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BEGIN:VEVENT
SUMMARY:Shahn Majid (Queen Mary University)
DTSTART:20221010T140000Z
DTEND:20221010T150000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/1
DESCRIPTION:Title: Quantum Riemannian Geometry of the A_n graph\nby Shahn Majid (Que
en Mary University) as part of European Quantum Algebra Lectures (EQuAL)\n
\n\nAbstract\nWe solve for quantum Riemannian geometries on the finite lat
tice interval • − • − · · · − • with $n$ nodes (the Dynkin
graph of type $A_n$) and find that they are necessarily $q$-deformed with
$q$ a root of unity. This comes out of the intrinsic geometry and not by a
ssuming any quantum group in the picture. Specifically\, we discover a nov
el ‘boundary effect’ whereby\, in order to admit a quantum-Levi Civita
connection\, the ‘metric weight’ at any edge is forced to be greater
pointing towards the bulk compared to towards the boundary\, with ratio gi
ven by $(i + 1_)q/(i)_q$ at node $i$\, where $(i)_q$ is a $q$-integer. The
Christoffel symbols are also $q$-deformed. The limit $q \\to 1$ is the qu
antum Riemannian geometry of the natural numbers $N$ with rational metric
multiples $(i + 1)/i$ in the direction of increasing $i$. In both cases th
ere is a unique metric up to normalisation with zero Ricci scalar curvatur
e. Elements of QFT and quantum gravity are exhibited for $n = 3$ and for t
he continuum limit of the geometry of $N$. The Laplacian for the scaler-fl
at metric becomes the Airy equation operator $(1/ x) d^2/ dx^2$ in so far
as a limit exists. The talk is based on joint work with J. Argota-Quiroz a
vailable on arXiv: 2204.12212 (math.QA).\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorant Szegedy (University of Vienna)
DTSTART:20221024T140000Z
DTEND:20221024T150000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/2
DESCRIPTION:Title: Parity and Spin conformal field theory with boundaries and defects\nby Lorant Szegedy (University of Vienna) as part of European Quantum Al
gebra Lectures (EQuAL)\n\n\nAbstract\nRational conformal field theory (CFT
) on oriented surfaces is well understood in terms of 3-dimensional topolo
gical field theory (TFT). We extend these notions to surfaces with spin st
ructures using defects in oriented CFT and a modified TFT taking values in
super vector spaces.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catherine Meusburger (University of Erlangen-Nuremberg)
DTSTART:20221107T150000Z
DTEND:20221107T160000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/3
DESCRIPTION:Title: Turaev-Viro-Barrett-Westbury invariants with defects\nby Catherin
e Meusburger (University of Erlangen-Nuremberg) as part of European Quantu
m Algebra Lectures (EQuAL)\n\n\nAbstract\nTuraev-Viro-Barrett-Westbury sta
te sum models are concrete constructions\nof TQFTs based on triangulated 3
-manifolds and spherical fusion\ncategories. Introducing defects in these
models is of interest for\ndefect TQFTs and for applications in condensed
matter physics.\n\nIn the talk we explain how to construct Turaev-Viro-Bar
rett-Westbury\nstate sums with defects in terms of generalised 6j symbols.
Defect\nsurfaces are labeled with bimodule categories over spherical fusi
on\ncategories\, defect lines and points form graphs on these surfaces and
\nare labeled with bimodule functors and bimodule natural transformations.
\nWe show that the resulting state sums are triangulation independent\,\nc
ompute examples and interpret them.\n\nBased on https://arxiv.org/abs/2205
.06874\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukas Woike (University of Burgundy)
DTSTART:20221121T150000Z
DTEND:20221121T160000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/4
DESCRIPTION:Title: Quantum representations of mapping class groups and factorization hom
ology\nby Lukas Woike (University of Burgundy) as part of European Qua
ntum Algebra Lectures (EQuAL)\n\n\nAbstract\nQuantum representations of ma
pping class groups are finite-dimensional representations of mapping class
groups that have their origin in quantum algebra (e.g. the representation
theory of Hopf algebras) and that often has strong ties to three-dimensio
nal topological field theory. After explaining the interest in these repre
sentations from the perspectives of algebra\, topology and mathematical ph
ysics and how they can be formally described through modular functors\, I
will give an idea of the classical construction procedures. I will then pr
esent a new and more general construction procedure using cyclic and modul
ar operads\, as well as factorization homology. The main result of this ap
proach is a classification of modular functors. This is based on different
joint works with Lukas Müller and Adrien Brochier.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukas Müller (Max Planck Institute for Mathematics\, Bonn)
DTSTART:20221205T150000Z
DTEND:20221205T160000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/5
DESCRIPTION:Title: Reflection Structures and Spin Statistics in Low Dimensions\nby L
ukas Müller (Max Planck Institute for Mathematics\, Bonn) as part of Euro
pean Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nIn physics the spin o
f a particle determines its statistics.\n\nFurthermore\, physical systems
(in Euclidean signature) usually have a reflection structure\, i.e. an ide
ntification of orientation reversal with complex conjugation. Neither of t
hese two structures is part of Atiyah's original definition of topological
quantum field theories.\n\nThey can be formulated in the setting of funct
orial field theories as equivariant symmetric monoidal functors from a bor
dism category to an appropriate target. Based on the cobordism hypothesis
I will present a complete classification of such functors in dimension one
and two. The answers can be formulated in terms of algebraic objects asso
ciated to an internal fermionic symmetry (2-)group. The talk is based on j
oint work in progress with Luuk Stehouwer.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vanessa Miemietz (University of East Anglia)
DTSTART:20221219T150000Z
DTEND:20221219T160000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/6
DESCRIPTION:Title: Symmetric bimodules and Hopf algebras\nby Vanessa Miemietz (Unive
rsity of East Anglia) as part of European Quantum Algebra Lectures (EQuAL)
\n\n\nAbstract\nI will explain the basics of finitary 2-representation the
ory and explain a reduction theorem that motivates the study of certain ty
pes of 2-categories. I will then explain two examples of such\, associated
to Hopf algebras and symmetric bimodules\, and explain the connection bet
ween the two.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angela Tabiri (African Institute for Mathematical Sciences\, Ghana
)
DTSTART:20230213T150000Z
DTEND:20230213T160000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/7
DESCRIPTION:Title: Plane Curves which are Quantum Homogeneous Spaces\nby Angela Tabi
ri (African Institute for Mathematical Sciences\, Ghana) as part of Europe
an Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nPlane Curves which are
Quantum Homogeneous Spaces Abstract: In this talk\, we will discuss the co
nstruction of examples of quantum homogeneous spaces using the equation of
a plane curve. The Hopf algebras we construct are isomorphic to the quant
um plane and down-up algebras when the degree of the equation is two or th
ree respectively. Interesting properties and open problems about these Hop
f algebras will be discussed\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Kontrec (RIMS\, Kyoto University)
DTSTART:20230227T150000Z
DTEND:20230227T160000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/8
DESCRIPTION:Title: Representation theory and duality properties of some affine W-algebra
s\nby Ana Kontrec (RIMS\, Kyoto University) as part of European Quantu
m Algebra Lectures (EQuAL)\n\n\nAbstract\nOne of the most important famili
es of vertex algebras are affine vertex algebras and their associated $\\m
athcal{W}$-algebras\, which are connected to various aspects of geometry a
nd physics. Among the simplest examples of $\\mathcal{W}$-algebras is the
Bershadsky-Polyakov vertex algebra $\\mathcal{W}^k(\\mathfrak{g}\, f_{min}
)$\, associated to $\\mathfrak{g} = sl(3)$ and the minimal nilpotent elem
ent $f_{min}$.\nIn this talk we are particularly interested in the Bershad
sky-Polyakov algebra $\\mathcal W_k$ at positive integer levels\, for whi
ch we obtain a complete classification of irreducible modules.\nIn the cas
e $k=1$\, we show that this vertex algebra has a Kazama-Suzuki-type dual
isomorphic to the simple affine vertex superalgebra $L_{k'} (osp(1 \\vert
2))$ for $k'=-5/4$. This is joint work with D. Adamovic.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco De Renzi (University of Zurich)
DTSTART:20230313T150000Z
DTEND:20230313T160000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/9
DESCRIPTION:Title: Algebraic presentation of cobordisms and quantum invariants in dimens
ions 3 and 4\nby Marco De Renzi (University of Zurich) as part of Euro
pean Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nThe category 2Cob of
2-dimensional cobordisms is freely generated by a commutative Frobenius al
gebra: the circle. This yields a complete classification of 2-dimensional
TQFTs (Topological Quantum Field Theories). In this talk\, I will discuss
some consequences of analogous algebraic presentations in dimensions 3 and
4\, due to Bobtcheva and Piergallini. In both cases\, the fundamental alg
ebraic structures are provided by certain Hopf algebras called BPH algebra
s. In dimension 3\, I will consider the category 3Cob of connected cobordi
sms between connected surfaces with connected boundary. I will explain tha
t an algebraic presentation conjectured (or rather announced without proof
) by Habiro is in fact equivalent to the one established by Bobtcheva and
Piergallini. In dimension 4\, I will focus on a category denoted 4HB\, who
se morphisms are 2-deformation classes of 4-dimensional 2-handlebodies. I
will show that any unimodular ribbon category contains a BPH algebra\, whi
ch can be characterized very explicitly. This result proves the existence
of a very large family of TQFT functors on 4HB. Finally\, I will explain t
hat a unimodular ribbon category has the potential to detect exotic phenom
ena in dimension 4 only if it is neither semisimple nor factorizable. This
is a joint work with A. Beliakova\, I. Bobtcheva\, and R. Piergallini.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bojana Femic (Serbian Academy of Sciences and Arts)
DTSTART:20230327T140000Z
DTEND:20230327T150000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/10
DESCRIPTION:Title: Categorical centers and Yetter Drinfel`d-modules as 2-categorical (
bi)lax structures\nby Bojana Femic (Serbian Academy of Sciences and Ar
ts) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nJo
int work with Sebastian Halbig\n\nCenter categories of monoidal categories
${\\mathcal C}$ and of bimodule categories ${\\mathcal M}$ are very well
known and studied in the literature. \nWe consider the (weak) center categ
ory ${\\mathcal Z}(F\,{\\mathcal M}\,G)$ of a ${\\mathcal C}\\text{-} {\\m
athcal D}$-bimodule category ${\\mathcal M}$ twisted by two lax monoidal
functors \n$F:{\\mathcal E}\\to {\\mathcal D}$ and $G:{\\mathcal E}\\to {\
\mathcal C}$\, for another monoidal category ${\\mathcal E}$. (The weakn
ess corresponds to dealing with half-braidings\, while with strongness we
allude to (invertible) braidings.)\n\nWe show how the 2-categorical viewpo
int provides a deeper insight on such center categories. Namely\, for fix
ed bicategories ${\\mathcal B}$ and ${\\mathcal B}'$ there are bicategorie
s $\\operatorname{Lax}_{lx}({\\mathcal B}\,{\\mathcal B}')$ and $\\operato
rname{Lax}_{clx}({\\mathcal B}\,{\\mathcal B}')$ of lax functors ${\\mathc
al B} \\to {\\mathcal B}'$\, lax (resp. colax) transformations and their m
odifications. We reveal how in a specific case of ${\\mathcal B}$ and ${\
\mathcal B}'$ we can identify the hom-categories of these two bicategories
with the weak left (resp. right) twisted centers\, so that the horizontal
composition in the bicategories corresponds to the composition of weak t
wisted center categories between themselves. In this way we obtain a bicat
egory of weak left (resp. right) centers categories. We show how a full su
b-bicategory of both of them recovers the bicategory $TF({\\mathcal C}\,{\
\mathcal D})$ from [Shim\, Section 3]. Moreover\, we prove a more general
result in bicategories by which the rigidity of $TF({\\mathcal C}\,{\\ma
thcal D})$ is recovered. \n\nOn the other hand\, we introduce a 2-categor
y ${\\rm Bilax}({\\mathcal K}\,{\\mathcal K}')$ of bilax functors (among
2-categories ${\\mathcal K}$ and ${\\mathcal K}'$)\, bilax natural transfo
rmations and bilax modifications. Its 0-cells are a 2-categorification of
bilax functors of [Agui] and of bimonoidal functors of [CS]. We show how
bilax functors generalize the notions of bialgebras in braided monoidal ca
tegories\, $bimonads$ in 2-categories (with respect to Yang-Baxter opera
tors\, YBO's)\, and preserve bimonads (w.r.t. YBO's)\, $module$ $comonads$
and $comodule$ $monads$\, and $relative$ $bimonad$ $modules$. Moreover\,
the component functors of a bilax functor on hom-categories factor through
the category of $Hopf$ $bimodules$ (w.r.t. YBO's). (The 2-categorical not
ions in italic letters are introduced in our work.) \n\nWe finally show
that there is a 2-category equivalence ${\\rm Bilax} (1\, \\Sigma{\\mathca
l C})\\simeq{\\mathcal YD}(\\Sigma{\\mathcal C})$ and a faithful 2-functor
${\\rm Bilax}(1\,{\\mathcal K})\\hookrightarrow\\operatorname{Dist}({\\m
athcal K})$. Here ${\\mathcal YD}(\\Sigma{\\mathcal C})$ is a 2-category
of Yetter-Drinfel`d modules in a braided monoidal category ${\\mathcal C}
$ and $\\operatorname{Dist}({\\mathcal K})$ is the 2-category of mixed dis
tributive laws of [PW].\n\n\n[Agui] M. Aguiar\, S. Mahajan\, Monoidal func
tors\, species and Hopf algebras\, CRM Monograph Series 29 Amer. Math. Soc
. (2010).\n\n[CS] M. B. McCurdy\, R. Street\, What Separable Frobenius Mon
oidal Functors Preserve\,\nCahiers de Topologie et Geometrie Differentiell
e Categoriques 51/1 (2010).\n\n[Shim] K. Shimizu: Ribbon structures of the
Drinfel`d center\, arXiv:1707.09691 (2017a)\n\n[PW] J. Power\, H. Watanab
e\, Combining a monad and a comonad\, Theoretical Computer Science 280 (20
02)\, 137--262.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leandro Vendramin (Vrije Universiteit Brussel)
DTSTART:20230424T140000Z
DTEND:20230424T150000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/11
DESCRIPTION:Title: Nichols algebras\nby Leandro Vendramin (Vrije Universiteit Bruss
el) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nNi
chols algebras appear in several branches of mathematics\, going from Hopf
algebras and quantum groups\, to Schubert calculus and conformal field th
eories. In this talk\, we review the main problems related to Nichols alge
bras and I discuss some classification theorems and some applications.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Saracco (Université Libre de Bruxelles)
DTSTART:20230522T140000Z
DTEND:20230522T150000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/12
DESCRIPTION:Title: Closed categories\, modules and (one-sided) Hopf algebras\nby Pa
olo Saracco (Université Libre de Bruxelles) as part of European Quantum A
lgebra Lectures (EQuAL)\n\n\nAbstract\nA well-known characterization of Ho
pf algebras\, that I always found fascinating and elegant\, states that an
algebra A over a field k is a Hopf algebra if and only if its category of
modules is a closed monoidal category in such a way that the forgetful fu
nctor to vector spaces preserves the closed monoidal structure. We usually
split this result into two steps: the lifting of the monoidal structure c
orresponds to the bialgebra structure\, and then the further lifting of th
e closed structure as adjoint to the monoidal one corresponds to the exist
ence of an antipode. However\, closed structures can be defined independen
tly of monoidal ones and have their own dignity and importance. Which new
structure on our algebra A would correspond to lifting the closed structur
e of vector spaces alone? How would this relate with the familiar bialgebr
a and Hopf algebra structures coming from lifting the monoidal and closed
monoidal ones? It turns out that lifting the closed structure corresponds
to the existence of algebra maps 𝛿 : A -> A⊗A^op and ε : A -> k sati
sfying appropriate conditions. Moreover\, a quite unexpected source of exa
mples is provided by certain one-sided Hopf algebras\, i.e. bialgebras wit
h a morphism which is just a one-sided convolution inverse of the identity
. In this seminar\, based on an ongoing collaboration with Johannes Berger
and Joost Vercruysse which is continuing discussions with Gabriella Böhm
\, I will present our progresses in the study of these new algebraic struc
tures.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomoyuki Arakawa (RIMS\, Kyoto University)
DTSTART:20231005T090000Z
DTEND:20231005T100000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/13
DESCRIPTION:Title: Hilbert Schemes of the points in the plane and quasi-lisse vertex su
peralgebras\nby Tomoyuki Arakawa (RIMS\, Kyoto University) as part of
European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nFor each complex
reflection group $\\Gamma$ one can attach a canonical symplectic singulari
ty $\\mathcal{M}_{\\Gamma}$. Motivated by the 4D/2D duality discovered by
Beem et at.\, Bonetti\, Menegheli and Rastelli conjectured the existence
of a supersymmetric vertex operator algebra $\\mathbf{W}_{\\Gamma}$ whose
associated variety is isomorphic to $\\mathcal{M}_{\\Gamma}$. We prove th
is conjecture when the complex reflection group $\\Gamma$ is the symmetric
group $S_N$\, by constructing a sheaf of $\\hbar$-adic vertex algebras on
the Hilbert schemes of $N$-points in the plane. In physical terms\, the
vertex operator algebra $\\mathbf{W}_{S_N}$ corresponds\, by the 4D/2D
duality\, to the $4$-dimensional $\\mathcal{N}=4$ super Yang-Mills theory
with gauge group $SL_N$.\nThis is a joint work with Toshiro Kuwabara and S
ven Moller.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joost Vercruysse (Université Libre de Bruxelles)
DTSTART:20231019T090000Z
DTEND:20231019T100000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/14
DESCRIPTION:Title: Generalizations of Yetter-Drinfel'd modules and the center construct
ion of monoidal categories\nby Joost Vercruysse (Université Libre de
Bruxelles) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstr
act\nThis is joint work with Ryan Aziz. A Yetter-Drinfel'd module over a b
ialgebra $H$\, is at the same time a module and a comodule over $H$ satisf
ying a particular compatibility condition. It is well-known that the categ
ory of Yetter-Drinfel'd modules (say\, over a finite dimensional Hopf alge
bra $H$) is equivalent to the center of the monoidal category of $H$-(co)m
odules as well as to the category of modules over the Drinfel'd double of
$H$. Caenepeel\, Militaru and Zhu introduced a generalized version of Yett
er-Drinfeld modules. More precisely\, they consider two bialgebras $H$\, $
K$\, together with an bimodule coalgebra $C$ and a bicomodule algebra $A$
over them. A generalized Yetter-Drinfel'd module in their sense\, is an $A
$-module that is at the same time a $C$-comodule satisfying a certain comp
atibility condition. Under finiteness conditions\, they showed that these
modules are exactly modules of a suitably constructed smash product build
out of $A$ and $C$. The aim of this talk is to show how the category of th
ese generalized Yetter-Drinfel'd can be obtained as a relative center of t
he category of $A$-modules\, viewed as a bi-actegory over the categories o
f $H$-modules and $K$-modules. Moreover\, we also show how other variation
s of Yetter-Drinfel'd modules\, such as anti-Yetter-Drinfel'd modules\, ar
ise as a particular case and we discuss the bicategorical structure that a
rises this way.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Norton (University of Kent)
DTSTART:20231214T100000Z
DTEND:20231214T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/15
DESCRIPTION:Title: Decomposition numbers for unipotent blocks with small sl_2-weight in
finite classical groups\nby Emily Norton (University of Kent) as part
of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nThere are man
y familiar module categories admitting a categorical action of a Lie algeb
ra. The combinatorial shadow of such an action often yields answers to mod
ule-theoretic questions\, for instance via crystals. In proving a conjectu
re of Gerber\, Hiss\, and Jacon\, it was shown by Dudas\, Varagnolo\, and
Vasserot that the category of unipotent representations of a finite classi
cal group has such a categorical action. In this talk I will explain how w
e can use the categorical action to deduce closed formulas for certain fam
ilies of decomposition numbers of these groups. This is joint work with Ol
ivier Dudas.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Dyckerhoff (University of Hamburg)
DTSTART:20231102T100000Z
DTEND:20231102T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/16
DESCRIPTION:Title: Complexes of stable $\\infty$-categories\nby Tobias Dyckerhoff (
University of Hamburg) as part of European Quantum Algebra Lectures (EQuAL
)\n\n\nAbstract\nDerived categories have come to play a decisive role in a
wide range of topics. Several recent developments\, in particular in the
context of topological Fukaya categories\, arouse the desire to study not
just single categories\, but rather complexes of categories. In this talk\
, we will discuss examples of such complexes in algebra\, topology\, algeb
raic geometry\, and symplectic geometry\, along with some results and conj
ectures involving them. Based on joint work with Merlin Christ and Tashi W
alde.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frank Taipe (Université Paris-Saclay)
DTSTART:20231116T100000Z
DTEND:20231116T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/17
DESCRIPTION:Title: Quantum Transformation Groupoids\nby Frank Taipe (Université Pa
ris-Saclay) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbst
ract\nWe define quantum transformation groupoids\, a class of multiplier H
opf algebroids generalizing transformation groupoids and algebraic quantum
groups. An interesting characteristic of this algebraic class is that it
admits a Pontryagin-like duality. In the first part of the talk\, we will
discuss how the study of quantum transformation groupoids appears in a Gal
ois-type theory of inclusions of von Neumann algebras. Then in the second
part\, we will give the construction of a quantum transformation groupoid
from a braided commutative measured Yetter-Drinfeld *-algebra on an algebr
aic quantum group in the sense of A. Van Daele.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Azat Gainutdinov (Université de Tours\, CNRS)
DTSTART:20231130T100000Z
DTEND:20231130T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/18
DESCRIPTION:Title: Non-semisimple link and manifold invariants for symplectic fermions<
/a>\nby Azat Gainutdinov (Université de Tours\, CNRS) as part of European
Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nI will talk about link an
d three-manifold invariants defined in terms of a non-semisimple finite ri
bbon category C together with a choice of tensor ideal and modified trace.
If the ideal is all of C\, these invariants agree with those defined by L
yubashenko in the 90’s\, and as we show\, they only depend on the Grothe
ndieck class of the objects labelling the link. These invariants are there
fore not able to determine non-split extensions. However\, we observed an
interesting phenomenon: if one chooses an intermediate proper ideal betwee
n C and the minimal ideal of projective objects\, the invariants do distin
guish non-trivial extensions. This is demonstrated in the case of C being
the ribbon category of N pairs of symplectic fermions. This is a joint wor
k with J. Berger and I. Runkel.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Bazlov (University of Manchester)
DTSTART:20240118T100000Z
DTEND:20240118T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/19
DESCRIPTION:Title: Cocycle and Galois cocycle twists of algebras\, representations and
orders\nby Yuri Bazlov (University of Manchester) as part of European
Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nIn a construction known as
Drinfeld twist\, a 2-cocycle on a Hopf algebra H is used to modify the co
product on H as well as the associative product in any H-module algebra A.
I am interested to know to what extent the representation theory of the t
wist of A can be recovered from that of A\; the A#H-module category\, unch
anged under the twist\, plays a role here. I will talk about an applicatio
n of this idea to rational Cherednik-type algebras\, which led\, in a join
t work with E. Jones-Healey\, to establishing nontrivial isomorphisms betw
een braided and classical versions of these algebras. Twists also help to
approach representation theory of the so-called mystic reflection groups\,
defined by the Chevalley-Serre-Shephard-Todd property of their action on
a quantum polynomial ring. An important source of twists\, motivated by to
rsors in geometry\, should be cocycles arising from (Hopf-)Galois extensio
ns of algebras\, and I will discuss this in the context of constructing or
ders and normal integral bases in central simple algebras over a number fi
eld.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fiona Torzewska (University of Bristol)
DTSTART:20240201T100000Z
DTEND:20240201T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/20
DESCRIPTION:Title: Topological quantum field theories and homotopy cobordisms\nby F
iona Torzewska (University of Bristol) as part of European Quantum Algebra
Lectures (EQuAL)\n\n\nAbstract\nI will begin by explaining the constructi
on of a category CofCos\, whose objects are topological spaces and whose m
orphisms are cofibrant cospans. Here the identity cospan is chosen to be o
f the form $X\\to X\\times [0\,1]\\rightarrow X$\, in contrast with the us
ual identity in the bicategory $Cosp(V)$ of cospans over a category $V$. T
he category $CofCos$ has a subcategory $HomCob$ in which all spaces are ho
motopically 1-finitely generated. There exist functors into HomCob from a
number of categorical constructions which are potentially of use for model
ling particle trajectories in topological phases of matter: embedded cobor
dism categories and motion groupoids for example. Thus\, functors from Hom
Cob into Vect give representations of the aforementioned categories.\n\nI
will also construct a family of functors $Z_G\\colon HomCob\\to Vect$\, on
e for each finite group $G$\, and show that topological quantum field theo
ries previously constructed by Yetter\, and an untwisted version of Dijkgr
aaf-Witten\, generalise to functors from HomCob. I will construct this fun
ctor in such a way that it is clear the images are finite dimensional vect
or spaces\, and the functor is explicitly calculable. I will also give exa
mple calculations throughout.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Bridgeman (Ghent University)
DTSTART:20240215T100000Z
DTEND:20240215T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/21
DESCRIPTION:Title: Invertible Bimodule Categories and Generalized Schur Orthogonality\nby Jacob Bridgeman (Ghent University) as part of European Quantum Alge
bra Lectures (EQuAL)\n\n\nAbstract\nThe Schur orthogonality relations are
a cornerstone in the representation theory of groups. We utilize a general
ization to weak Hopf algebras to provide a new\, readily verifiable condit
ion on the skeletal data for deciding whether a given bimodule category is
invertible and therefore defines a Morita equivalence. Ultimately\, the c
ondition arises from Schur orthogonality relations on the characters of th
e annular algebra associated to a module category. As a first application\
, we provide an algorithm for the construction of the full skeletal data o
f the invertible bimodule category associated to a given module category\,
which is obtained in a unitary gauge when the underlying categories are u
nitary. As a second application\, we show that our condition for invertibi
lity is equivalent to the notion of MPO-injectivity\, thereby closing an o
pen question concerning tensor network representations of string-net model
s exhibiting topological order. Work with Laurens Lootens and Frank Verstr
aete. Based on arXiv: 2211.01947\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martina Balagovic (University of Newcastle)
DTSTART:20240229T100000Z
DTEND:20240229T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/22
DESCRIPTION:Title: Braided Module Categories\nby Martina Balagovic (University of N
ewcastle) as part of European Quantum Algebra Lectures (EQuAL)\n\nAbstract
: TBA\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Dimofte (University of Edinburgh)
DTSTART:20240314T100000Z
DTEND:20240314T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/23
DESCRIPTION:Title: Finding quantum groups in QFT\nby Tudor Dimofte (University of E
dinburgh) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstra
ct\nI will explain a construction leading to the structure of a braided mo
dule category over the braided category of finite dimensional representati
ons of a quantum group\, and discuss what we can hope to say about such a
category. Joint work with Stefan Kolb.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexis Langlois-Rémillard (Hausdorff Center for Mathematics\, Uni
versität Bonn)
DTSTART:20240509T090000Z
DTEND:20240509T100000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/24
DESCRIPTION:Title: Quotients of the affine Temperley-Lieb algebras with a view towards
generalised Deligne interpolation categories\nby Alexis Langlois-Rémi
llard (Hausdorff Center for Mathematics\, Universität Bonn) as part of Eu
ropean Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nThe affine (and per
iodic) Temperley-Lieb algebras appeared in the study of conformal field th
eories as useful tools to study the continuum scaling limits of critical s
tatistical models. The fusion of their modules is believed to be connected
to the fusion of bulk fields in CFT. However\, the connection is not obvi
ous. In part to seek the ideal structure to investigate the scaling limit\
, we study certain quotients of the affine Temperley-Lieb algebras\, which
we name uncoiled algebras\, and we study their Jones-Wenzl idempotents. I
n this talk\, we will present the uncoiled algebras\, the construction of
their Jones-Wenzl idempotents and investigate the traces of these\, relati
ng it to the extremal weight projectors of Queffelec and Wedrich. Time per
mitting\, we will investigate a generalisation of these structures related
to Deligne interpolation categories. \n\nThis is based on joint work with
Alexi Morin-Duchesne\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Léo Schelstraete (Université catholique de Louvain)
DTSTART:20240523T090000Z
DTEND:20240523T100000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/25
DESCRIPTION:Title: Odd Khovanov homology and higher representation theory\nby Léo
Schelstraete (Université catholique de Louvain) as part of European Quant
um Algebra Lectures (EQuAL)\n\n\nAbstract\nKhovanov homology is a homologi
cal invariant of links categorifying the Jones polynomial. It is by now we
ll-understood through the lens of higher representation theory\, categorif
ying the relationship between the Jones polynomial and the representation
theory of Uq(sl2). Surprisingly\, there exists another categorification of
the Jones polynomial\, called odd Khovanov homology. Subsequently\, highe
r odd (or “super”) analogues were discovered in representation theoret
ic and geometric contexts. In this talk\, I will begin with a gentle intro
duction to the above\, and then explain how odd Khovanov homology can be u
nderstood as stemming from a supercategorification of the representation t
heory of Uq(gl2). This is joint work with Pedro Vaz.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agustina Czenky (University of Oregon)
DTSTART:20240606T080000Z
DTEND:20240606T090000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/26
DESCRIPTION:Title: Unoriented 2-dimensional TQFTs and the category Rep(S_t \\wr Z_2)\nby Agustina Czenky (University of Oregon) as part of European Quantum A
lgebra Lectures (EQuAL)\n\n\nAbstract\nLet k be an algebraically closed fi
eld of characteristic zero. The category of oriented 2-dimensional cobordi
sms can be understood in purely algebraic terms via a description by gener
ators and relations\; moreover\, it is possible to recover from it the Del
igne category Rep(S_t)\, which interpolates the category of finite-dimensi
onal representations of the symmetric group S_n from n a positive integer
to any parameter t in k. We show an analogous story happens in the unorien
ted case: via its description by generators and relations\, we recover the
generalized Deligne category Rep(S_t \\wr Z_2)\, which interpolates the c
ategory of finite-dimensional representations of the wreath product S_t \\
wr Z_2.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabio Calderón Mateus (Universidad de los Andes)
DTSTART:20240620T130000Z
DTEND:20240620T140000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/27
DESCRIPTION:Title: Classification of graded Hopf algebra quotients\nby Fabio Calder
ón Mateus (Universidad de los Andes) as part of European Quantum Algebra
Lectures (EQuAL)\n\n\nAbstract\nLet $G$ be a group. A Hopf algebra $H$ is
called $G$-graded if $H$ is $G$-graded as an algebra\, and the grading is
compatible with the comultiplication\, counit and antipode. Examples of su
ch Hopf algebras include cocentral extensions of Hopf algebras and the twi
sted Drinfeld double of groups. In this talk\, we present a classification
of Hopf ideals for a $G$-graded (quasi-)Hopf algebra based on the followi
ng parametrization: normal subgroups $N$ of $G$\, Hopf ideals in the homog
eneous component of the identity $H_e$ that are invariant under $N$\, and
$G$-equivariant trivializations of a specific quotient constructed with th
ese parameters. This approach incorporates ideas from earlier work by Cés
ar Galindo and Corey Jones\, who parameterized all fusion subcategories ar
ising from equivariantization through a group action on a fusion category.
However\, in our results\, the Hopf algebras are not necessarily semisimp
le\, and $G$ is not necessarily finite. This talk is based on ongoing join
t work with César Galindo.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Barrett (University of Nottingham)
DTSTART:20241009T090000Z
DTEND:20241009T100000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/28
DESCRIPTION:Title: Gray categories with duals and their diagrams\nby John Barrett (
University of Nottingham) as part of European Quantum Algebra Lectures (EQ
uAL)\n\n\nAbstract\nGray categories with a coherent notion of duals are ca
ptured well by a calculus of three-dimensional diagrams\, generalising the
familiar string diagrams for braided categories. The talk will discuss wh
at is in the paper with this title (Advances in Mathematics\, Volume 450\,
2024\, 109740)\, what got left out\, and what is still missing.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Burciu (Institute of Mathematics of Romanian Academy)
DTSTART:20241023T090000Z
DTEND:20241023T100000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/29
DESCRIPTION:Title: Burnside vanishing type properties for fusion categories\nby Seb
astian Burciu (Institute of Mathematics of Romanian Academy) as part of Eu
ropean Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nA classical result
of Burnside in the character theory of finite groups states that any irred
ucible non-linear character of a finite group vanishes on at least one ele
ment of the group. In this talk\, we show that a similar vanishing propert
y holds for weakly integral fusion categories. It is known that Harada’
s identity\, related with the product of all conjugacy class sums of a fin
ite group\, is a consequence of Burnside’s vanishing property of charact
ers. We prove a similar formula for any weakly integral fusion category an
d discuss some other new consequences of this result. This is partially jo
int work with S. Palcoux.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hankyung Ko (Uppsala University)
DTSTART:20241106T100000Z
DTEND:20241106T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/30
DESCRIPTION:Title: Diagrammatic singular Soergel bimodules\nby Hankyung Ko (Uppsala
University) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbs
tract\nIn joint work with Ben Elias\, Nicolas Libedinsky\, Leonardo Patimo
\, we construct a diagrammatic basis of the morphism spaces of singular So
ergel bimodules\, analogous to the diagrammatic basis for the regular Soer
gel bimodules given by Elias-Williamson (modelled on the algebraic `light
leaves' basis due to Libedinsky). The talk is an introduction to this diag
rammatics and related combinatorics\, where we also aim to draw some singu
lar light leaves.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zahra Nazemian (Universitaet Graz)
DTSTART:20241204T100000Z
DTEND:20241204T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/32
DESCRIPTION:Title: Poisson Modules over Hopf Poisson Order Algebras\nby Zahra Nazem
ian (Universitaet Graz) as part of European Quantum Algebra Lectures (EQuA
L)\n\n\nAbstract\nHopf Poisson order (HPO) algebras were introduced and st
udied by Brown\, Nazemian\, and Zhang (preprint\, 2024). We investigate th
e class of Poisson modules over HPO algebras and show that it forms a mono
idal category.\n \nMoreover\, we prove that the left homological integral
of an HPO algebra $H$\, denoted $ \\int_H^l$\, is a left Poisson module. I
t is also a right Poisson module if and only if $\\int_H^l = \\int_H^r $.
\n \nReferences:\n- Hopf Poisson Order Algebras\, K. Brown\, Z. Nazemian\,
and J.J. Zhang\, (preprint\, 2024).\n- Homological Integrals of Hopf Alge
bras\, D.-M. Lu\, Q.-S. Wu\, and J.J. Zhang\, Trans. Amer. Math. Soc. 359
(2007)\, 4945–4975.\n- Category of Poisson Modules over HPO Algebras\, Z
. Nazemian\, in progress.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mizuki Oikawa (University of Tokyo)
DTSTART:20241218T100000Z
DTEND:20241218T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/33
DESCRIPTION:Title: Center construction for group-crossed tensor categories\nby Mizu
ki Oikawa (University of Tokyo) as part of European Quantum Algebra Lectur
es (EQuAL)\n\n\nAbstract\nIn this talk\, I will talk about my recent gener
alization of the Drinfeld center construction for group-crossed tensor cat
egories. A group-crossed tensor category is a tensor category with compati
ble group action and grading\, which naturally appear in two-dimensional c
onformal theory as categories of twisted modules. Indeed\, my construction
for such categories yields categories "braided for a matched pair of grou
ps"\, which is a notion introduced recently by Natale. I will also talk ab
out my work in preparation: an equivariant version of Müger's factorizati
on theorem and a group-crossed version of Morita equivalence.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ramona Wolf (University of Siegen)
DTSTART:20250122T100000Z
DTEND:20250122T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/34
DESCRIPTION:Title: Computing F-symbols for the center of a fusion category via tube alg
ebras\nby Ramona Wolf (University of Siegen) as part of European Quant
um Algebra Lectures (EQuAL)\n\n\nAbstract\nApplications of fusion categori
es often require the F-symbols to be known explicitly\, for example\, for
constructing lattice models in physics. Although\, in principle\, these ma
trices can always be determined by solving the pentagon equation\, this ta
sk is often difficult in practice since it corresponds to solving a vast s
ystem of coupled polynomial equations in a large number of variables. This
is especially true if we are interested in the center of a fusion categor
y\, which typically has too many objects and multiplicities to allow for a
direct calculation of the F-symbols. In this talk\, I will discuss how on
e can construct the center (including the F-symbols) from a known fusion c
ategory using representation theory of the tube algebra of the category.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Lachowska (École Polytechnique Fédérale de Lausanne)
DTSTART:20250205T100000Z
DTEND:20250205T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/35
DESCRIPTION:Title: Combinatorics of the center of the small quantum group\nby Anna
Lachowska (École Polytechnique Fédérale de Lausanne) as part of Europea
n Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nThe small quantum group
$u_q(g)$ associated to the Lie algebra $g$ and a root of unity $q$ was int
roduced by Lusztig in 1990 and plays an important role in quantum and modu
lar representation theory. Despite significant advances in the last two ye
ars\, the dimension of the center of $u_q(g)$ is unknown in general. I wil
l describe the combinatorial aspects of the problem\, in particular the r
elation between the center of $u_q(g)$ and the space of the diagonal coinv
ariants\, the Harish-Chandra center and the Higman ideal.\nThis is a joint
work with Qi You\, Nicolas Hemelsoet and Oscar Kivinen.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nivedita (University of Oxford)
DTSTART:20250219T104500Z
DTEND:20250219T114500Z
DTSTAMP:20260411T230113Z
UID:EQuAL/36
DESCRIPTION:Title: Models for 2-Hilb and 3-Hilb as target categories for Functorial Fie
ld Theories\nby Nivedita (University of Oxford) as part of European Qu
antum Algebra Lectures (EQuAL)\n\n\nAbstract\nWe introduce W*-Cat\, the bi
category of complete W*‐categories\, functors and natural transformation
s and discuss its equivalence with the Morita category of von Neumann alge
bras (vN2). We highlight some analogies of W*‐categories with Hilbert sp
aces pointing towards W*-Cat being a model for 2-Hilb (based on https://ar
xiv.org/abs/2411.01678). We also introduce a categorified analogue of von
Neumann algebras\, motivating definition of a Bicommutant Category such th
at the Morita category of bicommutant categories would model 3-Hilb. This
is work in progress.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edmund Heng (IHES)
DTSTART:20250305T100000Z
DTEND:20250305T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/37
DESCRIPTION:Title: 1-step beyond semisimple algebras: fusion quivers\nby Edmund Hen
g (IHES) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstrac
t\nThe study of module categories over fusion categories have focussed mos
tly on the semisimple ones. In this talk I will introduce the notion of fu
sion quivers and their representations\, the categories of which form here
ditary (global projective dimension 1) abelian module categories over fusi
on categories. This naive “one-step” generalisation from semisimple mo
dule categories uncovers a wealth of interesting new connections to Coxete
r theory. In particular\, I will present a classification result in the sp
irit of Gabriel: the finite-representation-type fusion quivers are classif
ied by the Coxeter—Dynkin diagrams\; the latter includes the (crystallog
raphic) Dynkin diagram from Lie algebras ABCDEFG and\, perhaps surprisingl
y\, also the non-crystallographic diagrams H and I\, which all together cl
assify the finite Coxeter groups. This is based on joint work with Ben Eli
as.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaoting Zhang (China Normal University)
DTSTART:20250319T100000Z
DTEND:20250319T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/38
DESCRIPTION:Title: Fusion-stable tilting/stability structures on triangulated categorie
s\nby Xiaoting Zhang (China Normal University) as part of European Qua
ntum Algebra Lectures (EQuAL)\n\n\nAbstract\nWe study fusion-stable tiltin
g/stability structures on triangulated categories and show that the space
of Fusion-stable stability conditions form a complex manifold. As an appli
cation\, we give a new proof of $K(\\pi\,1)$-conjecture for finite non-sim
ply laced Coxeter-Dynkin type. This is a joint work with Qiu Yu.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaac Oppong (University of Greenwich)
DTSTART:20250507T090000Z
DTEND:20250507T100000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/39
DESCRIPTION:Title: Derivations and Hochschild cohomology of quantum nilpotent algebras<
/a>\nby Isaac Oppong (University of Greenwich) as part of European Quantum
Algebra Lectures (EQuAL)\n\n\nAbstract\nWe compute the derivations of Qua
ntum Nilpotent Algebras under a technical (but necessary) assumption on th
e center. As a consequence\, we give an explicit description of the first
Hochschild cohomology group of $U_q^+(\\mathfrak{g})$\, the positive part
of the quantized enveloping algebra of a finite-dimensional complex simple
Lie algebra $\\mathfrak{g}$. Our results are obtained leveraging an initi
al cluster constructed by Goodearl and Yakimov.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cesar Galindo (Universidad de los Andes)
DTSTART:20250521T120000Z
DTEND:20250521T130000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/40
DESCRIPTION:Title: Zestings for Hopf algebras\nby Cesar Galindo (Universidad de los
Andes) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract
\nIn this talk\, I will present a framework for "zestings" of Hopf algebra
s\, a technique we hve extended from fusion categories to general tensor c
ategories. I will provide a detailed translation of the categorical zestin
g construction into explicit Hopf algebraic terms. We show how associative
zesting of a Hopf algebra's comodule category yields a coquasi-Hopf algeb
ra\, where the comodule category of this new structure is precisely the ze
sted category.\n\nFurthermore\, we present concrete formulas for construct
ing zestings of pointed Hopf algebras\, particularly for cyclic group grad
ings\, encompassing both diagonal and non-diagonal braided vector spaces.
Finally\, I will illustrate this construction with new examples of coquasi
-Hopf algebras\, including those derived from Nichols algebras of super ty
pe A(1|2) and the Fomin-Kirillov algebra in three variables.\n\nThis is jo
int work with Ivan Angiono and Giovanny Mora.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Macpherson (Instituto Superior Técnico Lisboa)
DTSTART:20250604T090000Z
DTEND:20250604T100000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/41
DESCRIPTION:Title: Constructing a categorified evaluation 2-functor for affine sl(3)\nby James Macpherson (Instituto Superior Técnico Lisboa) as part of Eur
opean Quantum Algebra Lectures (EQuAL)\n\nAbstract: TBA\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Lentner (Universität Hamburg)
DTSTART:20250618T090000Z
DTEND:20250618T100000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/42
DESCRIPTION:Title: Proving the Logarithmic Kazhdan-Lusztig Correspondence\nby Simon
Lentner (Universität Hamburg) as part of European Quantum Algebra Lectur
es (EQuAL)\n\n\nAbstract\nThe logarithmic Kazhdan-Lusztig correspondence b
y B. Feigin and others is a conjectural equivalence between braided tensor
categories of representations of quantum groups and of certain vertex alg
ebras\, which are algebras with an analytic flavour that appear in quantum
field theory. I will give a gentle introduction into the physics side and
recall some previous result of mine that certain analytic operators calle
d screenings fulfill the relations of an associated Nichols algebra.\n\nIn
arXiv:2501.10735 I recently gave a proof of the conjectural category equi
valence in quite general situations\, also including Nichols algebras beyo
nd quantum groups\, under the assumption that the vertex algebra side is a
nalytically nice enough. The proof is based on joint work with T. Creutzig
and M. Rupert\, in which we settled first small cases. The proof is almos
t completely algebraic and interesting in its own right\, the essential st
atement is: Every braided tensor category together with a big commutative
algebra A\, such that the category of local A-modules is semisimple and th
e category of A-modules contains no additional simple modules\, is equival
ent to representations of a quantum group associated to a Nichols algebra\
, which is determined by certain Ext1-groups. In a certain sense\, this is
a categorical and braided version of the Andruskiewitsch-Schneider progra
m\, and prominently uses important results in this area by I. Angiono and
others.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenichi Shimizu (Shibaura Institute of Technology)
DTSTART:20250924T090000Z
DTEND:20250924T100000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/43
DESCRIPTION:Title: Simple algebras in Rep(uq(sl2))\nby Kenichi Shimizu (Shibaura In
stitute of Technology) as part of European Quantum Algebra Lectures (EQuAL
)\n\n\nAbstract\nThe notion of an algebra in a tensor category plays an im
portant role in the theory of tensor categories and their applications. Si
mple algebras in finite tensor categories\, much like in ordinary ring the
ory\, form one of the most fundamental classes of algebras. Although simpl
e algebras are especially important in Morita theory of finite tensor cate
gories\, the basic theory of simple algebras is not yet fully developed. I
n this talk\, I will present some Morita theoretic results on module categ
ories over finite tensor categories and explain how these results can be a
pplied to construct simple algebras with additional properties\, such as b
eing Frobenius or symmetric Frobenius. I will also present examples in the
category Rep(uq(sl2)) of modules over the small quantum sl2 at a root of
unity of odd order. This talk is based on joint work with Daisuke Nakamura
\, Hin Wan Ng and Taiki Shibata.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Halbig (Universität Marburg)
DTSTART:20251008T090000Z
DTEND:20251008T100000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/44
DESCRIPTION:Title: A non-semisimple version of the Kitaev model\nby Sebastian Halbi
g (Universität Marburg) as part of European Quantum Algebra Lectures (EQu
AL)\n\n\nAbstract\nIn 1997\, Alexei Kitaev proposed a foundational model f
or fault-tolerant quantum computation based on complex semisimple Hopf alg
ebras. Its key feature is a topologically invariant code space which is co
nstructed using combinatorial data encoded by a graph embedded into a clos
ed oriented surface. This ensures robustness against a wide range of error
s. Beyond applications in quantum computing\, the model has remarkable con
nections with combinatorics\, Hopf algebra representation theory\, homolog
ical algebra\, and topological quantum field theories. In this talk\, base
d on joint work with U.\\ Krähmer\, we present a generalisation of the Ki
taev model to arbitrary finite-dimensional Hopf algebras. Two challenges p
revent a straightforward approach. First\, the extended Hilbert space\, a
Yetter--Drinfeld module whose invariant submodule is the code space\, reli
es on an involutive antipode---a condition equivalent to the underlying Ho
pf algebra being semisimple. Second\, topological invariance is proven usi
ng projectors assembled from (co)integrals. Since we do not have these too
ls at our disposal\, we follow a new approach\, inspired by homological co
nsiderations. We introduce involutive Hopf bimodules\, which are related t
o coefficients of Hopf cyclic cohomology and allow us to form appropriate\
, Yetter–Drinfeld valued\, variants of extend Hilbert spaces. Instead of
considering invariant submodules\, the analoga of the code spaces arise a
s bitensor products---combinations of cotensor and tensor products. Our pr
oof of their topological invariance relies on a notion of excision and use
s actions of a group related to mapping class groups. Towards computing bi
tensor products\, we discuss induction-restriction type identities\, which
are particularly useful for eg. small quantum groups.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rhiannon Savage (University College London)
DTSTART:20251022T090000Z
DTEND:20251022T100000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/45
DESCRIPTION:Title: Stacks in Derived Bornological Geometry\nby Rhiannon Savage (Uni
versity College London) as part of European Quantum Algebra Lectures (EQuA
L)\n\n\nAbstract\nRecent foundational work by Ben-Bassat\, Kelly\, and Kre
mnizer describes a model for derived analytic geometry as homotopical geom
etry relative to the infinity category of simplicial commutative complete
bornological rings. In this talk\, we will discuss a representability theo
rem for derived stacks in these contexts and we will set out some new foun
dations for derived smooth geometry. We will also briefly discuss the repr
esentability of the derived moduli stack of non-linear elliptic partial di
fferential equations by an object we call a derived C∞-bornological affi
ne scheme.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Sanford (University of Edinburgh)
DTSTART:20251105T100000Z
DTEND:20251105T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/46
DESCRIPTION:Title: A Curious Braided Category over R\nby Sean Sanford (University o
f Edinburgh) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbs
tract\nIn quantum mechanics\, time reversal symmetry is generally understo
od in terms of an antiunitary operator. When a fusion category over C has
an antiunitary symmetry\, the fixed points of such a symmetry form a fusi
on category over the real numbers. Since fusion categories are meant to d
escribe systems of particles\, the resulting real fusion category describe
s those particles that are time-reversal invariant.\n \nIn recent joint wo
rk with Thibault Décoppet (https://arxiv.org/abs/2412.15019)\, we discove
red a certain braided fusion category over R that represents a higher dime
nsional analogue of the quaternions. Based on recent conjectures regarding
the Witt group of nondegenerate braided fusion categories\, we expect tha
t this category generates the kernel of the map Witt(Vec_R)->Witt(Vec_C)\,
which is just Z/2.\n \nIn this talk\, I will describe this curious catego
ry: its fusion rules and braiding\, how it comes about\, and it's signific
ance from the perspective of condensed matter.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melody Molander (The Ohio State University)
DTSTART:20251119T100000Z
DTEND:20251119T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/47
DESCRIPTION:Title: Skein Theory of Affine ADE Subfactor Planar Algebras\nby Melody
Molander (The Ohio State University) as part of European Quantum Algebra L
ectures (EQuAL)\n\n\nAbstract\nThe Kuperberg Program seeks to describe pre
sentations of subfactor planar algebras in order to classify them and prov
e results about their corresponding categories purely diagrammatically. Th
is program has been completed for index less than 4 and remains an area of
ongoing research for index greater than 4. This talk will discuss the pro
gram at index 4. At this index\, planar algebras other than Temperley-Lieb
have an affine $A$\, $D$\, or $E$ principal graph. Categories correspondi
ng to some of the affine A planar algebras are monoidally equivalent to cy
clic pointed fusion categories. For affine $E_7$\, to prove sufficiency of
its presentation\, we define a jellyfish algorithm. I will describe the j
ellyfish algorithm using a half braiding and discuss that it gives a well-
defined surjective function onto $C$.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Zetto (Universität Hamburg)
DTSTART:20251203T100000Z
DTEND:20251203T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/48
DESCRIPTION:Title: Cauchy-completions and extended TFTs\nby Markus Zetto (Universit
ät Hamburg) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbs
tract\nAn enriched category is said to be Cauchy-complete if it admits all
absolute colimits — those weighted colimits that commute with every enr
iched functor. For instance\, an ordinary (Set-enriched) category is Cauch
y-complete precisely when it is idempotent complete\, while an Ab-enriched
category is so when it is both idempotent complete and additive.\n\nI wil
l extend this notion to enriched (∞\,n)-categories and explain how\, via
the cobordism hypothesis\, it yields a flexible and general formalism fo
r constructing and classifying framed fully extended topological field the
ories. In particular\, it clarifies the role of higher idempotents\, also
known as condensations in the sense of Gaiotto and Johnson-Freyd. Joint wo
rk in progress with David Reutter.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iordanis Romaidis (University of Edinburgh)
DTSTART:20251217T100000Z
DTEND:20251217T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/49
DESCRIPTION:Title: Holonomic skein modules\nby Iordanis Romaidis (University of Edi
nburgh) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract
\nFor a reductive group G and a quantum parameter q\, skein theory assigns
skein algebras to surfaces and skein modules to 3-manifolds. Skein module
s of closed 3-manifolds at generic q were conjectured by Witten to be fini
te-dimensional—a statement later proved by Gunningham\, Jordan\, and Saf
ronov. In this talk\, I will present joint work with David Jordan on a gen
eralization of this conjecture to 3-manifolds with boundary. In this setti
ng\, the finiteness property is replaced by the condition that the skein m
odule is holonomic over the boundary skein algebra. Roughly\, a module is
holonomic if it is finitely generated and has a Lagrangian support. We pro
ve holonomicity for skein modules of GL2 and SL2 by constructing transf
er bimodules\, and proving holonomicity preservation theorems analogous to
those in the classical theory of D-modules.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrià Marin Salvador (University of Oxford)
DTSTART:20260121T100000Z
DTEND:20260121T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/50
DESCRIPTION:Title: Continuous Tensor Categories and Direct Integrals\nby Adrià Mar
in Salvador (University of Oxford) as part of European Quantum Algebra Lec
tures (EQuAL)\n\n\nAbstract\nFinitely semisimple tensor categories are ubi
quitous in quantum algebra: they appear in the representation theory of Ho
pf algebras\, quantum groups\, TQFTs\, CFTs\, and others. However\, one us
ually needs extra adjectives to ensure that the categories one comes acros
s satisfy the necessary finite properties of finitely semisimple tensor ca
tegories. Without enough adjectives\, one sometimes encounters tensor cate
gories which are still “semisimple”\, but have continuously many simpl
e objects\, and a generic object is a direct integral of such simple objec
ts\, as opposed to a direct sum. In this talk\, we will introduce a new mo
del to treat these type of categories: continuous tensor categories\; and
provide some basic examples. Time permitting\, we will explore how continu
ous tensor categories allow us to compute certain categories appearing in
the study of non-rational 2d conformal field theories such as the non-comp
act boson and related theories.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jordan (University of Edinburgh)
DTSTART:20260204T100000Z
DTEND:20260204T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/51
DESCRIPTION:Title: Defects in skein theory\nby David Jordan (University of Edinburg
h) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nI w
ill give an overview of some recent progress constructing skein module inv
ariants of 3-manifolds with defects. The defects to be discussed come in
three different classes detailed below. Warning: with all these examples
to cover\, there might be precious few proofs!\n\nI will explain how "elec
tric-magnetic 1-form symmetry" arises in skein theory as invertible line d
efects\, and how it enters into (conjectural) electric-magnetic/Langlands/
S-duality\, following joint work with Gunningham and Safronov.\n\nI will t
hen discuss a recent work of Jennifer Brown and myself\; independent works
of Juan Ramon Gomez\; separate independent works of Julia Bierent and Mat
thias Vancraeynest\, which ares all around constructing defects in skein t
heory modelling parabolic induction and restriction (by non-invertible pla
ne defects)\, as well as Weyl group twists (by invertible line defects)\,
with applications to the quantum A-polynomial\, the irregular Deligne--Sim
pson problem and the abelianisation program of Gaiotto--Moore-Neitzke.\n\n
Finally\, I will touch on some nascent joint work with Eric Chen and Iorda
nis Romaidis aimed at constructing and analysing line defects associated t
o quantum symmetric pairs\, with a view towards exploring the relative Lan
glands program of Ben-Zvi--Sakellaridis--Venkatesh.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jaklitsch (University of Oslo)
DTSTART:20260218T100000Z
DTEND:20260218T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/52
DESCRIPTION:Title: ⊗-Frobenius functors and exact module categories\nby David Jak
litsch (University of Oslo) as part of European Quantum Algebra Lectures (
EQuAL)\n\n\nAbstract\nFrobenius algebras are structures relevant in multip
le disciplines such as subfactor theory\, conformal field theory or topolo
gical field theory. The purpose of the talk is to present results based on
arxiv:2501.16978 about preservation and construction of Frobenius algebra
s. We introduce the notion of ⊗-Frobenius functors and provide character
izations relating them with the other Frobenius-type functors. These are u
sed to twist module categories. Results on sufficient conditions for the p
reservation of certain properties under twisting and preservation of Frobe
nius algebras are summarized.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justine Fasquel (Université Bourgogne)
DTSTART:20260304T100000Z
DTEND:20260304T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/53
DESCRIPTION:Title: Partial VS Inverse quantum hamiltonian reductions\nby Justine Fa
squel (Université Bourgogne) as part of European Quantum Algebra Lectures
(EQuAL)\n\n\nAbstract\nW-algebras form a rich family of vertex algebras\,
arising from simple Lie algebras and their nilpotent orbits through a coh
omological procedure known as quantum hamiltonian reduction. As the nilpot
ent orbit grows\, the reduction becomes increasingly intricate\, while the
representation theory of the corresponding W-algebra is simplified. In th
is talk\, I would like to discuss two additional concepts\, the partial an
d inverse quantum hamiltonian reductions\, that help understanding the qua
ntum hamiltonian reduction and clarify how W‑algebras attached to differ
ent nilpotent orbits are related.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Huston (University of Leeds)
DTSTART:20260318T100000Z
DTEND:20260318T110000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/54
DESCRIPTION:Title: A gentle introduction to fusion 2-categories\nby Peter Huston (U
niversity of Leeds) as part of European Quantum Algebra Lectures (EQuAL)\n
\n\nAbstract\nFusion 2-categories are a generalization of fusion 1-categor
ies\, corresponding under the cobordism hypothesis to fully extended (3+1)
D TQFTs. In this talk\, I will motivate the definition of fusion 2-categor
y\, explore the classification of fusion 2-categories given in arxiv:2411.
05907\, and sketch some applications of fusion 2-categories in studying no
n-invertible symmetries.\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kürsat Sözer (Université de Lille)
DTSTART:20260422T090000Z
DTEND:20260422T100000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/55
DESCRIPTION:by Kürsat Sözer (Université de Lille) as part of European Q
uantum Algebra Lectures (EQuAL)\n\nAbstract: TBA\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Blas Torrecillas (Universidad de Almería)
DTSTART:20260506T090000Z
DTEND:20260506T100000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/56
DESCRIPTION:by Blas Torrecillas (Universidad de Almería) as part of Europ
ean Quantum Algebra Lectures (EQuAL)\n\nAbstract: TBA\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilaria Colazzo (University of Leeds)
DTSTART:20260520T090000Z
DTEND:20260520T100000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/57
DESCRIPTION:by Ilaria Colazzo (University of Leeds) as part of European Qu
antum Algebra Lectures (EQuAL)\n\nAbstract: TBA\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristina Anghel (Université Clermont Auvergne)
DTSTART:20260603T090000Z
DTEND:20260603T100000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/58
DESCRIPTION:by Cristina Anghel (Université Clermont Auvergne) as part of
European Quantum Algebra Lectures (EQuAL)\n\nAbstract: TBA\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Zorman (Universität Hamburg)
DTSTART:20260617T090000Z
DTEND:20260617T100000Z
DTSTAMP:20260411T230113Z
UID:EQuAL/59
DESCRIPTION:by Tony Zorman (Universität Hamburg) as part of European Quan
tum Algebra Lectures (EQuAL)\n\nAbstract: TBA\n
LOCATION:https://master.researchseminars.org/talk/EQuAL/59/
END:VEVENT
END:VCALENDAR