surfaces to the structure of their Floer complexes. The first will be a topological characterization of those Floer chains which represent the fundamental class in $CF_*(H,J)$ and which moreover lie in the image of some chain-level PSS map. This leads to a novel symplectically bi-invariant norm on the group of Hamiltonian diffeomorphisms, which is both $C^0$-continuous and computable in terms of the underlying dynamics. The second result explains how certain portions of the Hamiltonian Floer chain complex may be interpreted geometrically in terms of positively transverse singular foliations of the mapping torus, with singular leaves given by certain maximal collections of unlinked orbits of the suspended flow. This construction may be seen to provide a Floer-theoretic construction of the `torsion-low’ foliations which appear in Le Calvez’s theory of transverse foliations for surface homeomorphisms, thereby establishing a bridge between the two theories.

$\textbf{Pazit Haim-Kislev (Tel Aviv)}$

Title: Symplectic capacities of p-products

Abstract:
A generalization of the cartesian product and the free sum of two convex domains is the p-product operation. We investigate the behavior of symplectic capacities with respect to symplectic p-products, and we give applications related to Viterbo's volume-capacity conjecture and to p-decompositions of the symplectic ball.

$\textbf{Thibaut Mazuir (Paris)}$

Title: Higher algebra of A-infinity algebras in Morse theory

In this short talk, I will introduce the notion of n-morphisms between two A-infinity algebras. These higher morphisms are such that 0-morphisms correspond to standard A-infinity morphisms and 1-morphisms correspond to A-infinity homotopies. Their combinatorics are then encoded by new families of polytopes, which I call the n-multiplihedra and which generalize the standard multiplihedra. Elaborating on works by Abouzaid and Mescher, I will then explain how this higher algebra of A-infinity algebras naturally arises in the context of Morse theory, using moduli spaces of perturbed Morse gradient trees

Marie-Claude Arnaud (Paris)
2022-03-04 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/70/
Title: Invariant submanifolds for conformal dynamics (https://master.researchseminars.org/talk/SympZoominar/70/)
by Marie-Claude Arnaud (Paris) as part of Symplectic zoominar

Abstract
In a work with Jacques Fejoz, we consider the conformal dynamics on a symplectic manifold, i.e. for which the symplectic form is transformed colinearly to itself. In the non-symplectic case, we study the problem of isotropy and uniqueness of invariant submanifolds. More precisely, in this talk, I will explain a relation between topological entropy and isotropy and some uniqueness results.

Benoît Joly (Bochum)/Marco Castronovo (Columbia)/Agniva Roy (Georgia Tech)
2022-03-25 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/71/
Title: Three 20 min research talks (https://master.researchseminars.org/talk/SympZoominar/71/)
by Benoît Joly (Bochum)/Marco Castronovo (Columbia)/Agniva Roy (Georgia Tech) as part of Symplectic zoominar

Abstract
Benoît Joly (Bochum)

Title: Barcodes for Hamiltonian homeomorphisms of surfaces

Abstract: In this talk, we will study the Floer Homology barcodes from a dynamical point of view. Our motivation comes from recent results in symplectic topology using barcodes to obtain dynamical results. We will give the ideas of new constructions of barcodes for Hamiltonian homeomorphisms of surfaces using Le Calvez's transverse foliation theory. The strategy consists in copying the construction of the Floer and Morse Homologies using dynamical tools like Le Calvez's foliations.

Marco Castronovo (Columbia)

Title: Polyhedral Liouville domains

Abstract: I will explain the construction of a new class of Liouville domains that live in a complex torus of arbitrary dimension, whose boundary dynamics encodes information about the singularities of a toric compactification. The primary motivation for this work is to find a symplectic interpretation of some curious Laurent polynomials that appear in mirror symmetry for Fano manifolds; it also potentially opens a path to bound symplectic capacities of polarized projective varieties from below.

Agniva Roy (Georgia Tech)

Title: Constructions of High Dimensional Legendrians and Isotopies

Abstract: I will talk about an ongoing project that explores the construction of high dimensional Legendrian spheres from supporting open books and contact structures. The input is a Lagrangian disk filling of a Legendrian knot in the binding. We try to understand the relationship between different constructions from the same input, and suggest parallels, in the $S^{2n+1}$ case, to a construction defined by Ekholm for $\mathbb R^{2n+1}$.

Susan Tolman (UIUC)
2022-01-21 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/72/
Title: Beyond semitoric (https://master.researchseminars.org/talk/SympZoominar/72/)
by Susan Tolman (UIUC) as part of Symplectic zoominar

Abstract
A compact four dimensional completely integrable system $f:M\rightarrow \mathbb R^2$ is semitoric if it has only non-degenerate singularities, without hyperbolic blocks, and one of the components of generates a circle action. Semitoric systems have been extensively studied and have many nice properties: for example, the preimages $f^{-1}(x)$ are all connected. Unfortunately, although there are many interesting examples of semitoric systems, the class has some limitation. For example, there are blowups of $S^2\times S^2$ with Hamiltonian circle actions which cannot be extended to semitoric systems. We expand the class of semitoric systems by allowing certain degenerate singularities, which we call ephemeral singularities. We prove that the preimage $f^{-1}(x)$ is still connected for this larger class. We hope that this class will be large enough to include not only all compact four manifolds with Hamiltonian circle actions, but more generally all complexity one spaces. Based on joint work with D. Sepe.

Erman Cineli (Paris)
2022-02-25 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/73/
Title: Topological entropy of Hamiltonian diffeomorphisms: a persistence homology and Floer theory perspective (https://master.researchseminars.org/talk/SympZoominar/73/)
by Erman Cineli (Paris) as part of Symplectic zoominar

Abstract
In this talk I will introduce barcode entropy and discuss its connections to topological entropy. The barcode entropy is a Floer-theoretic invariant of a compactly supported Hamiltonian diffeomorphism, measuring, roughly speaking, the exponential growth under iterations of the number of not-too-short bars in the barcode of the Floer complex. The topological entropy bounds from above the barcode entropy and, conversely, the barcode entropy is bounded from below by the topological entropy of any hyperbolic locally maximal invariant set. As a consequence, the two quantities are equal for Hamiltonian diffeomorphisms of closed surfaces. The talk is based on a joint work with Viktor Ginzburg and Basak Gurel.

Umut Varolgunes (Boğaziçi)
2022-02-18 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/74/
Title: Reynaud models from relative Floer theory (https://master.researchseminars.org/talk/SympZoominar/74/)
by Umut Varolgunes (Boğaziçi) as part of Symplectic zoominar

Abstract
I will start by explaining the construction of a formal scheme starting with an integral affine manifold $Q$ equipped with a decomposition into Delzant polytopes. This is a weaker and more elementary version of degenerations of abelian varieties originally constructed by Mumford. Then I will reinterpret this construction using the corresponding Lagrangian torus fibration $X\rightarrow Q$ and relative Floer theory of its canonical Lagrangian section. Finally, I will discuss a conjectural generalization of the story to symplectic degenerations of CY symplectic manifolds to normal crossing symplectic varieties whose components are log CY.

Anton Izosimov (Arizona)
2022-03-18 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/75/
by Anton Izosimov (Arizona) as part of Symplectic zoominar

Abstract: TBA

Yann Rollin (Nantes)
2022-04-08 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/76/
Title: Lagrangians, symplectomorphisms and zeroes of moment maps (https://master.researchseminars.org/talk/SympZoominar/76/)
by Yann Rollin (Nantes) as part of Symplectic zoominar

Abstract
I will present two constructions of Kähler manifolds, endowed with Hamiltonian torus actions of infinite dimension. In the first example, zeroes of the moment map are related to isotropic maps from a surface in $\mathbb R^{2n}$. In the second example, which is actually a hyperKähler moment map, the zeroes are related to symplectic maps of the torus $\mathbb T^4$. The corresponding modified moment map flows have short-time existence. Polyhedral analogues of these constructions can be used to investigate piecewise linear symplectic geometry.

Kyler Siegel (USC)
2022-04-15 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/77/
Title: Singular plane curves and stable nonsqueezing phenomena (https://master.researchseminars.org/talk/SympZoominar/77/)
by Kyler Siegel (USC) as part of Symplectic zoominar

Abstract
The existence of rational plane curves of a given degree with prescribed singularities is a subtle and active area in algebraic geometry. This problem turns out to be closely related to difficult enumerative problems which arise in symplectic field theory, which in turn play a central role in the theory of high dimensional symplectic embeddings. In this talk I will discuss various perspectives on these enumerative problems and present a new closed formula for relevant curve counts as a sum over decorated trees.

Jack Smith (Cambridge)
2022-04-22 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/78/
Title: From Floer to Hochschild via matrix factorisations (https://master.researchseminars.org/talk/SympZoominar/78/)
by Jack Smith (Cambridge) as part of Symplectic zoominar

Abstract
Abstract:
The Hochschild cohomology of the Floer algebra of a Lagrangian L, and the associated closed-open string map, play an important role in the generation criterion for the Fukaya category and in deformation theory approaches to mirror symmetry. I will explain how, in the monotone setting, one can build a map from the Floer cohomology of L with certain local coefficients to (a version of) Hochschild cohomology. This map makes things much more geometric, by transferring the algebraic complexity to the world of matrix factorisations, and is an isomorphism when L is a torus.

Joel Fine (ULB)
2022-04-29 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/79/
Title: nots, minimal surfaces and J-holomorphic curves (https://master.researchseminars.org/talk/SympZoominar/79/)
by Joel Fine (ULB) as part of Symplectic zoominar

Abstract
Let $K$ be a knot or link in the 3-sphere, thought of as the ideal boundary of hyperbolic 4-space,
$H^4$. The main theme of my talk is that it should be possible to count minimal surfaces in $H^4$
which fill $K$ and obtain a link invariant. In other words, the count doesn’t change under isotopies of $K$. When one counts minimal disks, this is a theorem. Unfortunately there is currently a gap in the proof for more complicated surfaces. I will explain “morally” why the result should be true and how I intend to fill the gap. In fact, this (currently conjectural) invariant is a kind of Gromov–Witten invariant, counting $J$-holomorphic curves in a certain symplectic 6-manifold diffeomorphic to $S^4\times H^4$. The symplectic structure becomes singular at infinity, in directions transverse to the $S^2$ fibres. These singularities mean that both the Fredholm and compactness theories have fundamentally new features, which I will describe. Finally, there is a whole class of infinite-volume symplectic 6-manifolds which have singularities modelled on the above situation. I will explain how it should be possible to count $J$-holomorphic curves in these manifolds too, and obtain invariants for links in other 3-manifolds.

Kevin Ruck (Augsburg)
2022-05-06 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/80/
Title: Tate homology and powered flybys (https://master.researchseminars.org/talk/SympZoominar/80/)
by Kevin Ruck (Augsburg) as part of Symplectic zoominar

Abstract
In this talk I want to show that in the planar circular restricted three body problem there are infinitely many symmetric consecutive collision orbits for all energies below the first critical energy value. By using the Levi-Civita regularization we will be able to distinguish between two different orientations of these orbits and prove the above claim for both of them separately. In the first part of the talk I want to explain the motivation behind this result, especially its connection to powered flybys. Afterwards I will introduce the main technical tools, one needs to prove the above statement, like Lagrangian Rabinowitz Floer Homology and its $G$-equivariant version. To be able to effectively calculate this $G$-equivariant Lagrangian RFH, we will relate it to the Tate homology of the group $G$. With this tool at hand we will then finally be able to prove that there are infinitely many consecutive collision orbits all facing in a specific direction.

Daniel Rudolf (Bochum)/Miguel Pereira (Augsburg)/Maksim Stokić (Tel Aviv)
2022-05-27 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/81/
Title: Three 20min research talks (https://master.researchseminars.org/talk/SympZoominar/81/)
by Daniel Rudolf (Bochum)/Miguel Pereira (Augsburg)/Maksim Stokić (Tel Aviv) as part of Symplectic zoominar

Abstract
Daniel Rudolf (Bochum)

Title: Viterbo‘s conjecture for Lagrangian products in $\mathbb R^4$

Abstract:
We show that Viterbo‘s conjecture (for the EHZ-capacity) for convex Lagrangian products in $\mathbb R^4$ holds for all Lagrangian products (any trapezoid in $\mathbb R^2$)x(any convex body in $\mathbb R^2$). Moreover, we classify all equality cases of Viterbo’s conjecture within this configuration and show which of them are symplectomorphic to a Euclidean ball. As by-product, we conclude sharp systolic Minkowski billiard inequalities for geometries which have trapezoids as unit balls. Finally, we show that the flows associated to the above mentioned equality cases (which are polytopes) satisfy a weak Zoll property, namely, that every characteristic that is almost everywhere away from lower-dimensional faces is closed, runs over exactly 8 facets, and minimizes the action.

Miguel Pereira (Augsburg)

Title: The Lagrangian capacity of toric domains

Abstract:
In this talk, I will state a conjecture giving a formula for the Lagrangian capacity of a convex or concave toric domain. First, I will explain a proof of the conjecture in the case where the toric domain is convex and 4-dimensional, using the Gutt-Hutchings capacities as well as the McDuff-Siegel capacities. Second, I will explain a proof of the conjecture in full generality, but assuming the existence of a suitable virtual perturbation scheme which defines the curve counts of linearized contact homology. This second proof makes use of Siegel's higher symplectic capacities.

Maksim Stokić (Tel Aviv)

Title: $C^0$ contact geometry of isotropic submanifolds

Abstract: A homeomorphism is called contact if it can be written as a $C^0$-limit of contactomorphisms. The contact version of Eliashberg-Gromov rigidity theorem states that smooth contact homeomorphisms preserve the contact structure. A submanifold $L$ of a contact manifold $(Y,\xi)$ is called isotropic if $\xi\vert_{TL}=0$. Isotropic submanifolds of maximal dimension are called Legendrian, otherwise we call them subcritical isotropic. In this talk, we will try to answer whether the isotropic property is preserved by contact homeomorphisms. It is expected that subcritical isotropic submanifolds are flexible, while we expect that Legendrians are rigid. We show that subcritical isotropic curves are flexible, and we give a new proof of the rigidity of Legendrians in dimension 3. Moreover, we provide a certain type of rigidity of Legendrians in higher dimensions.

Claude Viterbo (Paris)
2022-05-20 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/82/
Title: Gamma-support, gamma-coisotropic subsets and applications (https://master.researchseminars.org/talk/SympZoominar/82/)
by Claude Viterbo (Paris) as part of Symplectic zoominar

Abstract
To an element in the completion of the set of Lagrangians for the spectral distance we associate a support. We show that such a support is $\gamma$-coisotropic (a notion we shall define in the talk) and we shall give examples and counterexamples of $\gamma$-coisotorpic sets that can be (or cannot be) $\gamma$-supports. Finally we give some applications of these notions to singular support of sheaves (joint work with S. Guillermou) and dissipative dynamics, allowing us to extend the notion of Birkhoff attractor (joint with V. Humilière).

Guangbo Xu (Texas A&M)
2022-06-03 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/83/
Title: Integer-valued Gromov-Witten type invariants (https://master.researchseminars.org/talk/SympZoominar/83/)
by Guangbo Xu (Texas A&M) as part of Symplectic zoominar

Abstract
Abstract:

Gromov-Witten invariants for a general target are rational-valued but not necessarily integer-valued. This is due to the contribution of curves with nontrivial automorphism groups. In 1997 Fukaya and Ono proposed a new method in symplectic geometry which can count curves with a trivial automorphism group. While ordinary Gromov-Witten invariants only use the orientation on the moduli spaces, this integer-valued counts are supposed to also use the (stable) complex structure on the moduli spaces. In this talk I will present the recent joint work with Shaoyun Bai in which we rigorously defined the integer-valued Gromov-Witten type invariants in genus zero for a symplectic manifold. This talk is based on the preprint https://arxiv.org/abs/2201.02688.

Yoel Groman (HUJI)
2022-06-17 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/84/
Title: Locality and deformations in relative symplectic cohomology (https://master.researchseminars.org/talk/SympZoominar/84/)
by Yoel Groman (HUJI) as part of Symplectic zoominar

Abstract
Relative symplectic cohomology is a Floer theoretic invariant associated with compact subsets K of a closed or geometrically bounded symplectic manifold M. The motivation for studying it is that it is often possible to reduce the study of global Floer theory of M to the Floer theory of a handful of local models covering M which one hopes will be easier to compute (Varolgunes’ spectral sequence). As an example, it is expected that at least in the setting of the Gross-Siebert program, the mirror can be pieced together from the relative symplectic cohomologies of neighborhoods of fibers of an SYZ fibration (singular or not). However, even when K is a well understood model, such as the Weinstein neighborhood of a Lagrangian torus, the construction of relative SH is rather unwieldy. In particular, it is not entirely obvious how to relate the symplectic cohomology of K relative to M with Floer theoretic invariants intrinsic to K. I will discuss a number of results, most of them in preparation, which aim to alleviate this difficulty in the setting Lagrangian torus fibrations with singularities. Partly joint with U. Varolgunes.

Julian Chaidez (IAS/PU)
2022-06-24 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/85/
Title: The Ruelle invariant and convexity in higher dimensions (https://master.researchseminars.org/talk/SympZoominar/85/)
by Julian Chaidez (IAS/PU) as part of Symplectic zoominar

Abstract
I will explain how to construct the Ruelle invariant of a symplectic cocycle over an arbitrary measure preserving flow. I will provide examples and computations in the case of Hamiltonian flows and Reeb flows (in particular, for toric domains). As an application of this invariant, I will construct toric examples of dynamically convex domains that are not symplectomorphic to convex ones in any dimension.

This talk is based on joint works arXiv:2012.12869 and arXiv:2205.00935 with Oliver Edtmair.

Pierre-Alexandre Mailhot/Nicole Magill/Ofir Karin (UdeM/Cornell/Tel Aviv)
2022-10-28 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/86/
Title: three 20 min research talks (https://master.researchseminars.org/talk/SympZoominar/86/)
by Pierre-Alexandre Mailhot/Nicole Magill/Ofir Karin (UdeM/Cornell/Tel Aviv) as part of Symplectic zoominar

Abstract
Pierre-Alexandre Mailhot (UdeM)

Title: The spectral diameter of a Liouville domains and its applications

Abstract: The spectral norm provides a lower bound to the Hofer norm. It is thus natural to ask whether the diameter of the spectral norm is finite or not. During this short talk, I will give a sketch of the proof that, in the case of Liouville domains, the spectral diameter is finite if and only if the symplectic cohomology of the underlying manifold vanishes. With that relationship in hand, we will explore applications to symplecticaly aspherical symplectic manifolds and Hofer geometry.

Nicole Magill (Cornell)

Title: A correspondence between obstructions and constructions for staircases in Hirzebruch surfaces

Abstract: The ellipsoidal embedding function of a symplectic four manifold M measures how much the symplectic form on M must be dilated in order for it to admit an embedded ellipsoid of some eccentricity. It generalizes the Gromov width and ball packing numbers. In most cases, finitely many obstructions besides the volume determine the function. If there are infinitely many obstructions determining the function, M is said to have an infinite staircase. This talk will give a classification of which Hirzebruch surfaces have infinite staircases. We will focus on explaining the correspondence between the obstructions coming from exceptional classes and the constructions from almost toric fibrations. We define a way to mutate triples of exceptional classes to produce new triples of exceptional classes, which corresponds to mutations in almost toric fibrations. This is based on various joint work with Dusa McDuff, Ana Rita Pires, and Morgan Weiler.

Ofir Karin (Tel Aviv)

Title: Approximation of Generating Function Barcode for HamiltonianDiffeomorphisms

Abstract: Persistence modules and barcodes are used in symplectic topology to define new invariants of Hamiltonian diffeomorphisms, however methods that explicitly calculate these barcodes are often unclear. In this talk I will define one such invariant called the GF-barcode of compactly supported Hamiltonian diffeomorphisms of $\mathbb R^{2n}$ by applying Morse theory to generating functions quadratic at infinity associated to such Hamiltonian diffeomorphisms and provide an algorithm (i.e a finite sequence of explicit calculation steps) that approximates it along with a few computation examples. This is joint work with Pazit Haim-Kislev.

Ipsita Datta (IAS)
2022-11-04 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/87/
by Ipsita Datta (IAS) as part of Symplectic zoominar

Abstract: TBA

Roger Casals (UC Davis)
2022-11-11 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/88/
by Roger Casals (UC Davis) as part of Symplectic zoominar

Abstract: TBA

Yash Deshmukh (Columbia)/Lea Kenigsberg (Columbia)/Thomas Massoni (Princeton)
2022-11-25 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/89/
Title: three 20 min research talks (https://master.researchseminars.org/talk/SympZoominar/89/)
by Yash Deshmukh (Columbia)/Lea Kenigsberg (Columbia)/Thomas Massoni (Princeton) as part of Symplectic zoominar

Abstract
Yash Deshmukh (Columbia)

Title: Moduli spaces of nodal curves from homotopical algebra

Abstract: I will discuss how the Deligne-Mumford compactification of curves arises from the uncompactified moduli spaces of curves as a result of some algebraic operations related to (pr)operadic structures on the moduli spaces. I will describe how a variation of this naturally gives rise to another new partial compactification of moduli spaces curves. Time permitting, I will indicate how it is related to secondary operations on symplectic cohomology and discuss some ongoing work in this direction.

Lea Kenigsberg (Columbia)

Title: Coproduct structures, a tale of two outputs

Abstract: I will motivate the study of coproducts and describe a new coproduct structure on the symplectic cohomology of Liouville manifolds. Time permitting, I will indicate how to compute it in an example to show that it's not trivial. This is based on my thesis work, in progress.

Thomas Massoni (Princeton)

Title: Non-Weinstein Liouville domains and three-dimensional Anosov flows

Abstract: Weinstein domains and their symplectic invariants have been extensively studied over the last 30 years. Little is known about non-Weinstein Liouville domains, whose first instance is due to McDuff. I will describe two key examples of such domains in dimension four, and then explain how they fit into a general construction based on Anosov flows on three-manifolds. The symplectic invariants of these “Anosov Liouville domains” constitute new invariants of Anosov flows. The algebraic structure of their wrapped Fukaya categories is in stark contrast with the Weinstein case.

This is mostly based on joint work arXiv:2211.07453 with Kai Cieliebak, Oleg Lazarev and Agustin Moreno.

Robert Cardona (ICMAT)
2022-12-09 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/90/
Title: Periodic orbits and Birkhoff sections of stable Hamiltonian structures (https://master.researchseminars.org/talk/SympZoominar/90/)
by Robert Cardona (ICMAT) as part of Symplectic zoominar

Abstract
Abstract:

In this talk, we start by reviewing recent results on the dynamics of Reeb vector fields defined by contact forms on three-dimensional manifolds, and then introduce Reeb fields defined by stable Hamiltonian structures. These are more general and arise, for instance, in stable regular energy level sets of Hamiltonian systems. We give a characterization of Reeb fields that are aperiodic or that have finitely many periodic orbits (under a certain nondegeneracy assumption). Finally, we give sufficient conditions for the existence of an adapted broken book decomposition or the existence of a Birkhoff section. This is joint work with A. Rechtman.

Shaoyun Bai (SCGP)
2023-01-20 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/91/
Title: Arnold conjecture over integers (https://master.researchseminars.org/talk/SympZoominar/91/)
by Shaoyun Bai (SCGP) as part of Symplectic zoominar

Abstract
We show that for any closed symplectic manifold, the number of 1-periodic orbits of any non-degenerate Hamiltonian is bounded from below by a version of total Betti number over Z, which takes account of torsions of all characteristics. The proof relies on an abstract perturbation scheme (FOP perturbations) which allows us to produce integral pseudo-cycles from moduli space of J-holomorphic curves, and a geometric regularization scheme for moduli space of Hamiltonian Floer trajectories generalizing the recent work of Abouzaid-McLean-Smith. I will survey these ideas and indicate potential future developments. This is joint work with Guangbo Xu.

Semon Rezchikov (Princeton/IAS)
2023-01-27 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/92/
Title: Hyperbolicity of periodic points of Hamiltonian maps (https://master.researchseminars.org/talk/SympZoominar/92/)
by Semon Rezchikov (Princeton/IAS) as part of Symplectic zoominar

Abstract
Title: Hyperbolicity of periodic points of Hamiltonian maps

Abstract:
The basic invariant of a fixed point of a Hamiltonian diffeomorphism, besides its existence (which is implied by the proven Arnol'd Conjecture), is the number of eigenvalues of unit norm of the linearization of the map at the fixed point. When there are no such eigenvalues, the fixed point is said to be purely hyperbolic, and has characteristically different local dynamics from the contrasting partially elliptic case. In this talk, I will discuss how period doubling bifurcations can be used to make periodic points purely hyperbolic without appreciably changing Floer-theoretic invariants. Via a limiting process one can approximate Hamiltonian diffeomorphisms by hameomorphisms which behave as if they have only hyperbolic periodic points. We will review the dynamical background for such constructions, and if time permits, discuss upper and lower bounds on the growth rate of periodic points of these hameomorphisms

Marcelo Alves (UAntwerp)
2022-12-16 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/93/
Title: Hofer's geometry and braid stability (https://master.researchseminars.org/talk/SympZoominar/93/)
by Marcelo Alves (UAntwerp) as part of Symplectic zoominar

Abstract
The Hofer’s metric $d_H$ is a remarkable bi-invariant metric on the group of Hamiltonian diffeomorphisms of a symplectic manifold. In my talk, I will explain a result, obtained jointly with Matthias Meiwes, which says that the braid type of a set of periodic orbits of a Hamiltonian diffeomorphism on a closed surface is stable under perturbations that are sufficiently small with respect to Hofer’s metric. As a consequence of this we obtained that the topological entropy, seen as a function on the space of Hamiltonian diffeomorphisms of a closed surface, is lower semi-continuous with respect to the Hofer metric $d_H$.

If time permits, I will explain related questions for Reeb flows on 3-manifolds and Hamiltonian diffeomorphisms on higher-dimensional symplectic manifolds, and recent progress on these problems obtained by myself, Meiwes, Abror Pirnapasov and Lucas Dahinden.

Christian Lange (LMU München)
2023-01-13 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/94/
Title: Orbifolds and systolic inequalities (https://master.researchseminars.org/talk/SympZoominar/94/)
by Christian Lange (LMU München) as part of Symplectic zoominar

Abstract
In this talk, I will first discuss some instances in which orbifolds occur in geometry and dynamics, in particular, in the context of billiards and systolic inequalities. Then I will present topological conditions for an orbifold to be a manifold together with applications to foliations and to Besse geodesic and Reeb flows (joint work with Manuel Amann, Marc Kegel and Marco Radeschi). Here a flow is called Besse if all its orbits are periodic. Such flows are related to systolic inequalities. Namely, I will explain a characterization of contact forms on 3-manifolds whose Reeb flow is Besse as local maximizers of certain ''higher" systolic ratios, and mention other related systolic-like inequalities (joint work with Alberto Abbondandolo, Marco Mazzucchelli and Tobias Soethe).

David White (NSCU)/Kai Hugtenburg (Edinburgh)/Patricia Dietzsch (ETH)
2023-02-10 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/95/
Title: Three 20min research talks (https://master.researchseminars.org/talk/SympZoominar/95/)
by David White (NSCU)/Kai Hugtenburg (Edinburgh)/Patricia Dietzsch (ETH) as part of Symplectic zoominar

Abstract
David White (NSCU)

Title: Symplectic instanton homology of knots and links in 3-manifolds

Abstract: Powerful homology invariants of knots in 3-manifolds have emerged from both the gauge-theoretic and the symplectic kinds of Floer theory: on the gauge-theoretic side is the instanton knot homology of Kronheimer-Mrowka, and on the symplectic the (Heegaard) knot Floer homology developed independently by Ozsváth-Szabó and by Rasmussen. These theories are conjecturally equivalent, but a precise connection between the gauge-theoretic and symplectic sides here remains to be understood. We describe a construction designed to translate singular instanton knot homology more directly into the symplectic domain, a so-called symplectic instanton knot homology: We define a Lagrangian Floer homology invariant of knots and links which extends a 3-manifold invariant developed by H. Horton. The construction proceeds by using specialized Heegaard diagrams to parametrize an intersection of traceless $SU(2)$ character varieties. The latter is in fact an intersection of Lagrangians in a symplectic manifold, giving rise to a Lagrangian Floer homology. We discuss its relation to singular instanton knot homology, as well as the formal properties which this suggests and methods to prove these properties.

Kai Hugtenburg (Edinburgh)

Title: Open Gromov-Witten invariants from the Fukaya category

Abstract: Enumerative mirror symmetry is a correspondence between closed Gromov-Witten invariants of a space $X$, and period integrals of a family $Y$. One of the predictions of Homological Mirror Symmetry is that the closed Gromov-Witten invariants can be obtained from the Fukaya category. For Calabi-Yau varieties this has been demonstrated by Ganatra-Perutz-Sheridan. Recently, enumerative mirror symmetry has been extended, by including open Gromov-Witten invariants and extended period integrals. It is natural to expect that open Gromov-Witten invariants can be obtained from the Fukaya category. In this talk I will outline a construction which will demonstrate this for certain open Gromov-Witten invariants.

Patricia Dietzsch (ETH)

Title: Lagrangian Hofer metric and barcodes

Abstract: Filtered Lagrangian Floer homology gives rise to a barcode associated to a pair of Lagrangians. It is well-known that the lengths of the finite bars and the spectral distance are lower bounds of the Lagrangian Hofer metric. In this talk we are interested in a reverse inequality.
I will explain an upper bound of the Lagrangian Hofer distance between equators in the cylinder in terms of a weighted sum of the lengths of the finite bars and the spectral distance.

Yusuke Kawamoto (ETH)
2023-02-17 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/96/
Title: Hypersurface singularities and spectral invariants (https://master.researchseminars.org/talk/SympZoominar/96/)
by Yusuke Kawamoto (ETH) as part of Symplectic zoominar

Abstract
Title: Hypersurface singularities and spectral invariants

Abstract: We discuss the relation between hypersurface singularities (e.g. ADE, $\tilde E_6$, $\tilde E_7$, $\tilde E_8$, etc) and spectral invariants, which are symplectic invariants coming from Floer theory.

Noah Porcelli (Imperial College London)
2023-02-24 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/97/
Title: Floer theory and framed cobordisms between exact Lagrangian submanifolds (https://master.researchseminars.org/talk/SympZoominar/97/)
by Noah Porcelli (Imperial College London) as part of Symplectic zoominar

Abstract
Title: Floer theory and framed cobordisms between exact Lagrangian submanifolds

Abstract:
Lagrangian Floer theory is a useful tool for studying the structure of the homology of Lagrangian submanifolds. In some cases, it can be used to detect more- we show it can detect the framed bordism class of certain Lagrangians and in particular recover a result of Abouzaid-Alvarez-Gavela-Courte-Kragh about smooth structures on Lagrangians in cotangent bundles of spheres. The main technical tool we use is Large's recent construction of a stable-homotopical enrichment of Lagrangian Floer theory.
This is based on joint work-in-progress with Ivan Smith.

Marco Mazzucchelli (ENS-Lyon)
2023-03-03 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/98/
by Marco Mazzucchelli (ENS-Lyon) as part of Symplectic zoominar

Abstract: TBA

Georgios Dimitroglou Rizell (Uppsala)
2023-03-31 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/99/
Title: A relative Calabi-Yau structure for Legendrian contact homology (https://master.researchseminars.org/talk/SympZoominar/99/)
by Georgios Dimitroglou Rizell (Uppsala) as part of Symplectic zoominar

Abstract
The duality long exact sequence relates linearised Legendrian contact homology and cohomology and was originally constructed by Sabloff in the case of Legendrian knots. We show how the duality long exact sequence can be generalised to a relative Calabi-Yau structure, as defined by Brav and Dyckerhoff. We also discuss the generalised notion of the fundamental class and give applications. The structure is established through the acyclicity of a version of Rabinowitz Floer Homology for Legendrian submanifolds with coefficiens in the Chekanov-Eliashberg DGA. This is joint work in progress with Legout.

Yaron Ostrover (TAU)
2023-03-24 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/100/
Title: Symplectic Barriers (https://master.researchseminars.org/talk/SympZoominar/100/)
by Yaron Ostrover (TAU) as part of Symplectic zoominar

Abstract
In this talk we discuss the existence of a new type of rigidity of symplectic embeddings coming from obligatory intersections with symplectic planes. This is based on a joint work with P. Haim-Kislev and R. Hind.

Yuhan Sun (Rutgers)
2023-03-17 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/101/
Title: Heaviness and relative symplectic cohomology (https://master.researchseminars.org/talk/SympZoominar/101/)
by Yuhan Sun (Rutgers) as part of Symplectic zoominar

Abstract
For a compact subset $K$ of a closed symplectic manifold, Entov-Polterovich introduced the notion of (super)heaviness, which reveals surprising symplectic rigidity. When $K$ is a Lagrangian submanifold, there is a well-established criterion for its heaviness, by using closed-open maps. We will discuss an equivalence between the heaviness and the non-vanishing of the relative symplectic cohomology, for a general compact set $K$. Joint with C.Y.Mak and U.Varolgunes.

Brayan Ferreira (IMPA)/Roman Krutowski (UCLA)/Amanda Hirschi (Cambridge)
2023-04-21 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/102/
Title: Three 20min research talks (https://master.researchseminars.org/talk/SympZoominar/102/)
by Brayan Ferreira (IMPA)/Roman Krutowski (UCLA)/Amanda Hirschi (Cambridge) as part of Symplectic zoominar

Abstract
Brayan Ferreira (IMPA)

Title: Gromov width of disk cotangent bundles of spheres of revolution

Abstract: The question of whether a Symplectic manifold embeds into another is central in Symplectic topology. Since Gromov nonsqueezing theorem, it is known that this is a different problem from volume preserving embeddings. Symplectic capacities are invariants that give obstructions to symplectic embeddings. The first example of a symplectic capacity is given by the Gromov width, which measures the biggest ball that can be symplectically embedded into a symplectic manifold. In this talk, we are going to discuss the Gromov width for the example of disk cotangent bundles of spheres of revolution. The main results are for the Zoll cases and for the case of ellipsoids of revolution. The main tools are action angle coordinates (Arnold-Liouville theorem) and ECH capacities. This is joint work with Alejandro Vicente and Vinicius Ramos.

Roman Krutowski (UCLA)

Title: Maslov index formula in Heegaard Floer homology

Abstract: The formula introduced by Robert Lipshitz for Heegaard Floer homology is now one of the basic tools for those working with HF homology. The convenience of the formula is due to its combinatorial nature. In the talk, we will discuss the recent combinatorial proof of this formula.

Amanda Hirschi (Cambridge)

Title: Global Kuranishi charts for Gromov-Witten moduli spaces and a product formula

Abstract: I will describe the construction of a global Kuranishi chart for moduli spaces of stable pseudoholomorphic maps of any genus and explain how this allows for a straightforward definition of GW invariants. For those not convinced of its usefulness, I will sketch how this can be used to obtain a formula for the GW invariants of a product. This is joint work with Mohan Swaminathan.

Michael Entov (Technion)
2023-05-05 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/103/
Title: Kahler-type and tame embeddings of balls into symplectic manifolds (https://master.researchseminars.org/talk/SympZoominar/103/)
by Michael Entov (Technion) as part of Symplectic zoominar

Abstract
A symplectic embedding of a disjoint union of domains into a symplectic manifold M is said to be of Kahler type (respectively tame) if it is holomorphic with respect to some (not a priori fixed) integrable complex structure on M which is compatible with (respectively tamed by) the symplectic form. I'll discuss when Kahler-type embeddings of disjoint unions of balls into a closed symplectic manifold exist and when two such embeddings can be mapped into each other by a symplectomorphism. If time permits, I'll also discuss the existence of tame embeddings of balls, polydisks and parallelepipeds into tori and K3 surfaces.

This is a joint work with M.Verbitsky.

Michael Bialy (TAU)
2023-04-28 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/104/
Title: Locally maximizing orbits and rigidity for convex billiards (https://master.researchseminars.org/talk/SympZoominar/104/)
by Michael Bialy (TAU) as part of Symplectic zoominar

Abstract
Given a convex billiard table, one defines the set $\mathcal M$ swept by locally maximizing orbits for convex billiard. This is a remarkable closed invariant set which does not depend (under certain assumptions) on the choice of the generating function. I shall show how to get sharp estimates on the measure of this set, recovering as a corollary rigidity result for centrally symmetric convex billiards. Also I shall discuss rigidity of Mather $\beta$ function.
Based on joint works with Andrey E. Mironov, Sergei Tabachnikov and Daniel Tsodikovich.

Pierrick Bousseau (UGA)
2023-04-14 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/105/
Title: Quivers, flow trees and log curves (https://master.researchseminars.org/talk/SympZoominar/105/)
by Pierrick Bousseau (UGA) as part of Symplectic zoominar

Abstract
Donaldson-Thomas (DT) invariants of a quiver with potential can be expressed in terms of simpler attractor DT invariants by a universal formula. The coefficients in this formula are calculated combinatorially using attractor flow trees. In joint work with Arguz (arXiv:2302.02068), we prove that these coefficients are genus 0 log Gromov-Witten invariants of d-dimensional toric varieties, where d is the number of vertices of the quiver. This result follows from a log-tropical correspondence theorem which relates (d-2)-dimensional families of tropical curves obtained as universal deformations of attractor flow trees, and rational log curves in toric varieties.

Vinicius Ramos (IMPA)
2023-05-19 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/106/
Title: The Toda lattice, billiards and the Viterbo conjecture (https://master.researchseminars.org/talk/SympZoominar/106/)
by Vinicius Ramos (IMPA) as part of Symplectic zoominar

Abstract
Abstract:
The Toda lattice is one of the earliest examples of non-linear completely integrable systems. Under a large deformation, the Hamiltonian flow can be seen to converge to a billiard flow in a simplex. In the 1970s, action-angle coordinates were computed for the standard system using a non-canonical transformation and some spectral theory. In this talk, I will explain how to adapt these coordinates to the situation of a large deformation and how this leads to new examples of symplectomorphisms of Lagrangian products with toric domains. In particular, we find a sequence of Lagrangian products whose symplectic systolic ratio is one and we prove that they are symplectic balls. This is joint work with Y. Ostrover and D. Sepe.

Joé Brendel (TAU)
2023-05-26 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/107/
Title: Local exotic tori (https://master.researchseminars.org/talk/SympZoominar/107/)
by Joé Brendel (TAU) as part of Symplectic zoominar

Abstract
We discuss exotic Lagrangian tori in dimension greater than or equal to six. First, we give another approach to Auroux's result that there are infinitely many tori in $\mathbb R^6$ which are distinct up to symplectomorphisms of the ambient space. The exotic tori we construct naturally appear in a two-​parameter family, some of which are not monotone. Small enough tori in this family can be embedded by a Darboux chart into any tame symplectic manifold and one can show that they are still distinct up to symplectomorphisms.

Russell Avdek (Paris)
2023-10-20 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/108/
Title: Convex hypersurfaces, contact homology, and relative GW (https://master.researchseminars.org/talk/SympZoominar/108/)
by Russell Avdek (Paris) as part of Symplectic zoominar

Abstract
While convex hypersurfaces are well understood in 3d contact topology, we are just starting to explore their basic properties in high dimensions. I will describe how to compute contact homologies (CH) of their neighborhoods, which can be used to infer tightness in any dimension. Then I’ll give a general construction of high-dimensional convex hypersurfaces in the style of Gompf’s fiber sum. For these convex hypersurfaces, relative Gromov-Witten can often compute CH in the style of Diogo-Lisi. We’ll work through some interesting examples.

Paul Seidel (MIT)
2023-10-13 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/109/
Title: Symplectic cohomology relative to a smooth divisor (https://master.researchseminars.org/talk/SympZoominar/109/)
by Paul Seidel (MIT) as part of Symplectic zoominar

Abstract: TBA

Lukas Nakamura (Uppsala); Habib Alizadeh (UdeM); Han Lou (UGA)
2023-10-27 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/110/
Title: Three 20min research talks (https://master.researchseminars.org/talk/SympZoominar/110/)
by Lukas Nakamura (Uppsala); Habib Alizadeh (UdeM); Han Lou (UGA) as part of Symplectic zoominar

Abstract
I. Lukas Nakamura (Uppsala)

Title: A metric on the contactomorphism group of an orderable contact manifold

Abstract: We discuss some properties of a pseudo-metric on the contactomorphism group of a strict contact manifold M induced by the maximum/minimum of Hamiltonians. We show that it is non-degenerate if and only if M is orderable and that its metric topology agrees with the interval topology introduced by Chernov and Nemirovski. We also discuss analogous results on isotopy classes of Legendrian submanifolds and on universal covers.

II. Habib Alizadeh (UdeM)

Title: Fragmentation in dimension four and its application to spectral estimators

Abstract: We show a new Hamiltonian fragmentation result for four-dimensional symplectic polydisks. As an application to our result, we prove -continuity of the spectral estimators defined by Polterovich and Shelukhin for polydisks.

III. Han Lou (UGA)

Title: On the Hofer Zehnder conjecture for semipositive symplectic manifolds

Abstract: Arnold conjecture says that the number of 1-periodic orbits of a Hamiltonian diffeomorphism is greater than or equal to the dimension of the Hamiltonian Floer homology. In 1994, Hofer and Zehnder conjectured that there are infinitely many periodic orbits if the equality doesn't hold. In this talk, I will show that the Hofer-Zehnder conjecture is true for semipositive symplectic manifolds with semisimple quantum homology. This is a joint work with Marcelo Atallah.

Ciprian Manolescu (Stanford)
2023-11-17 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/111/
Title: A knot Floer stable homotopy type (https://master.researchseminars.org/talk/SympZoominar/111/)
by Ciprian Manolescu (Stanford) as part of Symplectic zoominar

Abstract
Given a grid diagram for a knot or link K in the three-sphere, we construct a spectrum whose homology is the knot Floer homology of K. We conjecture that the homotopy type of the spectrum is an invariant of K. Our construction does not use holomorphic geometry, but rather builds on the combinatorial definition of grid homology. We inductively define models for the moduli spaces of pseudo-holomorphic strips and disk bubbles, and patch them together into a framed flow category. The inductive step relies on the vanishing of an obstruction class that takes values in a complex of positive domains with partitions. (This is joint work with Sucharit Sarkar.)

John Etnyre (Georgia Tech)
2023-12-15 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/112/
Title: Symplectic embeddings of rational homology balls into projective space (https://master.researchseminars.org/talk/SympZoominar/112/)
by John Etnyre (Georgia Tech) as part of Symplectic zoominar

Abstract
I will discuss how to build small symplectic caps for contact manifolds as a step in building small closed symplectic 4-manifolds. As an application of the construction, I will give explicit handlebody descriptions of symplectic embeddings of rational homology balls into \(\mathbb{CP}^2\). This is joint work with Hyunki Min, Lisa Piccirillo, and Agniva Roy.

Oliver Edtmair (Berkeley)
2023-11-03 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/113/
Title: The subleading asymptotics of symplectic Weyl laws (https://master.researchseminars.org/talk/SympZoominar/113/)
by Oliver Edtmair (Berkeley) as part of Symplectic zoominar

Abstract
Spectral invariants defined via Embedded Contact Homology (ECH) or the closely related Periodic Floer Homology (PFH) satisfy a Weyl law: Asymptotically, they recover symplectic volume. This Weyl law has led to striking applications in dynamics (smooth closing lemma) and \(C^0\) symplectic geometry (simplicity conjecture). In this talk, I will report on work in progress concerning the subleading asymptotics of symplectic Weyl laws. I will explain the connection to symplectic packing problems and the algebraic structure of groups of Hamiltonian diffeomorphisms and homeomorphisms.

Julien Dardennes (Toulouse); Arnaud Maret (Paris); Luya Wang (Stanford)
2023-12-08 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/114/
Title: Three 20min research talks (https://master.researchseminars.org/talk/SympZoominar/114/)
by Julien Dardennes (Toulouse); Arnaud Maret (Paris); Luya Wang (Stanford) as part of Symplectic zoominar

Abstract
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I. Julien Dardennes (Toulouse)

Title: The coarse distance from dynamically convex to convex

Abstract: Chaidez and Edtmair have recently found the first examples of dynamically convex domains in $\mathbb{R}^4$ that are not symplectomorphic to convex domains, answering a long-standing open question.
In this talk, we present new examples of such domains without referring to Chaidez-Edtmair’s criterion. We also show that these domains are arbitrarily far from the set of symplectically convex domains in $\mathbb{R}^4$ with respect to the coarse symplectic Banach-Mazur distance by using an explicit numerical criterion for symplectic non-convexity (joint work with J. Gutt, V. Ramos and J. Zhang).

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II. Arnaud Maret (Paris)

Title: Complex projective spaces via surface groups representations

Abstract: My plan is to explain how complex projective spaces can be identified with components of totally elliptic representations of the fundamental group of a punctured sphere into \(PSL(2,\mathbb{R})\). I will explain how this identification realizes the pure mapping class group of the punctured sphere as a subgroup of the group of Hamiltonian diffeomorphisms of the complex projective space.

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III. Luya Wang (Stanford)

Title: Deformation inequivalent symplectic structures and Donaldson's four-six question

Abstract: Studying symplectic structures up to deformation equivalences is a fundamental question in symplectic geometry. Donaldson asked: given two homeomorphic closed symplectic four-manifolds, are they diffeomorphic if and only if their stabilized symplectic six-manifolds, obtained by taking products with $\mathbb{CP}^1$ with the standard symplectic form, are deformation equivalent? I will discuss joint work with Amanda Hirschi on showing how deformation inequivalent symplectic forms remain deformation inequivalent when stabilized, under certain algebraic conditions. This gives the first counterexamples to one direction of Donaldson’s “four-six” question and the related Stabilizing Conjecture by Ruan.

Eduardo Fernández (U of Georgia)
2024-01-19 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/115/
Title: Cabling families of Legendrian embeddings (https://master.researchseminars.org/talk/SympZoominar/115/)
by Eduardo Fernández (U of Georgia) as part of Symplectic zoominar

Abstract
I will discuss a recursive formula for the homotopy type of the space of Legendrian embeddings of sufficiently positive cables with the maximal Thurston-Bennequin invariant. Via this formula, we identify infinitely many new components within the space of Legendrian embeddings in the standard contact 3-sphere that satisfy an injective h-principle. These components include those containing positive Legendrian torus knots with the maximal Thurston-Bennequin invariant. This work is a collaboration with Hyunki Min.

Matthias Meiwes (Tel Aviv)
2023-11-24 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/116/
Title: $C^0$ stability of topological entropy for 3-dimensional Reeb flows (https://master.researchseminars.org/talk/SympZoominar/116/)
by Matthias Meiwes (Tel Aviv) as part of Symplectic zoominar

Abstract
The $C^0$ distance on the space of contact forms on a contact manifold has been studied recently by different authors. It can be thought of as an analogue for Reeb flows of the Hofer metric on the space of Hamiltonian diffeomorphisms. In this talk, I will explain some recent progress on the stability properties of the topological entropy with respect to this distance obtained in collaboration with M. Alves, L. Dahinden, and A. Pirnapasov. Our main result states that the topological entropy for closed contact 3-manifolds is lower semi-continuous in the $C^0$ distance for $C^{\infty}$-generic contact froms. Applying our methods to geodesic flows of surfaces, we obtain that the points of lower-semicontinuity of the topological entropy include non-degenerate metrics. In particular, given a geodesic flow of such a metric with positive topological entropy, the topological entropy does not vanish for sufficiently $C^0$-small perturbations of the metric.

Yusuf Barış Kartal (Edinburgh)
2023-12-22 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/117/
Title: Equivariant Floer homotopy via Morse-Bott theory (https://master.researchseminars.org/talk/SympZoominar/117/)
by Yusuf Barış Kartal (Edinburgh) as part of Symplectic zoominar

Abstract
Floer homotopy type refines the Floer homology by associating a (stable) homotopy type to an Hamiltonian, whose homology gives the Hamiltonian Floer homology. In particular, one expects the existing structures on the latter to lift as well, such as the circle actions. On the other hand, constructing a genuine circle action even in the Morse theory is problematic: one usually cannot choose Morse-Smale pairs/Floer data that is invariant under the circle action. In this talk, we show how to extend the framework of Floer homotopy theory to the Morse-Bott setting, in order to tackle this problem. In the remaining time, we explain how to relate the Floer homotopy type to the free loop spaces of exact Lagrangian submanifolds equivariantly, and discuss applications to recovering information about the topology of the underlying manifold from its symplectic cohomology. Joint work with Laurent Cote.

Francesco Morabito (Paris); Filip Brocic (UdeM); Valentin Bosshard (ETH)
2024-01-05 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/118/
Title: Three 20min research talks (https://master.researchseminars.org/talk/SympZoominar/118/)
by Francesco Morabito (Paris); Filip Brocic (UdeM); Valentin Bosshard (ETH) as part of Symplectic zoominar

Abstract
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I. Francesco Morabito (Paris)

Title: TBA

Abstract: TBA

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II. Filip Brocic (UdeM)

Title: Riemannian distance and symplectic embeddings in cotangent bundle

Abstract:
In the talk, I will introduce a distance-like function on the zero section of the cotangent bundle using symplectic embeddings of standard balls inside an open neighborhood of the zero section. I will provide some examples which illustrate the properties of such a function. The main result that I will present is a relationship between the length structure associated to the introduced distance and the usual Riemannian length. Time permitting, I will explain a connection with the strong Viterbo conjecture for certain domains.

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III. Valentin Bosshard (ETH)

Title: TBA

Abstract: TBA

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Johanna Bimmermann (Bochum); Soham Chanda (Rutgers); Valerio Assenza (IMPA)
2024-01-26 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/119/
Title: Three 20min research talks (https://master.researchseminars.org/talk/SympZoominar/119/)
by Johanna Bimmermann (Bochum); Soham Chanda (Rutgers); Valerio Assenza (IMPA) as part of Symplectic zoominar

Abstract
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I. Johanna Bimmermann (Bochum)

Title: From magnetically twisted to hyperkähler

Abstract: The tangent bundle of a Kähler manifold admits in a neighborhood of the zero section a hyperkähler structure. From a symplectic point of view, this means we have three symplectic structures all compatible with a single metric. Two of the three symplectic structures are easy to describe in terms of the canonic symplectic structure. The third one is harder to describe, but in the case of hermitian symmetric spaces, there is an explicit formula found by Biquard and Gauduchon. In this talk, I will construct a surprising diffeomorphism of the tangent bundle of a hermitian symmetric space that identifies this third symplectic structure with the magnetically twisted symplectic structure, where the twist is given by the Kähler form on the base.

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II. Soham Chanda (Rutgers)

Title: Augmentation varieties and disk potential

Abstract: Dimitroglou-Rizell-Golovko constructs a family of Legendrians in prequantization bundles by taking lifts of monotone Lagrangians. These lifted Legendrians have a Morse-Bott family of Reeb chords. We construct a version of Legendrian Contact Homology (LCH) for Rizell-Golovko's lifted Legendrians by counting treed disks. Our formalism of LCH allows us to obtain augmentations from certain non-exact fillings. We prove a conjecture of Rizell-Golovko relating the augmentation variety assoiciated to the LCH of a lifted Legendrian and the disk potential of the base Lagrangian. As an application, we show that lifts of monotone Lagrangian tori in projective spaces with different disk-potentials, e.g. as constructed by Vianna, produce non-isotopic Legendrian tori in contact spheres. The above work is a joint project with Blakey, Sun and Woodward.

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III. Valerio Assenza (IMPA)

Title: On the geometry of magnetic flows

Abstract: A magnetic system is the toy model for the motion of a charged particle moving on a Riemannian manifold endowed with a magnetic force. To a magnetic flow we associate an operator, called the magnetic curvature operator. Such an operator encodes together the geometrical properties of the Riemannanian structure together with terms of perturbation due to magnetic interaction, and it carries crucial informations of the magnetic dynamics. For instance, in this talk, we see how a level of the energy positively curved, in this new magnetic sense, carries a periodic orbit. We also generalize to the magnetic case the classical Hopf's rigity and we introduce the notion of magnetic flatness for closed surfaces.

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Dylan Cant (UdeM)
2024-02-09 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/120/
Title: Extensible positive loops and vanishing of symplectic cohomology (https://master.researchseminars.org/talk/SympZoominar/120/)
by Dylan Cant (UdeM) as part of Symplectic zoominar

Abstract
I will discuss the relationship between positive loops of contactomorphisms of a fillable contact manifold and the symplectic cohomology (SH) of the filling. The main result is that the existence of a positive loop which is "extensible" implies SH vanishes. We also discuss the relationship between non-extensible loops and exotic mapping classes in the symplectomorphism group. The results have a relative (Lagrangian) formulation: an extensible positive loop of fillable Legendrians implies the wrapped Floer cohomology of the filling vanishes. As an application, one obtains a criterion for a positive loop to be non-extensible; interestingly enough, non-extensible loops provide a nice construction of exotic symplectic mapping classes (in the absolute case) and exotic Lagrangian fillings (in the relative case).

Alberto Abbondandolo (Bochum)
2024-02-16 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/121/
Title: Symplectic capacities of domains close to the ball and Banach-Mazur geodesics in the space of contact forms (https://master.researchseminars.org/talk/SympZoominar/121/)
by Alberto Abbondandolo (Bochum) as part of Symplectic zoominar

Abstract
An old open question in symplectic topology is whether all normalized capacities coincide on convex bounded domains in the standard symplectic vector space. I will discuss this question for domains which are close to the Euclidean ball and its connection with the geometry of the space of contact forms with a Banach-Mazur pseudo-metric. This talk is based on a recent joint work with Gabriele Benedetti and Oliver Edtmair.

Robert Lipshitz (Oregon)
2024-03-08 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/122/
Title: Strongly invertible knots, Khovanov homotopy, and localization (https://master.researchseminars.org/talk/SympZoominar/122/)
by Robert Lipshitz (Oregon) as part of Symplectic zoominar

Abstract
Strong inversions are a class of order-2 symmetries of knots in \(S^3\). Building on work of Seidel-Smith, Lidman-Manolescu, Stoffregen-Zhang, and others, we will describe a relationship between the Khovanov homology of a knot with a strong inversion and its quotients by the inversion. We will also give a modest application to surfaces in 4-space. This is joint work with Sucharit Sarkar. While there is no symplectic geometry in the talk, many of the ideas come from or may be useful in Floer-theoretic settings.

Ko Honda (UCLA)
2024-03-22 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/123/
Title: The Giroux correspondence in arbitrary dimensions (https://master.researchseminars.org/talk/SympZoominar/123/)
by Ko Honda (UCLA) as part of Symplectic zoominar

Abstract
Around twenty years ago Emmanuel Giroux formulated the equivalence of contact structures and open book decompositions with Weinstein pages up to stabilization. We establish the Giroux correspondence in full generality using the recent developments in convex hypersurface theory. This is joint work with Joe Breen and Yang Huang.

Álvaro Pelayo (Complutense University of Madrid)
2024-05-31 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/124/
Title: Toric and semitoric symplectic geometry: progress and challenges (https://master.researchseminars.org/talk/SympZoominar/124/)
by Álvaro Pelayo (Complutense University of Madrid) as part of Symplectic zoominar

Abstract
Toric integrable systems, also known as symplectic toric manifolds, arise as examples in different contexts within geometry and related areas. Semitoric integrable systems are a generalization of toric integrable systems in dimension four. In this talk I will discuss some classical and recent work on the symplectic geometry of toric and semitoric integrable systems. I will also mention some future challenges in the field.

Mark McLean (Stony Brook)
2024-06-28 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/125/
Title: Symplectic Orbifold Gromov-Witten Invariants (https://master.researchseminars.org/talk/SympZoominar/125/)
by Mark McLean (Stony Brook) as part of Symplectic zoominar

Abstract
Chen and Ruan constructed symplectic orbifold Gromov-Witten invariants more than 20 years ago. In ongoing work with Alex Ritter, we show that moduli spaces of pseudo-holomorphic curves mapping to a symplectic orbifold admit global Kuranishi charts. This allows us to construct other types of Gromov-Witten invariants, such as K-theoretic counts. The construction relies on an orbifold embedding theorem of Ross and Thomas.

Denis Auroux (Harvard)
2024-02-23 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/126/
Title: Floer-theoretic corrections to the geometry of moduli spaces of Lagrangian tori (https://master.researchseminars.org/talk/SympZoominar/126/)
by Denis Auroux (Harvard) as part of Symplectic zoominar

Abstract
Given a Lagrangian torus fibration on the complement of an anticanonical divisor in a Kahler manifold, one usually constructs a mirror space by gluing local charts (moduli spaces of objects of the Fukaya category supported on generic torus fibers) via wall-crossing transformations determined by counts of Maslov index 0 holomorphic discs; this mirror also comes equipped with a regular function (the superpotential) which enumerates Maslov index 2 holomorphic discs. Holomorphic discs of negative Maslov index deform this picture by introducing inconsistencies in the wall-crossing transformations; the geometric features of the corrected moduli space of objects of the Fukaya category can be understood in the language of extended deformations of Landau-Ginzburg models. We will illustrate this phenomenon on an explicit example (a 4-fold obtained by blowing up a toric variety), and, if time permits, discuss a family Floer approach to the geometry of the corrected mirror in this setting.

Yusuke Kawamoto (ETH)
2024-03-15 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/127/
Title: Quantitative Floer theory and coefficients (https://master.researchseminars.org/talk/SympZoominar/127/)
by Yusuke Kawamoto (ETH) as part of Symplectic zoominar

Abstract
I will discuss how much the choice of coefficients impacts the quantitative information of Floer theory, especially spectral invariants. In particular, I will present some phenomena that are specific to integer coefficients, including an answer to a variant of a question posed by Nancy Hingston. The material is based on a joint work with Egor Shelukhin.

Viktor Ginzburg (UCSC)
2024-05-10 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/128/
Title: Invariant sets and hyperbolic periodic orbits (https://master.researchseminars.org/talk/SympZoominar/128/)
by Viktor Ginzburg (UCSC) as part of Symplectic zoominar

Abstract
The presence of hyperbolic periodic orbits or invariant sets often has an affect on the global behavior of a dynamical system. In this talk we discuss two theorems along the lines of this phenomenon, extending some properties of Hamiltonian diffeomorphisms to dynamically convex Reeb flows on the sphere in all dimensions. The first one, complementing other multiplicity results for Reeb flows, is that the existence of a hyperbolic periodic orbit forces the flow to have infinitely many periodic orbits. This result can be thought of as a step towards Franks’ theorem for Reeb flows. The second result is a contact analogue of the higher-dimensional Le Calvez-Yoccoz theorem proved by the speaker and Gurel and asserting that no periodic orbit of a Hamiltonian pseudo-rotation is locally maximal. The talk is based on a joint work with Erman Cineli, Basak Gurel and Marco Mazzucchelli.

Yao Xiao (Stony Brook); Yoav Zimhony (TAU); Qi Feng (IGP-UST, Hefei)
2024-03-29 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/129/
Title: Three 20min research talks (https://master.researchseminars.org/talk/SympZoominar/129/)
by Yao Xiao (Stony Brook); Yoav Zimhony (TAU); Qi Feng (IGP-UST, Hefei) as part of Symplectic zoominar

Abstract: TBA

Yan-Lung Leon Li (CUHK); Levin Maier (Heidelberg); Austin Christian (Georgia Tech)
2024-04-12 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/130/
Title: Three 20min research talks (https://master.researchseminars.org/talk/SympZoominar/130/)
by Yan-Lung Leon Li (CUHK); Levin Maier (Heidelberg); Austin Christian (Georgia Tech) as part of Symplectic zoominar

Abstract
-----

I. Yan-Lung Leon Li (CUHK)

Title: Equivariant Lagrangian correspondence and a conjecture of Teleman

Abstract:

It has been a continuing interest, often with profound importance, in understanding the geometric and topological relationship between a Hamiltonian G-manifold Y and a symplectic quotient X. In this talk, we shall provide precise relations between their (equivariant) Lagrangian Floer theory. In particular, we will address a conjecture of Teleman, motivated by 3d mirror symmetry, on the 2d mirror construction of X from that of Y, which generalises Givental-Hori-Vafa mirror construction for toric varieties. The key technical ingredient is the Kim-Lau-Zheng’s equivariant extension of Fukaya’s Lagrangian correspondence tri-modules over equivariant Floer complexes. Joint work with Siu-Cheong Lau and Naichung Conan Leung.

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II. Levin Maier (Heidelberg)

Title: On Mañé's critical value for the two-component Hunter-Saxton system

Abstract:

In this talk, we will introduce Mañé's critical value for a Hamiltonian PDE, the two-component Hunter-Saxton system. We will introduce the magnetic two-component Hunter-Saxton system (M2HS), which is a magnetic geodesic equation on an infinite-dimensional Lie group. We prove that this magnetic system is magnetic isomorphic to a magnetic system on an infinite-dimensional sphere. Surprisingly each magnetic geodesic is tangent to the 3-sphere obtained by intersecting the ambient sphere with a complex plane. We use this geometric description of the (M2HS) to give explicit criteria for blow-ups and prove the existence of global weak solutions.

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III. Austin Christian (Georgia Tech)

Title: Persistent Legendrian contact homology

Abstract:

This talk will report on an REU whose goal was to introduce the notion of persistence into Legendrian contact homology. The LCH of a Legendrian knot is computed as the homology of the knot's Chekanov-Eliashberg DGA and is a well-studied invariant of Legendrian isotopy types. For a given Legendrian embedding, the Chekanov-Eliashberg DGA admits a natural filtration, allowing for the computation of persistent homology. The purpose of this REU was to initiate the study of the resulting filtered homology. The project was joint with M. Basu, E. Clayton, D. Irvine, F. Mooers, and W. Shen.

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Shira Tanny (IAS)
2024-04-19 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/131/
Title: From Gromov–Witten theory to the closing lemma (https://master.researchseminars.org/talk/SympZoominar/131/)
by Shira Tanny (IAS) as part of Symplectic zoominar

Abstract
An old question of Poincaré concerns creating periodic orbits via perturbations of a flow/diffeomorphism. While pseudoholomorphic methods have successfully addressed this question in dimensions 2-3, the higher-dimensional case remains less understood. I will describe a connection between this question and Gromov–Witten invariants, which goes through a new class of invariants of symplectic cobordisms. This is a joint work with Julian Chaidez.

Ivan Smith (Cambridge)
2024-05-17 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/132/
Title: Bordism of flow modules and exact Lagrangians (https://master.researchseminars.org/talk/SympZoominar/132/)
by Ivan Smith (Cambridge) as part of Symplectic zoominar

Abstract
We discuss constraints on exact Lagrangian embeddings obtained from considering bordism classes of flow modules over Lagrangian Floer flow categories. This talk reports on joint work with Noah Porcelli.

Lenhard Ng (Duke)
2024-05-24 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/133/
Title: New algebraic invariants of Legendrian links (https://master.researchseminars.org/talk/SympZoominar/133/)
by Lenhard Ng (Duke) as part of Symplectic zoominar

Abstract
For the past 25 years, Legendrian contact homology has played a key role in contact topology. I'll discuss a package of new invariants for Legendrian knots and links that builds on Legendrian contact homology and is derived from rational symplectic field theory. This includes a Poisson bracket on Legendrian contact homology and a symplectic structure on augmentation varieties. Time permitting, I'll also describe an unexpected connection to cluster theory for a family of Legendrian links associated to positive braids. Parts of this are joint work in progress with Roger Casals, Honghao Gao, Linhui Shen, and Daping Weng.

Agustin Moreno (Heidelberg)
2024-05-03 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/134/
by Agustin Moreno (Heidelberg) as part of Symplectic zoominar

Abstract: TBA

Dan Cristofaro-Gardiner (Maryland)
2024-06-14 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/135/
Title: Two or infinity (https://master.researchseminars.org/talk/SympZoominar/135/)
by Dan Cristofaro-Gardiner (Maryland) as part of Symplectic zoominar

Abstract
It is conjectured that every Reeb flow on a closed three-manifold has either two, or infinitely many, simple periodic orbits. I will survey what is currently known about this conjecture. Then, I will try to explain some of the key ideas behind recent joint work proving it, as long as the associated contact structure has torsion Chern class. Then, I will state some related open questions.

Alexandru Oancea (Strasbourg)
2024-10-11 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/136/
Title: Floer homology with DG coefficients. Applications to cotangent bundles (https://master.researchseminars.org/talk/SympZoominar/136/)
by Alexandru Oancea (Strasbourg) as part of Symplectic zoominar

Abstract
Given a path-connected topological space \(X\), a differential graded (DG) local system (or derived local system) is a module over the DGA of chains on the based loop space of \(X\). I will explain how to define in the symplectically aspherical case Hamiltonian Floer homology with coefficients in a DG local system, how this homology fits into a filtered homological toolbox, and will present a number of dynamical applications to cotangent bundles. This is joint work with Jean-François Barraud, Mihai Damian and Vincent Humilière. The construction of Floer homology with enriched coefficients was originally discovered by Barraud-Cornea, and it was revisited over the years in different settings by Abouzaid, Charette, Zhou, and Rezchikov.

Jean Gutt (IMT / INU Champollion)
2024-10-18 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/137/
Title: Ekeland-Hofer capacities as coming from positive \(S^1\) equivariant symplectic homology (https://master.researchseminars.org/talk/SympZoominar/137/)
by Jean Gutt (IMT / INU Champollion) as part of Symplectic zoominar

Abstract
Associated to a star-shaped domain in \(\mathbb{R}^{2n}\) are two increasing sequences of capacities: the Ekeland-Hofer capacities and the so-called Gutt-Hutchings capacities. I shall recall both constructions and then present the main theorem that they are the same. This is joint work with Vinicius Ramos.

Adrien Currier (Nantes); Adi Dickstein (Tel Aviv); Elliot Gathercole (Lancaster)
2024-10-25 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/138/
Title: Three 20min research talks (https://master.researchseminars.org/talk/SympZoominar/138/)
by Adrien Currier (Nantes); Adi Dickstein (Tel Aviv); Elliot Gathercole (Lancaster) as part of Symplectic zoominar

Abstract
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I. Adrien Currier (Nantes)

Title: Exact Lagrangians in cotangent bundles with locally conformally symplectic structure

Abstract:

First considered by Lee in the 40s, locally conformally symplectic (LCS) geometry appears as a generalization of symplectic geometry which allows for the study of Hamiltonian dynamics on a wider range of manifolds while preserving the local properties of symplectic geometry. After a long period of hibernation (especially as far as the topological aspect is concerned), interest in this subject has picked up again recently. However, to this day, the field of LCS topology remains vastly unexplored.

In this talk, we will introduce the various objects of LCS geometry and their behavior through both definitions and examples. We will also explore some questions around an LCS version of the nearby Lagrangian conjecture and some of the connections between LCS and contact geometry.

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II. Adi Dickstein (Tel Aviv)

Title: Relative symplectic cohomology of pairs

Abstract:

Relative symplectic cohomology, an invariant of subsets in a symplectic manifold, was recently introduced by Varolgunes. In this talk, I will present a generalization of this invariant to pairs of subsets, which shares similar properties with the singular cohomology of pairs, such as excision and a product structure. Using this new invariant, I will demonstrate new symplectic rigidity phenomena. Joint with Yaniv Ganor, Leonid Polterovich and Frol Zapolsky.

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III. Elliot Gathercole (Lancaster)

Title: Superheavy skeleta for non-normal crossings divisors

Abstract:

Given an anticanonical divisor in a projective variety, one naturally obtains a monotone Kähler manifold, and the divisor complement is naturally a Liouville manifold. For certain kinds of singular divisors, we will outline a result obtaining rigid (in particular, superheavy) neighbourhoods of the Lagrangian skeleton of the complement, of prescribed volume dependent on the divisor, and illustrate this with some interesting examples where the skeleton itself is superheavy.

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Sebastian Haney (Columbia); Milica Ðukic (Uppsala); Yann Guggisberg (Utrecht)
2024-11-15 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/139/
Title: Three 20min research talks (https://master.researchseminars.org/talk/SympZoominar/139/)
by Sebastian Haney (Columbia); Milica Ðukic (Uppsala); Yann Guggisberg (Utrecht) as part of Symplectic zoominar

Abstract
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I. Sebastian Haney (Columbia)

Title: Open enumerative mirror symmetry for lines in the mirror quintic

Abstract:

One of the earliest achievements of mirror symmetry was the prediction
of genus zero Gromov-Witten invariants for the quintic threefold in
terms of period integrals on the mirror. Analogous predictions for
open Gromov-Witten invariants in closed Calabi-Yau threefolds can be
formulated in terms of relative period integrals on the mirror, which
govern extensions of variations of Hodge structure. I will discuss
work in which I construct an immersed Lagrangian in the quintic which
supports a family of objects in the Fukaya category mirror to vector
bundles on lines in the mirror quintic, and deduce its open
Gromov-Witten invariants from homological mirror symmetry. The domain
of this Lagrangian immersion is a closed 3-manifold obtained by gluing
together two copies of a cusped hyperbolic 3-manifold. The open
Gromov-Witten invariants of the Lagrangian are irrational numbers
valued in the invariant trace field of the hyperbolic pieces.

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II. Milica Ðukic (Uppsala)

Title: A deformation of the Chekanov-Eliashberg dg algebra using pseudoholomorphic annuli

Abstract:

We introduce an SFT-type invariant for Legendrian knots in \(\mathbb{R}^3\), which is a deformation of the Chekanov-Eliashberg differential graded algebra. The differential includes components that count index zero pseudoholomorphic disks with up to two positive punctures, annuli with one positive puncture, and a string topological component. We also describe a combinatorial way to compute the invariant from the Lagrangian projection.

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III. Yann Guggisberg (Utrecht)

Title: Instantaneous Hamiltonian diplaceability and arbitrary squeezability for critically negligible sets

Abstract:

This talk will be about joint work with Fabian Ziltener in which we show that a compact n-rectifiable subset of $\mathbb{R}^{2n}$ with vanishing n-Hausdorff measure can be displaced from itself by a Hamiltonian diffeomorphism arbitrarily close to the identity. This has the consequence that such a set can be arbitrarily symplectically squeezed, i.e. embedded into any neighborhood of the origin in $\mathbb{R}^{2n}$.

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Michael Hutchings (Berkeley)
2024-11-01 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/140/
Title: Classification of some open toric domains (https://master.researchseminars.org/talk/SympZoominar/140/)
by Michael Hutchings (Berkeley) as part of Symplectic zoominar

Abstract
We show that two generic, open, convex or concave toric domains in \(\mathbb{R}^4\) are symplectomorphic if and only if they agree up to reflection. The proof uses barcodes in positive \(S^1\)-equivariant symplectic homology, or equivalently in cylindrical contact homology.

Daniel Pomerleano (UMB)
2024-11-29 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/141/
Title: Non-commutative Cartier isomorphism and quantum cohomology (https://master.researchseminars.org/talk/SympZoominar/141/)
by Daniel Pomerleano (UMB) as part of Symplectic zoominar

Abstract
Kaledin established a Cartier isomorphism for cyclic homology of dg-categories over fields of characteristic p, generalizing a classical construction in algebraic geometry. In joint work with Paul Seidel, we showed that this isomorphism and related results imply concrete statements about the structure of quantum connections on monotone symplectic manifolds (both in characteristic p and characteristic zero).

I will explain these results and, if time permits, I will also describe some open questions concerning the enumerative interpretation of the Cartier isomorphism as well as connections to quantum Steenrod operations.

Felix Schlenk (Neuchâtel)
2024-11-22 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/142/
Title: New invariants for Hamiltonian isotopy classes of monotone Lagrangian torus fibers (https://master.researchseminars.org/talk/SympZoominar/142/)
by Felix Schlenk (Neuchâtel) as part of Symplectic zoominar

Abstract
Based on the exotic Lagrangian tori constructed in \(\mathbb{CP}^2\) by Vianna and Galkin-Mikhalkin, we construct for each Markov triple three monotone Lagrangian tori in the 4-ball, and for triples with distinct entries show that these tori lie in different Hamiltonian isotopy classes. Defining the outer radius of such a torus as the capacity of the smallest ball containing a representative of the Hamiltonian isotopy class, we compute the outer radius for an infinite sequence of tori and show it distinguishes these tori.

We do a similar study for monotone tori in the cube. If such a torus arises from a degeneration of \(S^2 \times S^2\) with triangular moment image, it gives rise to four different Hamiltonian isotopy classes of tori in the cube; on the other hand, if the monotone torus arises from a non-trivial degeneration with quadrilateral moment image, it gives rise to eight different Hamiltonian isotopy classes of tori in the cube. In particular, we find infinitely many pairs of monotone tori in \(S^2 \times S^2\) which are symplectomorphic but not Hamiltonian isotopic.

This talk is based on work joint with Richard Hind and Grisha Mikhalkin.

Thomas Kragh (Uppsala)
2024-12-13 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/143/
Title: Using h-cobordisms to detect non-trivial homotopy groups in spaces of Legendrian (https://master.researchseminars.org/talk/SympZoominar/143/)
by Thomas Kragh (Uppsala) as part of Symplectic zoominar

Abstract
In this talk I will first define the space of h-cobordisms associated to a manifold M. This space is known to have many non-trivial homotopy groups and in stable range (they can often be computed using Waldhausen's algebraic K-theory of spaces). I will then define maps from these spaces into certain spaces of Legendrians, and I will describe how we detect that these maps are to some extend non-trivial on homotopy groups. A special case is that we essentially (and in stable range) find two copies of the h-cobordism space of a point inside the space of Legendrians of the jet 1 bundle of the n-sphere based at a standard Legendrian unknot (the Whitney sphere).

Zhengyi Zhou (AMSS, CAS)
2025-01-17 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/144/
Title: Kähler compactification of \(\mathbb{C}^n\) and Reeb dynamics (https://master.researchseminars.org/talk/SympZoominar/144/)
by Zhengyi Zhou (AMSS, CAS) as part of Symplectic zoominar

Abstract
We will present two results in complex geometry: (1) A Kähler compactification of \(\mathbb{C}^n\) with a smooth divisor complement must be \(\mathbb{P}^n\), which confirms a conjecture of Brenton and Morrow under the Kähler assumption; (2) Any complete asymptotically conical Calabi-Yau metric on \(\mathbb{C}^3\) with a smooth link must be flat, confirming a modified version of Tian’s conjecture regarding the recognition of the flat metric among Calabi-Yau metrics in dimension 3. Both proofs rely on relating the minimal discrepancy number of a Fano cone singularity to its Reeb dynamics of the conic contact form. This is a joint work with Chi Li.

Jae Hee Lee (Stanford); Simon Vialaret (Bochum / Orsay); Kenneth Blakey (MIT)
2024-12-20 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/145/
Title: Three 20min research talks (https://master.researchseminars.org/talk/SympZoominar/145/)
by Jae Hee Lee (Stanford); Simon Vialaret (Bochum / Orsay); Kenneth Blakey (MIT) as part of Symplectic zoominar

Abstract
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I. Jae Hee Lee (Stanford)

Title: Quantum Steenrod operations, p-curvature, and representation theory

Abstract:

Quantum Steenrod operations are deformations of classical Steenrod operations on mod p cohomology defined by counts of genus 0 holomorphic curves with a p-fold symmetry, for a prime p. We explain their relationship with the p-curvature of the quantum connection, and survey recent developments. This relationship was first noticed through the study of quantum Steenrod operations of symplectic resolutions, a rich class of smooth symplectic manifolds arising from representation theory. We describe the role of quantum Steenrod operations in the 3D mirror symmetry program, which concerns a duality between such symplectic resolutions. Partly joint with Shaoyun Bai.

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II. Simon Vialaret (Bochum / Orsay)

Title: Systolic inequalities for \(S^1\)-invariant contact forms

Abstract:

In contact geometry, a systolic inequality aims to give a uniform upper bound on the shortest period of a periodic Reeb orbit for contact forms with fixed volume on a given manifold. This generalizes a well-studied notion in Riemannian geometry. It is known that there is no systolic inequality valid for all contact forms on any given contact manifold. In this talk, I will state a systolic inequality for contact forms that are invariant under a circle action in dimension three.

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III. Kenneth Blakey (MIT)

Title: Bounding Lagrangian intersections using Floer homotopy theory

Abstract:

I will describe a new lower bound on the number of intersection points of a Lagrangian pair, in the exact setting, using Steenrod squares on Lagrangian Floer cohomology which are defined via a Floer homotopy type.

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Surena Hozoori (Rochester)
2025-01-24 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/146/
Title: Regularity and persistence in non-Weinstein Liouville geometry via hyperbolic dynamics (https://master.researchseminars.org/talk/SympZoominar/146/)
by Surena Hozoori (Rochester) as part of Symplectic zoominar

Abstract
We explore the construction of non-Weinstein Liouville geometric objects based on Anosov 3-flows, introduced by Mitsumatsu, in the generalized framework of Liouville Interpolation Systems and non-singular partially hyperbolic flows. We discuss the subtle phenomena inherited from the regularity and persistence theory of hyperbolic dynamics in the resulting Liouville structures, and prove dynamical and geometric rigidity results in this context. Among other things, we show that Mitsumatsu's examples characterize 4-dimensional non-Weinstein Liouville geometry with 3-dimensional \(C^1\)-persistent transverse skeleton. Time permitting, we also draw applications to the regularity theory of the weak dominated bundles for non-singular partially hyperbolic 3-flows.

Zhen Gao (Augsburg); Zihong Chen (MIT); Jonghyeon Ahn (UIUC)
2025-01-31 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/147/
Title: Three 20min research talks (https://master.researchseminars.org/talk/SympZoominar/147/)
by Zhen Gao (Augsburg); Zihong Chen (MIT); Jonghyeon Ahn (UIUC) as part of Symplectic zoominar

Abstract
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I. Zhen Gao (Augsburg)

Title: Morse-Bott Floer homology and rectangular pegs

Abstract: The rectangular peg problem, an extension of the square peg problem, is easy to outline but challenging to prove through elementary methods. In this talk, I discuss how to show the existence and a generic multiplicity result assuming the Jordan curve is smooth, utilizing Morse-Bott Floer homology. In particular, we obtain a convenient formula for computing the algebraic intersection number of cleanly intersecting Lagrangian submanifolds, which is well consistent with the Euler characteristic of Morse-Bott Floer homology in the spirit of "categorification''.

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II. Zihong Chen (MIT)

Title: The exponential type conjecture for quantum connection

Abstract:

The (small) quantum connection is one of the simplest objects built out of Gromov-Witten theory, yet it gives rise to a repertoire of rich and important questions such as the Gamma conjectures and the Dubrovin conjectures. There is a very basic question one can ask about this connection: what is its formal singularity type? People's expectation for this is packaged into the so-called exponential type conjecture, and I will discuss a proof in the case of closed monotone symplectic manifolds. My approach follows a reduction mod p argument, by combining Katz's classical result on differential equations and the more recent quantum Steenrod operations.

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III. Jonghyeon Ahn (UIUC)

Title: \(S^1\)-equivariant relative symplectic cohomology and relative symplectic capacities

Abstract:

In this talk, I will construct an \(S^1\)-equivariant version of the relative symplectic cohomology developed by Varolgunes. As an application, I will construct a relative version of Gutt-Hutchings capacities and a relative version of symplectic (co)homology capacity. We will see that these relative symplectic capacities can detect the diplaceability and the heaviness of a compact subset of a symplectic manifold. We compare the first relative Gutt-Hutchings capacity and the relative symplectic (co)homology capacity and prove that they are equal to each other under a convexity assumption.

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Vukašin Stojisavljević (CRM, UdeM)
2025-02-28 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/148/
Title: On certain \(C^0\)-aspects of contactomorphism groups (https://master.researchseminars.org/talk/SympZoominar/148/)
by Vukašin Stojisavljević (CRM, UdeM) as part of Symplectic zoominar

Abstract
We will explore certain \(C^0\)-rigidity and flexibility phenomena in the study of contact transformations. In particular, we will show how the dichotomy between contact squeezing and non-squeezing is related to the Rokhlin property of the group of contact homeomorphisms. Assuming a more quantitative viewpoint, we will define new distances on the group of contact homeomorphisms and show that, in some cases, they satisfy a form of \(C^0\)-stability. A technical result behind this stability is \(C^0\)-continuity of Sandon's spectral invariants. The talk is based on a joint work with Baptiste Serraille.

Pierre-Alexandre Arlove (Strasbourg)
2025-02-21 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/149/
Title: Contact non-squeezing in various closed prequantizations (https://master.researchseminars.org/talk/SympZoominar/149/)
by Pierre-Alexandre Arlove (Strasbourg) as part of Symplectic zoominar

Abstract
I will describe and argue the existence of contact non-squeezing phenomena in contact lens spaces and in strongly orderable prequantizations.

The proof is based on the construction of contact capacities coming from spectral selectors defined on the contactomorphisms group of the latter contact manifolds. I will define all these notions during my talk.

Richard Hind (Notre Dame)
2025-02-14 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/150/
Title: Lagrangian intersections and the shape invariant (https://master.researchseminars.org/talk/SympZoominar/150/)
by Richard Hind (Notre Dame) as part of Symplectic zoominar

Abstract
We will outline the proof of an intersection result between embedded Lagrangian tori and certain 1 parameter families of product Lagrangian tori in the 4 dimensional symplectic cylinder. The theorem can be applied to give new computations of the shape invariant, describing the Lagrangian tori in some toric domains, and therefore to produce symplectic embedding obstructions. This is joint work with Ely Kerman.

Noah Porcelli (Imperial)
2025-03-21 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/151/
Title: Parametrised Whitehead torsion of families of nearby Lagrangians (https://master.researchseminars.org/talk/SympZoominar/151/)
by Noah Porcelli (Imperial) as part of Symplectic zoominar

Abstract
The parametrised Whitehead torsion is an invariant of families of manifolds, and can be viewed as a map to an algebraic K-theory space. A strong version of the nearby Lagrangian conjecture says that when applied to families of closed exact Lagrangians in a cotangent bundle, this invariant vanishes.

Abouzaid and Kragh showed that in this case, this map lands in the trivial path component of the target, i.e. is trivial on $\pi_0$. Using generating functions, we find strong constraints on what this map does to higher homotopy groups. I'll illustrate this with some concrete consequences for the symplectic mapping class group of $T^*T^n$ relative to the 0-section.

This is based on joint work-in-progress with Sylvain Courte.

Yin Li (Uppsala)
2025-03-28 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/152/
Title: Persistence of unknottedness of Lagrangian intersect (https://master.researchseminars.org/talk/SympZoominar/152/)
by Yin Li (Uppsala) as part of Symplectic zoominar

Abstract
The double bubble plumbing, first studied by Smith and Wemyss, is a Stein neighborhood of two Lagrangian 3-spheres intersecting cleanly along an unknotted circle in some 6-dimensional symplectic manifold. Depending on the identification of the normal bundle of the unknot, there are infinitely many such Stein neighborhoods. We prove that there is no Hamiltonian isotopy of the Lagrangian spheres in any of these Stein neighborhoods so that they become two spheres intersecting along a circle which is knotted in either component, contradicting what happens under smooth isotopies. The proof uses the exact Calabi-Yau structures on the wrapped Fukaya categories to classify spherical Lagrangians in double bubble plumbings. This is joint work with Johan Asplund.

Tara Holm (Cornell)
2025-04-18 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/153/
Title: Equivariant cohomology and the (symplectic) diffeotype of complexity-one four-manifolds (https://master.researchseminars.org/talk/SympZoominar/153/)
by Tara Holm (Cornell) as part of Symplectic zoominar

Abstract
In this talk, we will explore the relationship between the geometry and topology of a complexity-one four-manifold and the combinatorial data that encode it. We will use a generators-and-relations description for the even part of the equivariant cohomology of the manifold to see what geometric aspects the equivariant cohomology determines. Namely, it allows us to reconstruct the diffeotype but not the complex structure. The talk will be driven by specific examples and pictures. It is based on joint work with Liat Kessler and Susan Tolman.

Alexander Ritter (Oxford)
2025-05-09 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/154/
Title: Equivariant Floer theory for symplectic C*-manifolds (https://master.researchseminars.org/talk/SympZoominar/154/)
by Alexander Ritter (Oxford) as part of Symplectic zoominar

Abstract
The talk will be on recent progress in a series of joint papers with Filip Živanović, about a large class of non-compact symplectic manifolds, which includes semiprojective toric manifolds, quiver varieties, and conical symplectic resolutions of singularities. These manifolds admit a Hamiltonian circle action which is part of a pseudo-holomorphic action of a complex torus. The symplectic form on these spaces is highly non-exact, yet we can make sense of Hamiltonian Floer cohomology for functions of the moment map of the circle action. We showed that Floer theory induces a filtration by ideals on quantum cohomology. I will explain recent progress on equivariant Floer cohomology for these spaces, in which case we obtain a filtration on equivariant quantum cohomology. If time permits, I will also mention a presentation of symplectic cohomology and quantum cohomology for semiprojective toric manifolds.

Vinicius Ramos (IMPA)
2025-04-25 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/155/
Title: Integrable systems and toric contact forms on $\mathbb{RP}^3$ (https://master.researchseminars.org/talk/SympZoominar/155/)
by Vinicius Ramos (IMPA) as part of Symplectic zoominar

Abstract
It is well-known that the geodesic flow on ellipsoids of revolution is integrable. In joint work with Ferreira and Vicente, we used this fact to obtain a symplectomorphism between the unit disk bundle of such an ellipsoid without fiber and a toric domain. In this talk, I will explain this result and how we can also obtain a symplectomorphism between the whole unit disk bundle and a toric filling of \(\mathbb{RP}^3\), which can be concave or convex depending on the original ellipsoid. I will also explain how to generalize this idea to other situations.

Alexia Corradini (Cambridge); Ibrahim Trifa (ETH); Stefan Matijević (Bochum)
2025-04-11 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/156/
Title: Three 20min research talks (https://master.researchseminars.org/talk/SympZoominar/156/)
by Alexia Corradini (Cambridge); Ibrahim Trifa (ETH); Stefan Matijević (Bochum) as part of Symplectic zoominar

Abstract
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I. Alexia Corradini (Cambridge)

Title: The Lagrangian Ceresa cycle

Abstract: In algebraic geometry, the Ceresa cycle provided one of the first examples of a nullhomologous cycle which is not algebraically trivial. I will explain how one can obtain a mirror statement about the Lagrangian Ceresa cycle, a nullhomologous Lagrangian living in a symplectic six-torus. This requires introducing a new equivalence relation on Lagrangians in a symplectic manifold, algebraic Lagrangian cobordism, inspired by algebraic equivalence.

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II. Ibrahim Trifa (ETH)

Title: A local quasimorphism property for link spectral invariants

Abstract: Given a finite collection of disjoint Lagrangian circles on a symplectic surface satisfying some area constraints, Cristofaro-Gardiner, Humilière, Mak, Seyfaddini and Smith define a link spectral invariant, by computing the Lagrangian Floer homology of the product of the circles inside the symmetric product of the surface. When the surface is the sphere, this spectral invariant is a quasimorphism, however this is not the case for higher genus surfaces. In this talk, I will show that the link spectral invariants on higher genus surfaces are local quasimorphisms, i.e. that their restriction to Hamiltonian diffeomorphisms supported in any given topological disc inside the surface is a quasimorphism. This is a joint work with Cheuk Yu Mak.

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III. Stefan Matijević (Bochum)

Title: Systolic \(S^1\)-index and characterization of non-smooth Zoll convex bodies

Abstract: We define the systolic $S^1$-index of a convex body as the Fadell–Rabinowitz index of the space of centralized generalized systoles associated with its boundary. We show that this index is a symplectic invariant. Using the systolic $S^1$-index, we propose a definition of generalized Zoll convex bodies and prove that this definition is equivalent to the usual one in the smooth setting. Moreover, we show how generalized Zoll convex bodies can be characterized in terms of their Gutt–Hutchings capacities and we prove that the space of generalized Zoll convex bodies is closed in the space of all convex bodies. As a corollary, we establish that if the interior of a convex body is symplectomorphic to the interior of a ball, then such a convex body must be generalized Zoll, and in particular Zoll if its boundary is smooth.

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Joé Brendel (ETH)
2025-05-23 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/157/
Title: Markov staircases (https://master.researchseminars.org/talk/SympZoominar/157/)
by Joé Brendel (ETH) as part of Symplectic zoominar

Abstract
In this talk, we will discuss new infinite symplectic staircases. Much recent progress has been made in the study of infinite symplectic staircases arising from embedding problems of standard ellipsoids into various symplectic four-manifolds. We study new embedding problems, where the domains are "ellipsoid-like" neighbourhoods of Lagrangian pinwheels instead of standard ellipsoids. Using almost toric fibrations, we show that every Lagrangian pinwheel in the complex projective plane (and thus every Markov number) has an infinite symplectic staircase. This is joint work with Jonny Evans, Johannes Hauber and Felix Schlenk.

Rémi Leclercq (Paris)
2025-05-02 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/158/
Title: Local persistence of Lagrangian intersections (https://master.researchseminars.org/talk/SympZoominar/158/)
by Rémi Leclercq (Paris) as part of Symplectic zoominar

Abstract
Given a Lagrangian $L$, I will discuss the existence of a neighborhood $W$ of $L$ with the following property: for any Hamiltonian diffeomorphism $f$, if $f(L)$ is contained inside $W$, then $f(L)$ intersects $L$.

On the one hand, for any symplectic manifold of dimension at least 6, I will construct Lagrangians which do not admit any such neighborhoods. On the other hand, I will give conditions which ensure the existence of such neighborhoods for a large class of Lagrangians. These conditions actually ensure the exactness of certain nearby Lagrangians, and I will discuss further applications of this phenomenon. This is based on joint work with Marcelo Atallah, Jean-Philippe Chassé, and Egor Shelukhin.

Basak Gurel (UCF)
2025-05-30 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/159/
Title: Towards the HZ- and multiplicity conjectures for dynamically convex Reeb flows (https://master.researchseminars.org/talk/SympZoominar/159/)
by Basak Gurel (UCF) as part of Symplectic zoominar

Abstract
In this talk we discuss the multiplicity question for prime closed orbits of a dynamically convex Reeb flow on the boundary of a 2n-dimensional star-shaped domain. Our first main result asserts that such a flow has at least n prime closed Reeb orbits, settling a conjecture which is usually attributed to Ekeland. The second main theorem is that when, in addition, the domain is centrally symmetric and the Reeb flow is non-degenerate, the flow has either exactly n or infinitely many prime closed orbits. This is a higher-dimensional contact variant of Franks' celebrated 2-or-infinity theorem and, viewed from the symplectic dynamics perspective, settles a particular case of the contact Hofer-Zehnder conjecture. The talk is based on a joint work with Erman Cineli and Viktor Ginzburg.

Roman Krutowski (UCLA)
2025-05-16 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/160/
Title: Morse theory of loop spaces and Hecke algebras (https://master.researchseminars.org/talk/SympZoominar/160/)
by Roman Krutowski (UCLA) as part of Symplectic zoominar

Abstract
One can associate an HDHF (symmetric) wrapped Fukaya category to a Liouville domain by counting higher genus curves, which are required to be branched covers. For the cotangent bundle of an orientable surface with genus at least one Honda, Tian, and Yuan showed that the \(A_\infty\)-algebra associated with k disjoint cotangent fibers is quasi-equivalent to the HOMFLY-PT braid skein algebra of the surface.

In this talk, I will present a Morse-theoretic model that computes the HDHF \(A_\infty\)-algebra of k fibers of the cotangent bundle of an orientable smooth manifold. We use this model to describe the \(A_\infty\)-algebra of k cotangent fibers of the two-dimensional sphere, and show that it is quasi-equivalent to a certain dga. This talk is based on a joint work with Honda, Tian, and Yuan.

Shuo Zhang (MCM); Kifung Chan (CUHK); May Sela (HUJI)
2025-06-13 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/161/
Title: Three 20min research talks (https://master.researchseminars.org/talk/SympZoominar/161/)
by Shuo Zhang (MCM); Kifung Chan (CUHK); May Sela (HUJI) as part of Symplectic zoominar

Abstract
-----

I. Shuo Zhang (MCM)

Title: Composed Dehn twist exact sequence through quilts and \((A_\infty, n)\) modules

Abstract: We prove the quilted Floer cochain complexes form \( (A_\infty, n)\) modules over the Fukaya category \(Fuk(M \times M^-)\). Then we prove that when we restrict the input to mapping cones of product Lagrangians and graphs, the resulting bar-type complex can be identified with bar complex from ordinary Floer theory. As an application we prove two long exact sequences conjectured by Seidel that relates the Lagrangian Floer cohomology of a collection of (possibly intersecting) Lagrangian spheres \({L_i}\) and the fixed point Floer cohomology of composed Dehn twists \(\tau_{L_1} \circ \cdots \tau_{L_n}\) along them.

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II. Kifung Chan (CUHK)

Title: Mirror symmetry of nonabelian group actions

Abstract:
This talk is based on joint work with Naichung Conan Leung. We study the mirror symmetry of nonabelian group actions on symplectic manifolds. We show that the presence of a nonabelian symmetry imposes constraints on non-displaceable Lagrangian branes. This work is motivated by our earlier proposal to understand 3d mirror symmetry via SYZ-type transforms.

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III. May Sela (HUJI)

Title: Mirror symmetry for open Gromov–Witten invariants of Fano manifolds

Abstract: In this talk, I will introduce a class of numerical invariants associated with matrix factorizations, constructed to mirror open Gromov–Witten invariants. Matrix factorizations are algebraic objects expected to correspond, under mirror symmetry, to Lagrangian submanifolds in Fano manifolds. I will describe the non-Archimedean framework required for defining these invariants and present results concerning their structure. This is joint work with J. Solomon.

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Jacopo Stoppa (SISSA, Trieste)
2025-06-20 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/162/
Title: A toric case of the Thomas-Yau conjecture (https://master.researchseminars.org/talk/SympZoominar/162/)
by Jacopo Stoppa (SISSA, Trieste) as part of Symplectic zoominar

Abstract
We consider a class of Lagrangian sections L contained in certain Calabi-Yau Lagrangian fibrations (mirrors of toric weak Fano manifolds). We prove that a form of the Thomas-Yau conjecture holds in this case: L is Hamiltonian isotopic to a special Lagrangian section in this class if and only if a stability condition holds, in the sense of a slope inequality on objects in a set of exact triangles in the Fukaya-Seidel category. This agrees with general proposals by Li. Under more restrictive assumptions, this result can be used to show a precise relation with Bridgeland stability, as predicted by Joyce. Based on arXiv:2505.07228.

Michael Hutchings (Berkeley)
2025-10-17 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/163/
Title: Reeb orbits frequently intersecting a symplectic surface (https://master.researchseminars.org/talk/SympZoominar/163/)
by Michael Hutchings (Berkeley) as part of Symplectic zoominar

Abstract
Consider a symplectic surface in a three-dimensional contact manifold with boundary on Reeb orbits. We assume that the rotation numbers of the boundary Reeb orbits satisfy a certain inequality, and we also make a technical assumption that the Reeb vector field has a particular "nice" form near the boundary of the surface. We then show that there exist Reeb orbits which intersect the interior of the surface, with a lower bound on the frequency of these intersections in terms of the symplectic area of the surface and the contact volume of the three-manifold. No genericity of the contact form is assumed. The proof uses "elementary" spectral invariants of contact three-manifolds. An application of this result gives a very general relation between mean action and the Calabi invariant for area-preserving surface diffeomorphisms.

Filip Broćić (Augsburg)
2025-10-24 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/164/
Title: Arnol’d’s chord conjecture for conormal Legendrian lifts (https://master.researchseminars.org/talk/SympZoominar/164/)
by Filip Broćić (Augsburg) as part of Symplectic zoominar

Abstract
The chord conjecture, due initially to Arnol’d in the case of the standard
contact three-sphere, asserts the existence of a Reeb chord with boundary on every
closed Legendrian submanifold of a closed contact manifold for every contact form.
This conjecture was established in various settings by Cieliebak, Mohnke, Hutchings
and Taubes, and others. In this talk, I will sketch a proof of the chord conjecture for
conormal bundles of closed submanifolds of any closed manifold seen as Legendrians
in the co-sphere bundle. This generalizes a result of Grove in Riemannian geometry
regarding the existence of geodesics normal to the submanifold. The method of
proof involves wrapped Floer cohomology with local coeﬃcients. This talk is based
on joint work with Dylan Cant and Egor Shelukhin.

Shah Faisal (IRMA, Strasbourg)
2025-11-14 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/165/
Title: Extremal Lagrangian tori in toric domains (https://master.researchseminars.org/talk/SympZoominar/165/)
by Shah Faisal (IRMA, Strasbourg) as part of Symplectic zoominar

Abstract
The symplectic area of a Lagrangian submanifold $L$ in a symplectic manifold is defined as the minimal positive symplectic area of a smooth 2-disk with boundary on $L$. A Lagrangian torus is called extremal if it maximizes the symplectic area among all Lagrangian tori. I will explain that every extremal Lagrangian torus in the standard symplectic unit ball is entirely contained in the boundary of the ball. This result confirms a conjecture of Cieliebak and Mohnke in the affirmative. (Ref: arXiv:2504.13076)

Baptiste Serraille (ETH); Spencer Cattalani (Stony Brook); Giovanni Ambrosioni (ETH)
2025-10-31 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/166/
Title: Three 20min research talks (https://master.researchseminars.org/talk/SympZoominar/166/)
by Baptiste Serraille (ETH); Spencer Cattalani (Stony Brook); Giovanni Ambrosioni (ETH) as part of Symplectic zoominar

Abstract
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I. Baptiste Serraille (ETH)

Title: On a linear combination of link spectral invariants on the sphere

Abstract: Link spectral invariants and their homogenizations have been defined by Cristofaro-Gardiner et.al. In joint work with Ibrahim Trifa, we define a linear combination of such quasimorphism and show that it vanishes on the stabilizer of the equator in $S^2$. We will discuss this result and how it relates to the, still open, equator conjecture.

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II. Spencer Cattalani (Stony Brook)

Title: Ahlfors currents and symplectic non-hyperbolicity

Abstract: Rational curves are one of the main tools in symplectic geometry and provide a bridge to algebraic geometry. Complex lines are a more general class of curve that has the potential to connect symplectic and complex analytic geometry. These curves are non-compact, which presents a serious difficulty in understanding their symplectic aspects. In this talk, I will explain how Ahlfors currents can be used to resolve this difficulty and produce a theory parallel to that of rational curves. In particular, Ahlfors currents can be constructed via a continuity method, they control bubbling of holomorphic curves, and they form a convex set.

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III. Giovanni Ambrosioni (ETH)

Title: Approximability for Lagrangian submanifolds

Abstract: In this talk I will introduce a new notion of approximability for metric spaces that can be seen as a categorification of a concept introduced by Turing for metric groups and as a generalization of total-boundedness. I will explain how recent technological advances in symplectic topology and persistence category theory allow us to talk about approximablity of spaces of Lagrangian submanifolds and discuss applications to rigidity and complexity of Lagrangians, as well as potential relations to open problems in Lagrangian topology. This talk is based on joint work with Paul Biran and Octav Cornea.

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John Miller (UdeM); Julio Sampietro Christ (Paris); Salammbo Connolly (Paris)
2025-11-28 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/167/
Title: Three 20min research talks (https://master.researchseminars.org/talk/SympZoominar/167/)
by John Miller (UdeM); Julio Sampietro Christ (Paris); Salammbo Connolly (Paris) as part of Symplectic zoominar

Abstract
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I. TBD

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II. Julio Sampietro Christ (Paris)

Title: Equivariant Lagrangian non-displacements

Abstract: Lagrangian Floer theory is useful to detect non-displaceability of Lagrangian submanifolds via Hamiltonian isotopies. A related question, in the presence of a group action, is whether a certain Lagrangian is equivariantly displaceable, that is by a Hamiltonian isotopy that commutes with a group action. I will address this question in certain settings where the group is $\mathbb{Z}_2$, the key example being $S^1$-invariant Lagrangians in $\mathbb{C}^n$, by developing a $\mathbb{Z}_2$-equivariant Floer cohomology in the spirit of Seidel's construction and computing it using Biran-Khanevsky's Floer-Euler class. This is joint work with Dylan Cant.

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III. Salammbo Connolly (Paris)

Title: Continuation maps for the Morse fundamental group

Abstract: Given a Morse-Smale pair on a manifold \(M\), it is possible to entirely recover its fundamental group in a combinatorial manner. We call this construction the Morse fundamental group. Motivated by a similar construction of a « Floer fundamental group » by Barraud, and by the many uses of continuation maps in symplectic topology, I will explain in this talk how continuation maps give us functoriality and invariance of the Morse fundamental group, and what the differences are with the usual homological setup.

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Nicki Magill (Berkeley)
2025-12-12 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/168/
Title: Generalized convex toric domains and symplectic embedding problems (https://master.researchseminars.org/talk/SympZoominar/168/)
by Nicki Magill (Berkeley) as part of Symplectic zoominar

Abstract
A convex toric domain $X_\Omega$ is a 4-dimensional subset of $\mathbb{R}^4$, defined as the preimage of a bounded convex region $\Omega$ in the positive quadrant of $\mathbb{R}^2$ under the moment map. We consider how geometric features of $\Omega$ such as the curviness of its boundary and its affine perimeter impact symplectic packing problems. Some of our results come from considering the asymptotics of the ECH capacities. These capacities are known to obey a Weyl law and thus detect the volume of $X_\Omega$. We show that their subleading asymptotics detect the affine perimeter of $\Omega$. We’ll discuss how these asymptotic results lead to new applications in symplectic embedding problems. This is based on joint work with Dan Cristofaro-Gardiner and Dusa McDuff.

Oliver Edtmair (ETH)
2026-01-16 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/169/
Title: On the topological invariance of helicity (https://master.researchseminars.org/talk/SympZoominar/169/)
by Oliver Edtmair (ETH) as part of Symplectic zoominar

Abstract
Helicity is an invariant of divergence free vector fields on a three-manifold. One of its fundamental properties is invariance under volume preserving diffeomorphisms. Arnold, having derived an ergodic interpretation of helicity as an asymptotic Hopf invariant, asked whether helicity remains invariant under volume preserving homeomorphisms, and more generally, whether it admits an extension to topological volume preserving flows. In this talk, I will present an affirmative answer to both questions for non-singular flows. The proof draws on recent advances in $C^0$ symplectic geometry, in particular regarding the algebraic structure of the group of area preserving homeomorphisms, which I will also survey. This is based on joint work with Sobhan Seyfaddini.

Pierre-Alexandre Arlove (Strasbourg)
2025-12-19 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/170/
Title: Invariant distances on Legendrian spaces (https://master.researchseminars.org/talk/SympZoominar/170/)
by Pierre-Alexandre Arlove (Strasbourg) as part of Symplectic zoominar

Abstract
I will begin by motivating the study of invariant distances on spaces of Legendrians. I will then discuss two main results:

(a) the construction of a new unbounded invariant distance on the universal cover of many Legendrian isotopy classes ;

(b) the discreteness of any invariant distance on Legendrian isotopy classes.

In particular, we will see that (a) arises from contact rigidity, whereas (b) follows from contact flexibility.

Vincent Humilière (Paris)
2025-11-21 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/171/
Title: Higher dimensional Birkhoff attractors (https://master.researchseminars.org/talk/SympZoominar/171/)
by Vincent Humilière (Paris) as part of Symplectic zoominar

Abstract
The Birkhoff attractor is a closed invariant subset associated with any dissipative twist map of the annulus (of dimension 2), which was introduced by Birkhoff in 1932. We will see that it can be generalized to higher dimensions using tools from symplectic topology, namely the spectral distance and the gamma-support. This is based on joint work with Marie-Claude Arnaud and Claude Viterbo.

Elad Kosloff (HUJI); Joel Schmitz (Neuchâtel)
2026-01-23 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/172/
Title: Two 20min research talks (https://master.researchseminars.org/talk/SympZoominar/172/)
by Elad Kosloff (HUJI); Joel Schmitz (Neuchâtel) as part of Symplectic zoominar

Abstract
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I. Elad Kosloff (HUJI)

Title: Open Gromov-Witten invariants for even-dimensional Lagrangians

Abstract:
I'll introduce the genus zero open Gromov-Witten invariants for even-dimensional Lagrangians. The definition relies on a canonical family of bounding cochains satisfying the point-like condition of Solomon-Tukachinsky, with non-commutative coefficients. In dimension two, these recover Welschinger's invariants. I'll also present computations for even dimensional quadric hypersurfaces, demonstrating that these invariants can be non-vanishing in high dimensions with multiple boundary constraints.

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II. Joel Schmitz (Neuchâtel)

Title: Tropical wave-fronts & nodal tangles

Abstract:
Given a symplectic 4-manifold it may admit multiple toric fibrations. These can be seen as boundary points of the moduli space of almost toric fibrations. We will sketch that all toric fibrations are in the same connected component of this moduli space, as suggested by Symington. For this we use some results from tropical geometry.

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Pranav Chakravarthy (ULB)
2026-01-30 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/173/
Title: Non-squeezing and other rigidity results in LCS geometry (https://master.researchseminars.org/talk/SympZoominar/173/)
by Pranav Chakravarthy (ULB) as part of Symplectic zoominar

Abstract
Locally conformally symplectic (LCS) manifolds are generalisations of symplectic manifolds where the 2-form is not closed but instead satisfies the identity $d\omega= \eta \wedge \omega$ for a closed 1-form $\eta$. The study of these manifolds is equivalent to that of symplectic manifolds when $\eta$ is exact; however, they resemble the behaviour of contact manifolds when $\eta$ has no zeroes. Using the theory of generating functions for Lagrangians in the twisted cotangent bundle, we define spectral selectors for Hamiltonian LCS diffeomorphisms of $S^1 \times \mathbb{R}^{2n} \times S^1$ and $S^1 \times \mathbb{R}^{2n+1}$ and a LCS capacity for domains in $S^1 \times \mathbb{R}^{2n} \times S^1$, thereby giving us a version of the non-squeezing theorem on this manifold. Time permitting, we shall also see how we can define a partial order on the group of compactly supported LCS Hamiltonian diffeomorphisms on $S^1 \times \mathbb{R}^{2n} \times S^1$ and $S^1 \times \mathbb{R}^{2n+1}$ and a bi-invariant metric on the group of compactly supported LCS Hamiltonian diffeomorphisms of $S^1 \times \mathbb{R}^{2n} \times S^1$. This is joint work with Mélanie Bertelson and Margherita Sandon.

Zhijing Wendy Wang (Chicago)
2026-02-13 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/174/
Title: Complexity of Hofer’s geometry in some higher dimensional manifolds (https://master.researchseminars.org/talk/SympZoominar/174/)
by Zhijing Wendy Wang (Chicago) as part of Symplectic zoominar

Abstract
The group of Hamiltonian diffeomorphisms \(Ham(M, ω)\), equipped with the Hofer metric \(d_H\), is a central object in symplectic topology. A landmark result by Polterovich and Shelukhin established the profound geometric complexity of this group for surfaces and their products, showing that high powers are sparse in the metric space. More recently, Álvarez-Gavela et al. demonstrated that the free group embeds quasi-isometrically into Ham of surfaces, revealing its large-scale non-commutativity.

In this talk, I will review these results and present a generalization to some higher-dimensional symplectic manifolds, including surface bundles. We prove robust obstructions that prevent a Hamiltonian diffeomorphism from being a \(k\)-th power (for \(k ≥ 2\)) or from being embedded in a flow. We also show that every asymptotic cone of \((Ham(M, ω), d_H)\) for our higher-dimensional manifolds contains an embedded free group.

Emilia Konrad (Augsburg), Levin Maier (Heidelberg), Ciprian Bonciocat (Stanford)
2026-02-27 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/175/
Title: Three 20min research talks (https://master.researchseminars.org/talk/SympZoominar/175/)
by Emilia Konrad (Augsburg), Levin Maier (Heidelberg), Ciprian Bonciocat (Stanford) as part of Symplectic zoominar

Abstract
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I. Emilia Konrad (Augsburg)

Title: Construction of constrained Floer homology

Abstract:
We consider the symplectic area functional, constrained to loops of vanishing Hamiltonian mean value: It has the same critical points as the Rabinowitz action functional, and can be used to define a similar Floer homology. In contrast to RFH, it admits an intrinsic product structure, but also involves a non-local term in the gradient flow equation.

This talk will delve into the Fredholm and compactness results required to define CFH, and also discuss some remaining „mysteries“.

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II. Levin Maier (Heidelberg)

Title:
From geometric ydrodynamics to periodic geodesics on manifolds of mappings

Abstract:
In this talk, we begin by recalling Arnold’s geometric formulation of hydrodynamics and then extend this framework to a broader class of Hamiltonian systems, incorporating various PDEs arising in mathematical physics. This motivates the study of infinite-dimensional manifolds and, in particular, half Lie groups: topological groups in which right multiplication is smooth while left multiplication is only continuous. Important examples include groups of \(H^{s}\)- or \(C^{k}\)-diffeomorphisms of compact manifolds.

Within this setting, we establish several Hopf–Rinow type theorems for right-invariant magnetic systems and for certain Lagrangian systems on half Lie groups, thereby extending recent results of Bauer–Harms–Michor from the case of geodesic flows to this more general context. Finally, we show that any non-aspherical half Lie group equipped with a strong Riemannian metric necessarily admits a contractible periodic geodesic.

This talk is based partially on joint work with M. Bauer and F. Ruscelli.

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III. Ciprian Bonciocat (Stanford)

Title: Degenerate Lagrangian intersections and parametric Floer homotopy theory

Abstract:
In this talk I will introduce the idea of Floer homotopy theory and show how it can be used to give lower bounds on degenerate Lagrangian intersections, in the case of plumbings of cotangent bundles along a submanifold. The strength of the invariant comes from incorporating all additional choices involved in the construction of the stable homotopy type, resulting in a parameterized spectrum. The work is joint with Kenneth Blakey.

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Ko Honda (UCLA)
2026-03-27 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/176/
Title: Higher-dimensional Heegaard Floer homology and spectral networks (https://master.researchseminars.org/talk/SympZoominar/176/)
by Ko Honda (UCLA) as part of Symplectic zoominar

Abstract
Let $C$ be a closed surface and $\Sigma \subset T^*C$ a real exact Lagrangian surface associated to a spectral curve. In this talk we will first try to explain the context of this work (e.g., Higgs bundles and spectral curves). We then construct a homomorphism from the $\kappa$-strand braid skein algebra of $C$ to the $\kappa$-strand matrix-valued braid skein algebra of $\Sigma$ via higher-dimensional Heegaard Floer homology (HDHF). Finally we explore the adiabatic limit of this homomorphism, which yields a hybrid count of HDHF-type holomorphic curves coupled with certain Morse gradient graphs, called folded Morse trees. This is joint work with Tianyu Yuan and Yin Tian.

Umberto Hryniewicz (RWTH Aachen)
2026-02-20 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/177/
Title: Knot types of periodic Reeb orbits and their role in 4-dimensional symplectic topology (https://master.researchseminars.org/talk/SympZoominar/177/)
by Umberto Hryniewicz (RWTH Aachen) as part of Symplectic zoominar

Abstract
This talk, which is based on two joint works, one with Pedro Salomão and Richard Siefring and another with Michael Hutchings and Vinicius Ramos, revolves around the role that restrictions on the knot types of periodic Reeb orbits imposed by the assumption of dynamical convexity plays in 4-dimensional symplectic topology. For instance, for dynamically convex star-shaped domains in a 4-dimensional symplectic vector space, the minimal action among periodic Reeb orbits in the boundary which are unknotted and have self-linking number -1, called Hopf orbits, satisfies the axioms of a normalized symplectic capacity. This shows that this number is not larger than the cylindrical capacity. A result of Edtmair establishes the other inequality, and these two results combined yield that the minimal action of a Hopf orbit is equal to the cylindrical capacity of such a domain. We will discuss why is this equal to the first ECH capacity, which then explains the latter capacity in simple and purely symplectic geometric terms, with no need of Seiberg-Witten theory. We will also discuss why several transverse knot types in the standard contact 3-sphere cannot be realized as periodic Reeb orbits of a dynamically convex contact form.

Jonghyeon Ahn (IBS-CGP)
2026-03-06 14:15 - 15:45 | https://master.researchseminars.org/talk/SympZoominar/178/
Title: Barcode entropy and relative symplectic cohomology (https://master.researchseminars.org/talk/SympZoominar/178/)
by Jonghyeon Ahn (IBS-CGP) as part of Symplectic zoominar

Abstract
In this talk, I will discuss the barcode entropy—the exponential growth rate of the number of not-too-short bars—of the persistence module associated with the relative symplectic cohomology $SH_M(K)$ of a Liouville domain $K$ embedded in a symplectic manifold $M$. The main result establishes a quantitative link between this Floer-theoretic invariant and the dynamics of the Reeb flow on $\partial K$. More precisely, I will explain that the barcode entropy of the relative symplectic cohomology $SH_M(K)$ is bounded above by a constant multiple of the topological entropy of the Reeb flow on the boundary of the domain, where the constant depends on the embedding of $K$ into $M$.

Emmanuel Opshtein (Strasbourg)
2026-03-20 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/179/
Title: Legendrian barriers (https://master.researchseminars.org/talk/SympZoominar/179/)
by Emmanuel Opshtein (Strasbourg) as part of Symplectic zoominar

Abstract
In a previous work with Felix Schlenk, we showed that an analogue of the phenomenon of Lagrangian barriers holds in the contact framework in \(S^3\) : there exist (explicit) Legendrian complexes of arcs in \(S^3\) that have short Reeb chords to many Legendrian loops.

The aim of this talk is to explain that this phenomenon holds more generally in any prequantization bundle (of arbitrary dimension).

Marcelo Alves (Augsburg)
2026-04-17 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/180/
Title: Polytopes and \(C^0\)-Riemannian metrics with positive topological entropy (https://master.researchseminars.org/talk/SympZoominar/180/)
by Marcelo Alves (Augsburg) as part of Symplectic zoominar

Abstract
The topological entropy of geodesic flows has been extensively studied since the foundational works of Dinaburg and Manning. It measures the exponential complexity of the geodesic flow of a Riemannian manifold, and there are several results connecting it to the geometry and topology of a Riemannian manifold. In this talk I will explain how recent results obtained jointly with Dahinden, Meiwes, and Pirnapasov can be used to give a meaningful extension of the topological entropy to \(C^0\)-Riemannian metrics; i.e. Riemannian metrics which are continuous but not necessarily differentiable. Similarly, using contact geometry I will explain how we can talk in a meaningful way about the topological entropy of convex and starshaped polytopes in \(\mathbb{R}^4\), thinking of them as \(C^0\)-contact forms. This is joint work with Matthias Meiwes.

Eric Kilgore (USC)
2026-04-10 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/181/
Title: Equivariant contact Floer cohomology for quotient spaces (https://master.researchseminars.org/talk/SympZoominar/181/)
by Eric Kilgore (USC) as part of Symplectic zoominar

Abstract
I will discuss some recent work establishing the orderability of contact manifolds which arise as a quotient of an aspherically fillable manifold by a finite group action which extends (non-freely) to the filling. This generalizes the well known case of lens spaces. The main tool is a geometrically equivariant version of contact Floer cohomology parametrized by a higher categorical refinement of the Eliashberg—Polterovich relation on the contact isotopy group, which is locally constant away from the discriminant. This is joint work with Dylan Cant and Jun Zhang.

Stéphane Guillermou (Nantes)
2026-04-24 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/182/
Title: Density of fibers for the filtered Fukaya category of a cotangent bundle (https://master.researchseminars.org/talk/SympZoominar/182/)
by Stéphane Guillermou (Nantes) as part of Symplectic zoominar

Abstract
A well-known result of Abouzaid says that the wrapped Fukaya category of
a cotangent bundle is generated by one cotangent fiber. In the filtered
case this is not true, but the filtered Fukaya category comes with a
notion of interleaving distance. We will see that the iterated cones on
the cotangent fibers generate a dense subcategory. The proof makes use
of an embedding of the Fukaya category in the category of sheaves. This
answers a question of Biran, who gave another proof with Ambrosioni and
Cornea.

This is a joint work with Claude Viterbo and Bingyu Zhang.

Pedro Salomão (Shenzhen ICM)
2026-05-08 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/183/
Title: ECH constraints and twist dynamics in the spatial isosceles three-body problem (https://master.researchseminars.org/talk/SympZoominar/183/)
by Pedro Salomão (Shenzhen ICM) as part of Symplectic zoominar

Abstract
In this talk, I will describe the global dynamics of the spatial isosceles three-body problem, using ideas from Embedded Contact Homology. For energies below the critical level, the flow admits a disk-like global surface of section bounded by the Euler orbit. I will explain how estimates for the contact volume of the energy surface and for the rotation number of the Euler orbit, together with a refinement of Hutchings’ mean action theorem, force the existence of infinitely many periodic orbits and constrain their relative winding via a non-trivial twist interval. For energies above the critical level, for which the energy surface is unbounded, I will briefly discuss how the twist near infinity leads to the existence of infinitely many periodic and parabolic trajectories. This is joint work with Xijun Hu, Lei Liu, Yuwei Ou, and Zhiwen Qiao.

Daniel Álvarez-Gavela
2026-05-01 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/184/
Title: Legendrian and Lagrangian higher torsion (https://master.researchseminars.org/talk/SympZoominar/184/)
by Daniel Álvarez-Gavela as part of Symplectic zoominar

Abstract
The theory of higher Reidemeister torsion yields characteristic classes of (stable) fiber bundles of smooth manifolds. We use this theory to define a new family of invariants for Legendrians in 1-jet spaces which we collectively call Legendrian higher torsion. Any version of Legendrian higher torsion yields a Legendrian isotopy invariant consisting of a collection of real cohomology classes of the base manifold. For the class of tube bundles in the sense of Waldhausen we call the invariant tube torsion and we show that it consists of a union of cosets of a suitably normalized version of the Pontryagin character. For a nearby Lagrangian (with stably trivial Gauss map) we moreover show that there is a distinguished coset which is a Hamiltonian isotopy invariant and which we call nearby Lagrangian torsion. We do not know whether nearby Lagrangians must have trivial higher torsion, as would follow from the nearby Lagrangian conjecture. Although we work with generating functions, the story has a Floer-theoretic counterpart and I will state some concrete conjectures about the expected behavior of this theory. Joint work with K. Igusa and M. Sullivan.

Jun Zhang (USTC-IGP)
2026-05-15 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/185/
Title: Geometry and dynamics of domains in the cotangent bundles of tori (https://master.researchseminars.org/talk/SympZoominar/185/)
by Jun Zhang (USTC-IGP) as part of Symplectic zoominar

Abstract
In Euclidean spaces, star-shaped domains (also known as Liouville domains) are fundamental objects in modern symplectic geometry. Several important subclasses have been introduced and studied, including dynamically convex domains, geometrically convex domains, and toric domains. These classes are not only interesting in their own right but also exhibit deep interrelations. In this talk, we extend this discussion to (fiberwise) star-shaped domains in the cotangent bundles of tori. In particular, we introduce analogous subclasses in this new setting and explore classical topics such as large-scale geometric properties and embedding problems. This talk is based on joint work with Antong Zhu.

Yoel Groman (HUJI)
2026-06-12 13:15 - 14:45 | https://master.researchseminars.org/talk/SympZoominar/186/
by Yoel Groman (HUJI) as part of Symplectic zoominar

Abstract: TBA
