BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gavril Farkas (Humboldt University of Berlin) DTSTART:20200417T180000Z DTEND:20200417T193000Z DTSTAMP:20260419T185122Z UID:agstanford/1 DESCRIPTION:Title: Green’s conjecture via Koszul modules\nby Gavril Farkas (H umboldt University of Berlin) as part of Stanford algebraic geometry semin ar\n\n\nAbstract\nUsing ideas from geometric group theory we provide a nov el\napproach to Green’s Conjecture on syzygies of canonical curves. Via a\nstrong vanishing result for Koszul modules we deduce that a general\nca nonical curve of genus g satisfies Green’s Conjecture when the\ncharacte ristic is zero or at least $(g+2)/2$. Our results are new in\npositive cha racteristic (and answer positively a conjecture of Eisenbud\nand Schreyer) \, whereas in characteristic zero they provide a different\nproof for theo rems first obtained in two landmark papers by Voisin.\nJoint work with Apr odu\, Papadima\, Raicu and Weyman.\n LOCATION:https://master.researchseminars.org/talk/agstanford/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Kirsten Wickelgren (Duke) DTSTART:20200424T180000Z DTEND:20200424T193000Z DTSTAMP:20260419T185122Z UID:agstanford/2 DESCRIPTION:Title: There are $160\,839 \\langle 1 \\rangle + 160\,650 \\langle -1\\ rangle$ 3-planes in a 7-dimensional cubic hypersurface\nby Kirsten Wic kelgren (Duke) as part of Stanford algebraic geometry seminar\n\n\nAbstrac t\nIt is a result of Debarre--Manivel that the variety of $d$-planes on a generic complete intersection has the expected dimension. When this dimens ion is 0\, the number of such $d$-planes is given by the Euler number of a vector bundle on a Grassmannian. There are several Euler numbers from $A^ 1$-homotopy theory which take a vector bundle to a bilinear form. We equat e some of these\, including those of Barge-Morel\, Kass-W.\, Déglise-Jin- Khan\, and one suggested by M.J. Hopkins\, A. Raksit\, and J.-P. Serre usi ng duality of coherent sheaves. We establish integrality results for this Euler class\, and use this to compute the Euler classes associated to arit hmetic counts of d-planes on complete intersections in projective space in terms of topological Euler numbers over the real and complex numbers. The example in the title uses work of Finashin-Kharlamov. This is joint work with Tom Bachmann.\n LOCATION:https://master.researchseminars.org/talk/agstanford/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Burt Totaro (UCLA) DTSTART:20200501T190000Z DTEND:20200501T200000Z DTSTAMP:20260419T185122Z UID:agstanford/3 DESCRIPTION:Title: The Hilbert scheme of infinite affine space\nby Burt Totaro (UCLA) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nI wil l discuss the Hilbert scheme of $d$ points in affine $n$-space\, with some examples. This space has many irreducible components for $n$ at least 3 a nd is poorly understood. Nonetheless\, in the limit where $n$ goes to inf inity\, we show that the Hilbert scheme of $d$ points in infinite affine s pace has a very simple homotopy type. In fact\, it has the $A^1$-homotopy type of the infinite Grassmannian $BGL(d-1)$. Many questions remain. (Join t with Marc Hoyois\, Joachim Jelisiejew\, Denis Nardin\, Maria Yakerson.)\ n LOCATION:https://master.researchseminars.org/talk/agstanford/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Borys Kadets (MIT) DTSTART:20200501T174500Z DTEND:20200501T184500Z DTSTAMP:20260419T185122Z UID:agstanford/4 DESCRIPTION:Title: 38406501359372282063949 & all that: Monodromy of Fano problems\nby Borys Kadets (MIT) as part of Stanford algebraic geometry seminar\n \n\nAbstract\nA Fano problem is an enumerative problem of counting linear subspaces on complete intersections. Some familiar examples are finding th e number of lines on a cubic surface\, and finding the number of lines on the intersection of $2$ quadrics in $\\mathbb{P}^4$. Suppose a general com plete intersection of type $[d]=(d_1\, ...\, d_s)$ in $\\mathbb{P}^n$ cont ains finitely many $r$-planes. To this Fano problem\, described by the tri ple $([d]\,n\,r)$\, one can associate a group $G_{[d]\,n\,r}$\, the monodr omy group of the Fano problem\; it describes the permutations of $r$-plane s on a complete intersection of type $[d]$\, as the complete intersection varies. I will show that $G_{[d]\,n\,r}$ is either a symmetric or an alter nating group for almost all Fano problems with an explicit list of excepti ons\, and describe the monodromy groups of the exceptional problems. An in teresting feature of this computation is that it avoids any local calculat ions\, which seems necessary to get the result in full generality. This is joint work with Sachi Hashimoto.\n\nDiscussion during the talk will be at https://tinyurl.com/2020-05-01-a\n(and this will be deleted in 3 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Julie Desjardins (Toronto) DTSTART:20200508T174500Z DTEND:20200508T184500Z DTSTAMP:20260419T185122Z UID:agstanford/5 DESCRIPTION:Title: Density of rational points on a family of del Pezzo surface of d egree 1\nby Julie Desjardins (Toronto) as part of Stanford algebraic g eometry seminar\n\n\nAbstract\nLet $k$ be a number field and $X$ an algebr aic variety over $k$. We want to study the set of $k$-rational points $X(k )$. For example\, is $X(k)$ empty? If not\, is it dense with respect to th e Zariski topology? Del Pezzo surfaces are classified by their degrees $d$ (an integer between 1 and 9). Manin and various authors proved that for a ll del Pezzo surfaces of degree $>1$ is dense provided that the surface ha s a $k$-rational point (that lies outside a specific subset of the surface for $d=2$). For $d=1$\, the del Pezzo surface always has a rational point . However\, we don't know it the set of rational points is Zariski-dense. In this talk\, I present a result that is joint with Rosa Winter in which we prove the density of rational points for a specific family of del Pezzo surfaces of degree 1 over $k$.\n\nThe discussion for Julie Desjardins’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/stagMa y08a (and will be deleted after 3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Bjorn Poonen (MIT) DTSTART:20200508T190000Z DTEND:20200508T200000Z DTSTAMP:20260419T185122Z UID:agstanford/6 DESCRIPTION:Title: Bertini irreducibility theorems via statistics\nby Bjorn Poo nen (MIT) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nLe t $X \\subset \\mathbb{P}^n$ be a geometrically irreducible subvariety\nwi th $\\dim X \\ge 2$\, over any field.\nLet $\\check{\\mathbb{P}}^n$ be the moduli space\nparametrizing hyperplanes $H \\subset \\mathbb{P}^n$.\nLet $L \\subset \\check{\\mathbb{P}}^n$ be the locus parametrizing $H$\nfor wh ich $H \\cap X$ is geometrically irreducible.\nThe classical Bertini irred ucibility theorem states that\n$L$ contains a dense open subset of $\\chec k{\\mathbb{P}}^n$\,\nso the bad locus $L' := \\mathbb{P}^n - L$ satisfies $\\dim L' \\le n-1$.\nBenoist improved this to $\\dim L' \\le \\operatorna me{codim} X + 1$.\n\nWe describe a new way to prove and generalize such th eorems\,\nby reducing to the case of a finite field\nand studying the mean and variance\nof the number of points of a random hyperplane section.\nTh is is joint work with Kaloyan Slavov.\n\nThe discussion for Bjorn Poonen ’s talk is taking place not in the zoom-chat\, but at https://tinyurl.co m/stagMay08b (and will be deleted after 3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Rohini Ramadas (Brown) DTSTART:20200515T174500Z DTEND:20200515T184500Z DTSTAMP:20260419T185122Z UID:agstanford/7 DESCRIPTION:Title: The locus of post-critically finite maps in the moduli space of self-maps of $\\mathbb{P}^n$\nby Rohini Ramadas (Brown) as part of Sta nford algebraic geometry seminar\n\n\nAbstract\nA degree $d>1$ self-map $f $ of $\\mathbb{P}^n$ is called post critically finite (PCF) if its critica l hypersurface $C_f$ is pre-periodic for $f$\, that is\, if there exist in tegers $r \\geq 0$ and $k>0$ such that $f^{r+k}(C_f)$ is contained in $f^{ r}(C_f)$. \n\nI will discuss the question: what does the locus of PCF maps look like as a subset of the moduli space of degree $d$ maps on $\\mathbb {P}^n$? I’ll give a survey of many known results and some conjectures in dimension $1$. I’ll then present a result\, joint with Patrick Ingram a nd Joseph Silverman\, that suggests that in dimensions two or greater\, PC F maps are comparatively scarce in the moduli space of all self-maps.\n\nT he discussion for Rohini Ramadas’s talk is taking place not in zoom-chat \, but at https://tinyurl.com/2020-05-15-rr (and will be deleted after 3- 7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Rob Silversmith (Northeastern) DTSTART:20200515T190000Z DTEND:20200515T200000Z DTSTAMP:20260419T185122Z UID:agstanford/8 DESCRIPTION:Title: Studying subschemes of affine/projective space via matroids\ nby Rob Silversmith (Northeastern) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nGiven a homogeneous ideal $I$ in a polynomial ring\ , one may apply the following combinatorial operation: for each degree $d$ \, make a list of all subsets $S$ of the set of degree-$d$ monomials such that $S$ is the set of nonzero coefficients of an element of $I$. For each $d$\, this set of subsets is a combinatorial object called a matroid. As $d$ varies\, the resulting sequence of matroids is called the tropicalizat ion of $I$.\n\nI will discuss some of the many questions one can ask about tropicalizations of ideals\, and how they are related to some classical q uestions in combinatorial algebraic geometry\, such as the classification of torus orbits on Hilbert schemes of points in $\\mathbb{C}^2$. Some unex pected combinatorial objects appear: e.g. when studying tropicalizations o f subschemes of $\\mathbb{P}^1$\, one is led to Schur polynomials and bina ry necklaces.\n LOCATION:https://master.researchseminars.org/talk/agstanford/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Chenyang Xu (MIT) DTSTART:20200522T180000Z DTEND:20200522T193000Z DTSTAMP:20260419T185122Z UID:agstanford/9 DESCRIPTION:Title: K-moduli of Fano varieties\nby Chenyang Xu (MIT) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nOne main theme of the a lgebraic K-stability theory of Fano varieties is to use it to construct mo duli spaces of Fano varieties. This has once been beyond algebraic geomete rs’ imagination\, but K-stability is proven to give the right framework. By now except the properness\, all other main ingredients have essential ly been established\, based on the recent development of our understanding of K-stability theory and other inputs. In this talk\, we will give an ou tline of the construction\, with the focus on the essential role that the new characterisation of K-stability plays\, and its connection to minimal model program theory.\n LOCATION:https://master.researchseminars.org/talk/agstanford/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Bhargav Bhatt (University of Michigan) DTSTART:20200605T190000Z DTEND:20200605T200000Z DTSTAMP:20260419T185122Z UID:agstanford/11 DESCRIPTION:Title: A p-adic Riemann-Hilbert functor and vanishing theorems\nby Bhargav Bhatt (University of Michigan) as part of Stanford algebraic geom etry seminar\n\n\nAbstract\nI will discuss an ongoing project (joint with Jacob Lurie) aiming to construct a $p$-adic Riemann-Hilbert functor\, atta ching coherent complexes to constructible sheaves (with coefficients in $\ \mathbb{F}_p$\, $\\mathbb{Z}_p$ or $\\mathbb{Q}_p$) on a compact algebraic variety over a $p$-adic field. When combined with results on constructibl e sheaves\, these yields vanishing theorems (old and new) on the coherent side.\n\nThe discussion for Bhargav Bhatt’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/2020-06-05-bb (and will be deleted after 3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Wei Ho (University of Michigan) DTSTART:20200612T190000Z DTEND:20200612T200000Z DTSTAMP:20260419T185122Z UID:agstanford/12 DESCRIPTION:Title: Splitting Brauer classes\nby Wei Ho (University of Michigan ) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nGiven a Br auer class over a field\, what types of varieties split it? Or more geomet rically\, can we say anything about the varieties that map to a given Brau er-Severi variety? In this talk\, we will discuss some open questions rela ted to splitting Brauer classes. For example\, we will review some classic al algebro-geometric constructions that produce genus one curves splitting low index Brauer classes ((old) joint work with A.J. de Jong)\, and we wi ll explain why a Brauer class of any index is split by a torsor under an a belian variety (joint work with M. Lieblich).\n\nThe discussion for Wei Ho ’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/20 20-06-12-wh (and will be deleted after 3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuchen Liu (Yale) DTSTART:20200529T174500Z DTEND:20200529T184500Z DTSTAMP:20260419T185122Z UID:agstanford/13 DESCRIPTION:Title: Moduli spaces of quartic hyperelliptic K3 surfaces via K-stabil ity\nby Yuchen Liu (Yale) as part of Stanford algebraic geometry semin ar\n\n\nAbstract\nA general polarized hyperelliptic K3 surfaces of degree 4 is a double cover of $\\mathbf{P\n}^ 1 \\times \\mathbf{P}^1$ branched a long a bidegree $(4\,4)$ curve. Classically there are two compactification s of their moduli spaces: one is the GIT quotient of $(4\,4)$ curves\, the other is the Baily-Borel compactification of their periods. We show that K-stability provides a natural modular interpolation between these two com pactifications. This provides a new aspect toward a recent result of Laza- O'Grady. Based on joint work in progress with K. Ascher and K. DeVleming.\ n\nThe discussion for Yuchen Liu’s talk is taking place not in zoom-chat \, but at https://tinyurl.com/2020-05-29-yl (and will be deleted after 3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Margaret Bilu (NYU) DTSTART:20200612T174500Z DTEND:20200612T184500Z DTSTAMP:20260419T185122Z UID:agstanford/14 DESCRIPTION:Title: Arithmetic and motivic statistics via zeta functions\nby Ma rgaret Bilu (NYU) as part of Stanford algebraic geometry seminar\n\n\nAbst ract\nThe Grothendieck group of varieties over a field $k$ is the quotient of the free abelian group on isomorphism classes of algebraic varieties o ver k by the so-called cut-and-paste relations. Many results in number the ory have a natural motivic analogue which can be formulated in the Grothen dieck ring of varieties. For example\, Poonen's finite field Bertini theor em has a motivic counterpart due to Vakil and Wood\, though none of the tw o statements can be deduced from the other. We describe a conjectural way to unify the number-theoretic and motivic statements (when the base field is finite) in this and other examples\, and will provide some evidence tow ards it. A key step is to reformulate everything in terms of convergence o f zeta functions of varieties in several different topologies. This is joi nt work with Ronno Das and Sean Howe.\n LOCATION:https://master.researchseminars.org/talk/agstanford/14/ END:VEVENT BEGIN:VEVENT SUMMARY:John Christian Ottem (University of Oslo) DTSTART:20200710T190000Z DTEND:20200710T200000Z DTSTAMP:20260419T185122Z UID:agstanford/15 DESCRIPTION:Title: On (2\,3)-fourfolds\nby John Christian Ottem (University of Oslo) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nI wil l explain how tropical degenerations and birational specialization techniq ues can be used in rationality problems. In particular\, I will apply thes e techniques to study quartic fivefolds and complete intersections of a qu adric and a cubic in $\\mathbb{P}^6$. This is joint work with Johannes Nic aise.\n LOCATION:https://master.researchseminars.org/talk/agstanford/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura Escobar (Washington University St. Louis) DTSTART:20200717T190000Z DTEND:20200717T200000Z DTSTAMP:20260419T185122Z UID:agstanford/16 DESCRIPTION:Title: Wall-crossing phenomena for Newton-Okounkov bodies\nby Laur a Escobar (Washington University St. Louis) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nA Newton-Okounkov body is a convex set ass ociated to a projective variety\, equipped with a valuation. These bodies generalize the theory of Newton polytopes. Work of Kaveh-Manon gives an ex plicit link between tropical geometry and Newton-Okounkov bodies. We use t his link to describe a wall-crossing phenomenon for Newton-Okounkov bodies . This is joint work with Megumi Harada.\n\nThe discussion for Laura Escob ar Vega’s talk is taking place not in zoom-chat\, but at https://tinyurl .com/2020-07-17-lev (and will be deleted after 3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Brendan Hassett (Brown University / ICERM) DTSTART:20200724T190000Z DTEND:20200724T200000Z DTSTAMP:20260419T185122Z UID:agstanford/17 DESCRIPTION:Title: Symbols\, birational geometry\, and computations\nby Brenda n Hassett (Brown University / ICERM) as part of Stanford algebraic geometr y seminar\n\n\nAbstract\nWe are interested in G-birational equivalence of varieties where G is a finite group. Kontsevich-Tschinkel and Kresch-Tschi nkel have developed symbol formalism to construct invariants that show ric h internal structure. We present examples of computations of these invaria nts for varieties in small dimensions\, illustrating how they compare to e xisting classification techniques.\n LOCATION:https://master.researchseminars.org/talk/agstanford/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Dan Abramovich (Brown University) DTSTART:20200731T193000Z DTEND:20200731T203000Z DTSTAMP:20260419T185122Z UID:agstanford/18 DESCRIPTION:Title: Resolution and logarithmic resolution via weighted blowings up< /a>\nby Dan Abramovich (Brown University) as part of Stanford algebraic ge ometry seminar\n\n\nAbstract\nThis lecture combines resolution of singular ities\, logarithmic geometry and algebraic stacks. I will not assume famil iarity neither with resolution of singularities nor with logarithmic geome try. I report on work with Temkin and Wlodarczyk and work of Quek. Resolvi ng singularities in families requires logarithmic geometry. Surprisingly\, trying to do this canonically forces us to use stack-theoretic modificati ons. Surprisingly\, stack-theoretic modifications provides an efficient it erative resolution method in which the worst singularities are blown up wi thout regard to the history. Not so surprisingly\, to make exceptional div isors cooperate we need logarithmic geometry again.\n LOCATION:https://master.researchseminars.org/talk/agstanford/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Hannah Larson (Stanford University) DTSTART:20200821T190000Z DTEND:20200821T200000Z DTSTAMP:20260419T185122Z UID:agstanford/19 DESCRIPTION:Title: Brill--Noether theory over the Hurwitz space\nby Hannah Lar son (Stanford University) as part of Stanford algebraic geometry seminar\n \n\nAbstract\nLet $C$ be a curve of genus $g$. A fundamental problem in th e theory of algebraic curves is to understand maps of $C$ to projective sp ace of dimension r of degree d. When the curve $C$ is general\, the moduli space of such maps is well-understood by the main theorems of Brill-Noeth er theory. However\, in nature\, curves $C$ are often encountered already equipped with a map to some projective space\, which may force them to be special in moduli. The simplest case is when $C$ is general among curves of fixed gonality. Despite much study over the past three decades\, a si milarly complete picture has proved elusive in this case. In this talk\, I will discuss recent joint work with Eric Larson and Isabel Vogt that comp letes such a picture\, by proving analogs of all of the main theorems of B rill--Noether theory in this setting.\n\nThe discussion for Hannah Larson ’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/20 20-08-21-hl (and will be deleted after 3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Olsson (UC Berkeley) DTSTART:20200828T190000Z DTEND:20200828T200000Z DTSTAMP:20260419T185122Z UID:agstanford/20 DESCRIPTION:Title: Determinants and deformation theory of perfect complexes\nb y Martin Olsson (UC Berkeley) as part of Stanford algebraic geometry semin ar\n\n\nAbstract\nIn this talk I will discuss the interplay between the de formation theory of perfect complexes\, determinants\, and traces. I will discuss\, in particular\, the verification of an expected compatibility am ong these that has been used in various places in the literature. For the speaker this project also provided an entry-point to the world of $\\inft y$-categories\, and I will try to motivate why such a perspective is usefu l. This is joint work with Max Lieblich.\n LOCATION:https://master.researchseminars.org/talk/agstanford/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Rachel Webb (UC Berkeley) DTSTART:20200918T190000Z DTEND:20200918T200000Z DTSTAMP:20260419T185122Z UID:agstanford/21 DESCRIPTION:Title: Virtual cycle on the moduli space of maps to a complete interse ction\nby Rachel Webb (UC Berkeley) as part of Stanford algebraic geom etry seminar\n\n\nAbstract\nA driving question in Gromov-Witten theory is to relate the invariants of a complete intersection to the invariants of t he ambient variety. In genus-zero this can often be done with a ``twisted theory\,'' but this fails in higher genus. Several years ago\, Chang-Li pr esented the moduli space of p-fields as a piece of the solution to the hig her-genus problem\, constructing the virtual cycle on the space of maps to the quintic 3-fold as a cosection localized virtual cycle on a larger mod uli space (the space of p-fields). Their result is analogous to the classi cal statement that the Euler class of a vector bundle is the class of the zero locus of a generic section. I will discuss work joint with Qile Chen and Felix Janda where we extend Chang-Li's result to a more general settin g\, a setting that includes standard Gromov-Witten theory of smooth orbifo ld targets and quasimap theory of GIT targets.\n LOCATION:https://master.researchseminars.org/talk/agstanford/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Eur (Stanford) DTSTART:20200904T190000Z DTEND:20200904T200000Z DTSTAMP:20260419T185122Z UID:agstanford/22 DESCRIPTION:Title: Simplicial generation of Chow rings of matroids\nby Chris E ur (Stanford) as part of Stanford algebraic geometry seminar\n\n\nAbstract \nWe present a new set of generators for the Chow ring of a matroid. We s how that these generators behave like base-point-free divisors by establis hing that (i) they correspond to matroid operations that combinatorially m irror hyperplane pullbacks\, and (ii) the volume polynomial with respect t o these generators satisfies Hodge-type inequalities. We thereby generali ze Postnikov's results on generalized permutohedra\, and also give a simpl ified proof of the combinatorially relevant portion of the Hodge theory of matroids developed by Adiprasito-Huh-Katz. No knowledge of matroids will be assumed. This is joint work with Spencer Backman and Connor Simpson.\ n\nThe discussion for Christopher Eur’s talk is taking place not in zoom -chat\, but at https://tinyurl.com/2020-09-04-ce (and will be deleted aft er 3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Kobin (UC Santa Cruz) DTSTART:20200911T190000Z DTEND:20200911T200000Z DTSTAMP:20260419T185122Z UID:agstanford/23 DESCRIPTION:Title: Zeta functions and decomposition spaces\nby Andrew Kobin (U C Santa Cruz) as part of Stanford algebraic geometry seminar\n\n\nAbstract \nZeta functions show up everywhere in math these days. While some recent work has brought homotopical methods into the theory of zeta functions\, t here is in fact a lesser-known zeta function that is native to homotopy th eory. Namely\, every suitably finite decomposition space (aka 2-Segal spac e) admits an abstract zeta function as an element of its incidence algebra . In this talk\, I will show how many 'classical' zeta functions from numb er theory and algebraic geometry can be realized in this homotopical frame work\, and outline some preliminary work in progress with Julie Bergner an d Matt Feller towards a motivic version of the above story.\n\nThe discuss ion for Andrew Kobin’s talk is taking place not in zoom-chat\, but at ht tps://tinyurl.com/2020-09-11-ak (and will be deleted after 3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Richard Thomas (Imperial College London) DTSTART:20200925T190000Z DTEND:20200925T200000Z DTSTAMP:20260419T185122Z UID:agstanford/24 DESCRIPTION:Title: Square root Euler classes and counting sheaves on Calabi-Yau 4- folds\nby Richard Thomas (Imperial College London) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nI will explain a nice character istic class of $SO(2n\,\\mathbf{C})$ bundles in both Chow cohomology and K -theory\, and how to localise it to the zeros of an isotropic section. Thi s builds on work of Edidin-Graham\, Polishchuk-Vaintrob\, Anderson and man y others.\n\nThis can be used to construct an algebraic virtual cycle (and virtual structure sheaf) on moduli spaces of stable sheaves on Calabi-Yau 4-folds.\nIt recovers the real derived differential geometry virtual cycl e of Borisov-Joyce but has nicer properties\, like a torus localisation fo rmula. Joint work with Jeongseok Oh (KIAS).\n\nThe discussion for Richard Thomas’s talk is taking place not in zoom-chat\, but at https://tinyurl. com/2020-09-25-rt (and will be deleted after 3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Jarod Alper (University of Washington) DTSTART:20201023T190000Z DTEND:20201023T200000Z DTSTAMP:20260419T185122Z UID:agstanford/25 DESCRIPTION:Title: Coherent completeness and the local structure of algebraic stac ks\nby Jarod Alper (University of Washington) as part of Stanford alge braic geometry seminar\n\n\nAbstract\nFormal GAGA is an important theorem in formal geometry which categorizes coherent sheaves on a scheme proper o ver a complete local noetherian ring in terms of compatible families of co herent sheaves on the thickenings of its central fiber. We will discuss g eneralizations of this result to algebraic stacks and explain how such res ults can be used to prove local structure theorems for algebraic stacks. After reviewing joint work with Hall and Rydh which establishes a satisfac tory result in characteristic 0\, we will discuss partial progress in join t work with Hall and Lim on extending this result to positive characterist ic.\n LOCATION:https://master.researchseminars.org/talk/agstanford/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Aaron Landesman (Stanford) DTSTART:20201030T190000Z DTEND:20201030T200000Z DTSTAMP:20260419T185122Z UID:agstanford/26 DESCRIPTION:Title: The Torelli map restricted to the hyperelliptic locus\nby A aron Landesman (Stanford) as part of Stanford algebraic geometry seminar\n \n\nAbstract\nThe classical Torelli theorem states that the Torelli map\, sending a curve to\nits Jacobian\, is injective on points. However\, the T orelli map is not injective \non tangent spaces at points corresponding to hyperelliptic curves. This leads to\nthe natural question: If one restric ts the Torelli map to the locus of\nhyperelliptic curves\, is it then an i mmersion?\n\nWe give a complete answer to this question\, starting out by describing the\nclassical history and several surprising foundational gaps in the\nliterature. Along the way\, we will learn about Shinichi Mochizuk i's valuative\ncriterion for locally closed immersions and its relation to Brian Conrad's\nlibrary app idea.\n\nThe discussion for Aaron Landesman ’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/ 2020-10-30-al (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Juliette Bruce (UC Berkeley) DTSTART:20201002T190000Z DTEND:20201002T200000Z DTSTAMP:20260419T185122Z UID:agstanford/27 DESCRIPTION:Title: The top weight cohomology of $A_g$\nby Juliette Bruce (UC B erkeley) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nI w ill discuss recent work calculating the top weight cohomology of the modul i space $A_g$ of principally polarized abelian varieties of dimension $g$ for small values of $g$. The key idea is that this piece of cohomology is encoded combinatorially via the relationship between the boundary complex of a compactification of $A_g$ and the moduli space of tropical abelian va rieties. This is joint work with Madeline Brandt\, Melody Chan\, Margarida Melo\, Gwyneth Moreland\, and Corey Wolfe.\n LOCATION:https://master.researchseminars.org/talk/agstanford/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Ben Antieau (Northwestern) DTSTART:20210115T200000Z DTEND:20210115T210000Z DTSTAMP:20260419T185122Z UID:agstanford/28 DESCRIPTION:Title: Genus 1 curves in twisted projective spaces\nby Ben Antieau (Northwestern) as part of Stanford algebraic geometry seminar\n\n\nAbstra ct\nDoes every Severi—Brauer variety contain a (possibly singular) genus 1 curve? This basic question was asked by David Saltman and Pete Clark an d answered in low dimensions by Johan de Jong and Wei Ho. I will explain s omething of the history of the problem as well as recent joint work with A sher Auel where we show\, with the help of a nice observation of David Sal tman\, that the answer is `yes’ for twisted forms of $\\mathbb{P}^r$ for $r=6$ over global fields.\n\nThe discussion for Ben Antieau’s talk is t aking place not in zoom-chat\, but at https://tinyurl.com/2021-01-15-ba (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Karen Smith (University of Michigan) DTSTART:20201009T190000Z DTEND:20201009T200000Z DTSTAMP:20260419T185122Z UID:agstanford/29 DESCRIPTION:Title: Extremal Singularities in Prime Characteristic\nby Karen Sm ith (University of Michigan) as part of Stanford algebraic geometry semina r\n\n\nAbstract\nWhat is the most singular possible singularity? What can we say about its geometric and algebraic properties? This seemingly naive question has a sensible answer in characteristic $p$.\nThe "F-pure thresho ld\," which is an analog of the log canonical threshold\, can be used to "measure" how bad a singularity is. The F-pure threshold is a numerical in variant of a point on (say) a hypersurface---a positive rational number that is 1 at any smooth point (or more generally\, any F-pure point) but l ess than one in general\, with "more singular" points having smaller F-pur e thresholds. We explain a recently proved lower bound on the F-pure thre shold in terms of the multiplicity of the singularity. We also show that t here is a nice class of hypersurfaces---which we call "Extremal hypersurfa ces"---for which this bound is achieved. These have very nice (extreme!) g eometric properties. For example\, the affine cone over a non Frobenius sp lit cubic surface of characteristic two is one example of an "extremal sin gularity". Geometrically\, these are the only cubic surfaces with the prop erty that *every* triple of coplanar lines on the surface meets in a singl e point (rather than a "triangle" as expected)---a very extreme property i ndeed.\n\nThe discussion for Karen Smith’s talk is taking place not in z oom-chat\, but at https://tinyurl.com/2020-10-09-ks (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Barbara Fantechi (SISSA) DTSTART:20201016T190000Z DTEND:20201016T200000Z DTSTAMP:20260419T185122Z UID:agstanford/30 DESCRIPTION:Title: Infinitesimal deformations of semi-smooth varieties\nby Bar bara Fantechi (SISSA) as part of Stanford algebraic geometry seminar\n\n\n Abstract\nThis is a report on joint work with Marco Franciosi and Rita Par dini. Generalizing the standard definition for surfaces\, we call a variet y $X$ (over an alg closed field of char not 2) {\\em semi-smooth} if its s ingularities are \\'etale locally either $uv=0$ or $u^2=v^2w$ (pinch point )\; equivalently\, if $X$ can be obtained by gluing a smooth variety (the normalization of $X$) along an involution (with smooth quotient) on a smoo th divisor. They are the simplest singularities for non normal\, KSBA-stab le surfaces.\nFor a semi-smooth variety $X$\, we calculate the tangent she af $T_X$ and the infinitesimal deformations sheaf ${\\mathcal T}^1_X:={\\m athcal E}xt^1(\\Omega_X\,\\mathcal O_X)$ which determine the infinitesimal deformations and smoothability of $X$.\nAs an application\, we use Tziola s' formal smoothability criterion to show that every stable semi-smooth Go deaux surface (classified by Franciosi\, Pardini and S\\"onke) corresponds to a smooth point of the KSBA moduli space\, in the closure of the open l ocus of smooth surfaces.\n\nThe discussion for Barbara Fantechi’s talk i s taking place not in zoom-chat\, but at https://tinyurl.com/2020-10-16-bf (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Akhil Mathew (University of Chicago) DTSTART:20201106T200000Z DTEND:20201106T210000Z DTSTAMP:20260419T185122Z UID:agstanford/31 DESCRIPTION:Title: \\'Etale K-theory and motivic cohomology\nby Akhil Mathew ( University of Chicago) as part of Stanford algebraic geometry seminar\n\n\ nAbstract\nTwo key features of algebraic K-theory are its failure to\nsati sfy \\'etale descent\, and its motivic filtration in terms of higher\nChow groups in the case of smooth schemes over a field (but expected\nmore gen erally). I will explain a description of \\'etale K-theory\,\nwhich is the universal approximation to K-theory that satisfies\n\\'etale descent\; th is is joint work with Dustin Clausen. Moreover\,\nfollowing the recent wor k of Bhatt--Morrow--Scholze on topological\ncyclic homology\, I will also explain a construction of (an analog of)\nthe motivic filtration on \\'eta le K-theory (and \\'etale motivic\ncohomology) for arbitrary schemes (work in progress with Bhargav Bhatt\nand Dustin Clausen).\n LOCATION:https://master.researchseminars.org/talk/agstanford/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Taylor Dupuy (University of Vermont) DTSTART:20201113T200000Z DTEND:20201113T210000Z DTSTAMP:20260419T185122Z UID:agstanford/32 DESCRIPTION:Title: Abelian Varieties Over Finite Fields in the LMFDB\nby Taylo r Dupuy (University of Vermont) as part of Stanford algebraic geometry sem inar\n\n\nAbstract\nI will talk about things around the LMFDB database of isogeny classes of abelian varieties over finite fields (and maybe even ab out isomorphism classes). \n\nThese could include: \n--"Sato-Ain't" distri butions\, \n--weird Tate classes\, \n--Bizzaro Hodge co-levels (and very s trange Ax-Katz/Chevalley-Warning type congruences with fractional exponent !)\, \n--the counter-example to the conjecture of Ahmadi-Shparlinski\,\n-- what we know about angle ranks vs galois groups vs Newton polygons\,\n--ne w conjectures \n\nThe database and "census" is joint work with Kiran Kedla ya\, David Roe\, and Christelle Vincent (currently available on the arxiv) . The work on Tate classes is ongoing with Kiran Kedlaya and David Zureick -Brown.\n LOCATION:https://master.researchseminars.org/talk/agstanford/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Rahul Pandharipande (ETH Zurich) DTSTART:20201204T200000Z DTEND:20201204T210000Z DTSTAMP:20260419T185122Z UID:agstanford/33 DESCRIPTION:Title: The top Chern class of the Hodge bundle and the log Chow ring o f the moduli space of curves\nby Rahul Pandharipande (ETH Zurich) as p art of Stanford algebraic geometry seminar\n\n\nAbstract\nI will first exp lain how the top Chern class of the Hodge bundle is very complicated and t hen\nI will explain how it is very simple. Joint work with S. Molcho and J . Schmitt.\n LOCATION:https://master.researchseminars.org/talk/agstanford/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Takumi Murayama (Princeton University) DTSTART:20210122T200000Z DTEND:20210122T210000Z DTSTAMP:20260419T185122Z UID:agstanford/34 DESCRIPTION:Title: Grothendieck's localization problem\nby Takumi Murayama (Pr inceton University) as part of Stanford algebraic geometry seminar\n\n\nAb stract\nLet $f\\colon Y \\rightarrow X$ be a proper flat morphism of alge braic varieties. Grothendieck and Dieudonné showed that the smoothness of $f$ can be detected at closed points of $X$. Using André–Quillen homol ogy\, André showed that when $X$ is excellent\, the same conclusion holds when $f$ is a closed flat morphism between locally noetherian schemes. We give a new proof of André's result using a version of resolutions of sin gularities due to Gabber. Our method gives a uniform treatment of Grothend ieck's localization problem and resolves various new cases of this problem \, which asks whether similar statements hold for other local properties o f morphisms.\n LOCATION:https://master.researchseminars.org/talk/agstanford/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Soumya Sankar (The Ohio State University) DTSTART:20210129T200000Z DTEND:20210129T210000Z DTSTAMP:20260419T185122Z UID:agstanford/35 DESCRIPTION:Title: Derived equivalences of gerbey curves\nby Soumya Sankar (Th e Ohio State University) as part of Stanford algebraic geometry seminar\n\ n\nAbstract\nThe question of whether derived equivalences determine a vari ety has been studied widely. Antieau\, Krashen and Ward (AKW) studied the question of when two genus 1 curves are derived equivalent. A gerbey curve is a G_m gerbe over a usual curve. In joint work with Libby Taylor\, we e xplore the question of when two gerbey genus 1 curves are derived equivale nt. In this talk\, I will give some background on derived equivalences of varieties\, how they relate to derived equivalences of stacks and then tal k about some extensions of the results of AKW.\n\nThe discussion for Soumy a Sankar’s talk is taking place not in zoom-chat\, but at https://tinyur l.com/2021-01-29-ss (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Sean Keel (UT Austin) DTSTART:20210205T200000Z DTEND:20210205T210000Z DTSTAMP:20260419T185122Z UID:agstanford/36 DESCRIPTION:Title: Berkovich geometry and mirror symmetry\nby Sean Keel (UT Au stin) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nI will explain my Berkovich geometric construction\, joint with Tony Yu\, of the mirror to an affine log CY variety\, with the aim of convincing you of it s simplicity\, both in concept\, and technical detail.\n LOCATION:https://master.researchseminars.org/talk/agstanford/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Laure Flapan (Michigan State) DTSTART:20210212T200000Z DTEND:20210212T210000Z DTSTAMP:20260419T185122Z UID:agstanford/37 DESCRIPTION:Title: Fano manifolds associated to hyperkähler manifolds\nby Lau re Flapan (Michigan State) as part of Stanford algebraic geometry seminar\ n\n\nAbstract\nMany of the known examples of hyperkähler manifolds arise from geometric constructions that begin with a Fano manifold whose cohomol ogy looks like that of a K3 surface. In this talk\, I will focus on a prog ram whose goal is to reverse this process\, namely to begin with a hyperk ähler manifold and from it produce geometrically a Fano manifold. This is joint work in progress with K. O’Grady\, E. Macrì\, and G. Saccà.\n\n The discussion for Laure Flapan’s talk is taking place not in zoom-chat\ , but at https://tinyurl.com/2021-02-12-lf (and will be deleted after ~3 -7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Izzet Coskun (University of Illinois at Chicago) DTSTART:20210219T200000Z DTEND:20210219T210000Z DTSTAMP:20260419T185122Z UID:agstanford/38 DESCRIPTION:Title: Algebraic Hyperbolicity and Lang-type loci in hypersurfaces \nby Izzet Coskun (University of Illinois at Chicago) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nIn this talk\, I will discuss jo int work with Eric Riedl on algebraic hyperbolicity and Lang-type loci. I will describe an improvement of G. Xu's genus bounds which allow us to pro ve the algebraic hyperbolicity of very general quintic surfaces. The same technique allows us to obtain the classification of algebraically hyperbo lic surfaces in certain toric threefolds. Finally\, I will discuss Lang-ty pe loci for algebraic hyperbolicity in very general hypersurfaces.\n\nThe discussion for Izzet Coskun’s talk is taking place not in zoom-chat\, bu t at https://tinyurl.com/2021-02-19-ic (and will be deleted after ~3-7 d ays).\n LOCATION:https://master.researchseminars.org/talk/agstanford/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Matt Baker (Georgia Tech) DTSTART:20210402T190000Z DTEND:20210402T200000Z DTSTAMP:20260419T185122Z UID:agstanford/39 DESCRIPTION:Title: Pastures\, Polynomials\, and Matroids\nby Matt Baker (Georg ia Tech) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nA p asture is\, roughly speaking\, a field in which addition is allowed to be both multivalued and partially undefined. Pastures are natural objects fro m the point of view of $\\mathbf{F}_1$ geometry and Lorscheid’s theory o f ordered blueprints. I will describe a theorem about univariate polynomia ls over pastures which simultaneously generalizes Descartes’ Rule of Sig ns and the theory of Newton polygons. Conjecturally\, there should be a si milar picture for several polynomials in several variables generalizing tr opical intersection theory. I will also describe a novel approach to the t heory of matroid representations which revolves around a canonical univers al pasture\, called the “foundation”\, that one can attach to any matr oid. This is joint work with Oliver Lorscheid.\n\nThe discussion for Matt Baker’s talk is taking place not in zoom-chat\, but at https://tinyurl. com/2021-04-02-mb (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Jihao Liu (University of Utah) DTSTART:20210226T200000Z DTEND:20210226T210000Z DTSTAMP:20260419T185122Z UID:agstanford/40 DESCRIPTION:Title: Complements and local singularities in birational geometry\ nby Jihao Liu (University of Utah) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nThe theory of complements was introduced by Shokuro v when he investigated log flips of threefolds\, and plays an important ro le in many areas in birational geometry\, e.g. boundedness of Fano varieti es\, log Calabi-Yau fibrations\, K-stability theory\, etc. In a recent wor k\, we prove a complements conjecture of Shokurov\, and we apply this resu lt to the study of local singularities in birational geometry. Part of thi s talk is joint work with J. Han and V.V. Shokurov.\n LOCATION:https://master.researchseminars.org/talk/agstanford/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Arend Bayer (University of Edinburgh) DTSTART:20210305T200000Z DTEND:20210305T210000Z DTSTAMP:20260419T185122Z UID:agstanford/41 DESCRIPTION:Title: Fano varieties: from derived categories to geometry via stabili ty\nby Arend Bayer (University of Edinburgh) as part of Stanford algeb raic geometry seminar\n\n\nAbstract\nA Fano variety $X$ can be reconstruct ed from its bounded derived category $D^b(X)$. How to use this fact to ext ract\nconcrete geometric information from $D^b(X)$? \nIn this talk\, I wil l survey one such approach\, via certain subcategories of $D^b(X)$ called Kuznetsov components\, and stability conditions. Via moduli spaces of stab le objects inside Kuznetsov components\, this naturally leads to the recon struction of many natural moduli spaces classically associated to $X$. \nI n addition to results by a number of authors for Fano threefolds\, I will also discuss work in progress (joint with Bertram\, Macri\, Perry) for cub ic fourfolds. Combined with studying Brill-Noether loci\, this leads to th e construction of special surfaces on an infinite sequence of Hassett-spec ial cubic fourfolds. In some cases\, this leads to a natural reinterpretat ion of recent proofs of rationality of such cubic fourfolds via wall-cross ing.\n LOCATION:https://master.researchseminars.org/talk/agstanford/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuuji Tanaka (Kyoto University) DTSTART:20210313T000000Z DTEND:20210313T010000Z DTSTAMP:20260419T185122Z UID:agstanford/42 DESCRIPTION:Title: On the virtual Euler characteristics of the moduli spaces of s emistable sheaves on a complex projective surface\nby Yuuji Tanaka (Ky oto University) as part of Stanford algebraic geometry seminar\n\n\nAbstra ct\n(warning: notice unusual time)\n\nI'll deliver an overview of studies on the virtual Euler \ncharacteristics of the moduli spaces of semistable sheaves on a complex \nprojective surface. The virtual Euler characterist ic is a refinement of \nthe topological Euler characteristic for a proper scheme with a perfect \nobstruction theory，which was introduced by Fante chi and Goettsche\, and \nby Ciocan-Fontanine and Kapranov. Motivated by t he work of Vafa and \nWitten in the early 90's on the S-duality conjecture in N=4 super \nYang-Mills theory in physics\, Goettsche and Kool conjectu red that the \ngenerating function of the virtual Euler characteristics\, or other \nvariants\, of the moduli space of semistable sheaves on a compl ex \nprojective surfaces could be written in terms of modular forms (and t he \nSeiberg-Witten invariants)\, and they verified it in examples. I'll \ ndescribe the recent progress around this topic\, starting by mentioning \ nmore background materials such as the studies on the topological Euler \n characteristics of the moduli spaces.\n LOCATION:https://master.researchseminars.org/talk/agstanford/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Geoff Smith (UIC) DTSTART:20210507T190000Z DTEND:20210507T200000Z DTSTAMP:20260419T185122Z UID:agstanford/43 DESCRIPTION:Title: Normal bundles of rational curves and separably rationally conn ected varieties\nby Geoff Smith (UIC) as part of Stanford algebraic ge ometry seminar\n\n\nAbstract\nIn positive characteristic\, there are two d ifferent notions of rational connectedness: a variety can be rationally co nnected or separably rationally connected (SRC). SRC varieties share many of the nice properties that rationally connected varieties have in charact eristic 0. But\, while it is conjectured that smooth Fano varieties are SR C\, it is only known that they are rationally connected. In the last decad e\, several mathematicians have come up with different ways to show that g eneral Fano complete intersections are SRC. In this talk\, I'll explain th is story\, and then discuss an approach Izzet Coskun and I are using to sh ow that other sorts of varieties are SRC by comparing the normal bundle of a rational curve on a variety and its normal bundle to some subvariety co ntaining it. For instance\, I'll show that a Fano complete intersection of hypersurfaces each of degree at least 3 on a Grassmannian is SRC.\n\nThe discussion for Geoff Smith’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/2021-05-07-gs (and will be deleted after ~3-7 days ).\n LOCATION:https://master.researchseminars.org/talk/agstanford/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Nikolas Kuhn (Stanford University) DTSTART:20210326T190000Z DTEND:20210326T200000Z DTSTAMP:20260419T185122Z UID:agstanford/44 DESCRIPTION:Title: A blowup formula for virtual Donaldson invariants\nby Nikol as Kuhn (Stanford University) as part of Stanford algebraic geometry semin ar\n\n\nAbstract\nDonaldson invariants were a breakthrough in the study of smooth four-manifolds when they were introduced in the 1980s and even fou nd applications to the classification of compact complex surfaces. With th e advent of the virtual fundamental class\, it has become possible to give an elegant purely algebraic definition when working on a complex projecti ve surface X\, which was done by T. Mochizuki. The two definitions agree i n most cases\, and whether they agree in general comes down to knowing a b lowup formula for Mochizuki's invariants. We present a direct proof of suc h a blowup formula that generalizes earlier results by Göttsche-Nakajima- Yoshioka and has applications to other types of enumerative invariants of X. This is joint work with Yuuji Tanaka.\n\nThe discussion for Nikolas Kuh n’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/2 021-03-26-nk (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Joachim Jelisiejew (University of Warsaw) DTSTART:20210514T190000Z DTEND:20210514T200000Z DTSTAMP:20260419T185122Z UID:agstanford/45 DESCRIPTION:Title: Pathologies on the Hilbert scheme of points\nby Joachim Jel isiejew (University of Warsaw) as part of Stanford algebraic geometry semi nar\n\n\nAbstract\nIn the talk I will discuss recent advances in our under standing of singularities and components of the Hilbert scheme of points o n a higher-dimensional smooth variety. The key underlying tool\, interesti ng on its own\, is the Bialynicki-Birula decomposition in the singular set ting. I will mention some open questions.\n LOCATION:https://master.researchseminars.org/talk/agstanford/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Molcho (ETH) DTSTART:20210409T190000Z DTEND:20210409T200000Z DTSTAMP:20260419T185122Z UID:agstanford/46 DESCRIPTION:Title: The strict transform in logarithmic geometry\nby Sam Molcho (ETH) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nLet $ (X\,D)$ be a pair of a smooth variety and a normal crossings divisor. The loci of curves that admit a map to X with prescribed tangency along D exhi bit some pathological behavior: for instance\, the locus of maps to a prod uct $(X \\times Y\, D \\times E)$ does not coincide with the intersection of the loci of maps to $(X\,D)$ and $(Y\,E)$. In this talk I want to expla in how the root of such pathologies arises from the difference between tak ing the strict and total of a cycle under a very special kind of birationa l map\, called a logarithmic modification. I will discuss how for a logari thmic modification\, the strict transform of a cycle has a modular interpr etation\, and how its difference with the total transform can be explicitl y computed\, in terms of certain piecewise polynomial functions on a combi natorial shadow of the original spaces\, the tropicalization. Time permitt ing\, I will discuss some applications -- for instance\, how these calcula tions imply that loci of curves with a map to a toric variety lie in the t autological ring.\n LOCATION:https://master.researchseminars.org/talk/agstanford/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Samir Canning (UC San Diego) DTSTART:20210416T190000Z DTEND:20210416T200000Z DTSTAMP:20260419T185122Z UID:agstanford/47 DESCRIPTION:Title: The Chow rings of $M_7$\, $M_8$\, and $M_9$\nby Samir Canni ng (UC San Diego) as part of Stanford algebraic geometry seminar\n\n\nAbst ract\nThe rational Chow ring of the moduli space of smooth curves is known when the genus is at most $6$ by work of Mumford ($g=2$)\, Faber ($g=3$\, $4$)\, Izadi ($g=5$)\, and Penev-Vakil ($g=6$). In each case\, it is gene rated by the tautological classes. On the other hand\, van Zelm has shown that the bielliptic locus is not tautological when $g=12$. In recent joint work with Hannah Larson\, we show that the Chow rings of $M_7$\, $M_8$\, and $M_9$ are generated by tautological classes\, which determines the Cho w ring by work of Faber. I will explain an overview of the proof with an e mphasis on the special geometry of curves of low genus and low gonality.\n \nThe synchronous discussion for Sam Canning’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/2021-04-16-sc (and will be delet ed after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Temkin (HUJI) DTSTART:20210423T190000Z DTEND:20210423T200000Z DTSTAMP:20260419T185122Z UID:agstanford/48 DESCRIPTION:Title: Logarithmic resolution of singularities\nby Michael Temkin (HUJI) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nI wil l talk about a recent series of works with Abramovich and Wlodarczyk\, whe re a logarithmic analogue of the classical resolution of singularities of schemes in characteristic zero is constructed. Already for usual schemes\, the logarithmic algorithm is faster and more functorial\, though as a pri ce one has to work with log smooth ambient orbifolds rather than smooth am bient manifolds. But the main achievement is that essentially the same alg orithm resolves log schemes and even morphisms of log schemes\, yielding a major generalization of various semistable reduction theorems.\n\nThe syn chronous discussion for Michael Temkin’s talk is taking place not in zoo m-chat\, but at https://tinyurl.com/2021-04-23-mt (and will be deleted af ter ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Remy van Dobben de Bruyn (Princeton and IAS) DTSTART:20210430T190000Z DTEND:20210430T200000Z DTSTAMP:20260419T185122Z UID:agstanford/49 DESCRIPTION:Title: Constructing varieties with prescribed Hodge numbers modulo m i n positive characteristic\nby Remy van Dobben de Bruyn (Princeton and IAS) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nThe inv erse Hodge problem asks which possible Hodge diamonds can occur for smooth projective varieties. While this is a very hard problem in general\, Paul sen and Schreieder recently showed that in characteristic 0 there are no r estrictions on the modulo $m$ Hodge numbers\, besides the usual symmetries . In joint work with Matthias Paulsen\, we extend this to positive charact eristic\, where the story is more intricate.\n\nThe synchronous discussion for Remy van Dobben de Bruyn’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/2021-04-30-rvddb (and will be deleted after ~ 3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Eric Katz (Ohio State) DTSTART:20210521T190000Z DTEND:20210521T200000Z DTSTAMP:20260419T185122Z UID:agstanford/50 DESCRIPTION:Title: Iterated p-adic integration on semistable curves\nby Eric K atz (Ohio State) as part of Stanford algebraic geometry seminar\n\n\nAbstr act\nHow do you integrate a 1-form on an algebraic curve over the p-adic n umbers? One can integrate locally\, but because the topology is totally di sconnected\, it's not possible to perform analytic continuation. For good reduction curves\, this question was answered by Coleman who introduced an alytic continuation by Frobenius. For bad reduction curves\, there are two notions of integration: a local theory that is easy to compute\; and a gl obal single-valued theory that is useful for number theoretic applications . We discuss the relationship between these integration theories\, concent rating on the p-adic analogue of Chen's iterated integration which is impo rtant for the non-Abelian Chabauty method. We explain how to use combinato rial ideas\, informed by tropical geometry and Hodge theory\, to compare t he two integration theories and outline an explicit approach to computing these integrals. This talk will start from the beginning of the story and requires no background besides some fluency in algebraic geometry and topo logy. This is joint work with Daniel Litt.\n\nThe synchronous discussion f or Eric Katz’s talk is taking place not in zoom-chat\, but at https://ti nyurl.com/2021-05-21-ek (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Ulirsch (Goethe-Universität Frankfurt) DTSTART:20210604T190000Z DTEND:20210604T200000Z DTSTAMP:20260419T185122Z UID:agstanford/51 DESCRIPTION:Title: Tropical geometry and logarithmic compactifications of reductiv e algebraic groups\nby Martin Ulirsch (Goethe-Universität Frankfurt) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nIn this talk I will present two approaches towards the tropicalization of a reductive algebraic group $G$\, one via Mumford’s toroidal compactification\, the other via de Concini and Procesi’s wonderful compacitification. The Bruh at-Tits building of G and its root system will play a crucial role in both approaches. Using these insights I will propose two corresponding logarit hmic compactifications of $G$. The first approach will provide us with a n ew logarithmic perspective on toric (and more generally parabolic) vector bundles\, the other will allow us to study the geometry of the free group character variety at infinity\, thereby providing evidence for the geometr ic $P=W$ conjecture. Depending on the preferences of the audience I might also engage in some wild speculations concerning a yet-to-be-discovered lo garithmic incarnation of Simpson’s non-abelian Hodge correspondence. Par ts of this talk are based on ongoing joint work with Lorenzo Fantini and A lex Kuronya.\n\nThe synchronous discussion for Martin Ulirsch’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/2021-06-04-mu (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Dhruv Ranganathan (Cambridge) DTSTART:20210528T190000Z DTEND:20210528T200000Z DTSTAMP:20260419T185122Z UID:agstanford/52 DESCRIPTION:Title: Constructing logarithmic moduli\nby Dhruv Ranganathan (Camb ridge) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nIn re cent work\, Davesh Maulik and I built a theory “logarithmic” Donaldson -Thomas invariants\, and in the process we constructed a new version of th e Hilbert scheme of curves: one that is sensitive to the manner in which s ubschemes interact with a chosen simple normal crossings divisor. There ar e two inputs. The first is a piece of geometry\, which comes from study to rus orbit closures in Hilbert schemes\, following ideas of Kapranov and Te velev. The second is an exceedingly useful piece of formalism\, in the sha pe of tropical moduli spaces and an associated collection of Artin stacks. I’ll try to explain how to combine these ingredients to get what we get \, and also share some general lessons that we learned while working this stuff out.\n\nThe synchronous discussion for Dhruv Ranganathan’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/2021-05-28-dr (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Lena Ji (Princeton/Michigan) DTSTART:20210611T190000Z DTEND:20210611T200000Z DTSTAMP:20260419T185122Z UID:agstanford/53 DESCRIPTION:Title: The Noether–Lefschetz theorem\nby Lena Ji (Princeton/Mich igan) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nThe cl assical Noether–Lefschetz theorem says that for a very general surface $ S$ of degree $ \\geq 4$ in $\\mathbf{P}^3$ over the complex numbers\, the restriction map from the divisor class group on $\\mathbf{P}^3$ to $S$ is an isomorphism. In this talk\, we give an elementary proof of Noether–Le fschetz. We do not use any Hodge theory\, cohomology\, or monodromy. This argument has the additional advantage that it works over fields of arbitra ry characteristic and for singular varieties (for Weil divisors).\n\nThe s ynchronous discussion for Lena Ji’s talk is taking place not in zoom-cha t\, but at https://tinyurl.com/2021-06-11-lj (and will be deleted after ~ 3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Federico Scavia (UBC) DTSTART:20210730T190000Z DTEND:20210730T200000Z DTSTAMP:20260419T185122Z UID:agstanford/54 DESCRIPTION:Title: The Grothendieck ring of stacks\nby Federico Scavia (UBC) a s part of Stanford algebraic geometry seminar\n\n\nAbstract\nThe Grothendi eck ring of algebraic stacks was introduced by T. Ekedahl in \n2009\, foll owing up on work of other authors. It is a generalization of the \nGrothen dieck ring of varieties. For every linear algebraic group $G$\, we may \nc onsider the class of its classifying stack $BG$ in this ring. Computing th e \nclass of $BG$ is related to the famous rationality problem for fields of \n$G$-invariants (Noether's problem). I will give a brief introduction to the \nGrothendieck ring of stacks\, and then talk about some of my resu lts in this \narea.\n\nThe synchronous discussion for Federico Scavia’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/2021-07 -30-fs (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Raymond Cheng (Columbia) DTSTART:20210716T190000Z DTEND:20210716T200000Z DTSTAMP:20260419T185122Z UID:agstanford/55 DESCRIPTION:Title: $q$-bic Hypersurfaces\nby Raymond Cheng (Columbia) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nLet’s count: 1\, $ q$\, $q+1$\; here\, $q$ is a power of a prime $p$. In this talk\, I will s ketch an analogy between the geometry of a class of hypersurfaces over a f ield of positive characteristic $p$\, which I call $q$-bic hypersurfaces\, and the geometry of low degree hypersurfaces\, such as quadrics and cubic s\, over the complex numbers. For instance\, a smooth $q$-bic threefold ha s a smooth Fano surface of lines\, and the intermediate Jacobian of the th reefold is isogenous to the Albanese of the Fano surface.\n LOCATION:https://master.researchseminars.org/talk/agstanford/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Ritvik Ramkumar (Berkeley) DTSTART:20210806T190000Z DTEND:20210806T200000Z DTSTAMP:20260419T185122Z UID:agstanford/56 DESCRIPTION:Title: On the tangent space to the Hilbert scheme of points in $\\math bf{P}^3$\nby Ritvik Ramkumar (Berkeley) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nThe Hilbert scheme of $n$ points in $\\mat hbf{P}^2$ is smooth of dimension $2n$ and the tangent space to any monomia l subscheme admits a pleasant combinatorial description. On the other hand \, the Hilbert scheme of $n$ points in $\\mathbf{P}^3$ is almost always si ngular and there is a conjecture by Briançon and Iarrobino describing the monomial subscheme with the largest tangent space dimension. In this talk we will generalize the combinatorial description to the Hilbert scheme of points in $\\mathbf{P}^3$\, revealing new symmetries in the tangent space to any monomial subscheme. We will use these symmetries to prove many cas es of the conjecture and strengthen previous bounds on the dimension of th e Hilbert scheme. In addition\, we will also characterize smooth monomial points on the Hilbert scheme. This is joint work with Alessio Sammartano.\ n LOCATION:https://master.researchseminars.org/talk/agstanford/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Elden Elmanto (Harvard) DTSTART:20210813T190000Z DTEND:20210813T200000Z DTSTAMP:20260419T185122Z UID:agstanford/57 DESCRIPTION:Title: The completely decomposed arc topology and motivic applications \nby Elden Elmanto (Harvard) as part of Stanford algebraic geometry se minar\n\n\nAbstract\nI will introduce a Grothendieck topology\, the cdarc topology\, discovered in joint work with Marc Hoyois\, Ryomei Iwasa and Sh ane Kelly which is a completely decomposed counterpart to Bhatt and Mathew 's arc topology. It is a non-noetherian analog of Suslin-Voevodsky's cdh t opology and is thus useful in the study of K-theory and algebraic cycles. I will focus on two applications to algebraic cycles and K-theory:\n\n1) a n excision result for algebraic cycles (joint with Hoyois\, Iwasa and Kell y) and\n\n2) a motivic refinement of the equivalence $L_{cdh}K = KH$ (join t with Tom Bachmann and Matthew Morrow).\n\nThe synchronous discussion for Elden Elmanto’s talk is taking place not in zoom-chat\, but at https:// tinyurl.com/2021-08-13-ee (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Ming Hao Quek (Brown University) DTSTART:20210924T190000Z DTEND:20210924T200000Z DTSTAMP:20260419T185122Z UID:agstanford/58 DESCRIPTION:Title: Logarithmic resolution of singularities via multi-weighted blow -ups\nby Ming Hao Quek (Brown University) as part of Stanford algebrai c geometry seminar\n\n\nAbstract\nWe revisit the theorem of Hironaka that one can resolve the singularities of a singular\, reduced closed subscheme X of a smooth scheme Y over a field of characteristic zero\, such that th e singular locus of X is transformed to a simple normal crossings divisor. We propose a computable yet efficient algorithm\, which accomplishes this by taking successive proper transforms along a sequence of multi-weighted blow-ups\, where at each step\, the worst singular locus is blown up\, an d one witnesses an immediate improvement in singularities. Here\, multi-we ighted blow-ups are necessary to ensure that the ambient space remains smo oth (in fact\, also logarithmically smooth with respect to the logarithmic structure associated to the exceptional divisors)\, although one has to w ork more broadly with Artin stacks. This is joint work with Dan Abramovich .\n LOCATION:https://master.researchseminars.org/talk/agstanford/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Maria Yakerson (ETH) DTSTART:20210910T190000Z DTEND:20210910T200000Z DTSTAMP:20260419T185122Z UID:agstanford/59 DESCRIPTION:Title: Twisted K-theory in motivic homotopy theory\nby Maria Yaker son (ETH) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nIn this talk\, we will speak about algebraic K-theory of vector bundles twis ted by a Brauer class\, and its place in motivic homotopy theory. In parti cular\, we will discuss a new approach to the motivic spectral sequence fo r twisted K-theory\, constructed earlier by Bruno Kahn and Marc Levine. Th e talk is based on joint work in progress\, with Elden Elmanto and Denis N ardin.\n LOCATION:https://master.researchseminars.org/talk/agstanford/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Tom Graber (Caltech) DTSTART:20210723T190000Z DTEND:20210723T200000Z DTSTAMP:20260419T185122Z UID:agstanford/60 DESCRIPTION:Title: Virtual localization for relative obstruction theories and stab le log maps\nby Tom Graber (Caltech) as part of Stanford algebraic geo metry seminar\n\n\nAbstract\nI will discuss how to formulate and prove a l ocalization theorem for the virtual fundamental class of a moduli space wi th a relative perfect obstruction theory over a singular base. In the mot ivating example of the moduli space of stable log maps\, I will explain ho w this leads to sums over types of tropical curves and cycle classes on mo duli spaces of curves related to the double ramification cycle that have b een of recent interest in other contexts.\n LOCATION:https://master.researchseminars.org/talk/agstanford/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Denis Nardin (Regensburg) DTSTART:20210709T190000Z DTEND:20210709T200000Z DTSTAMP:20260419T185122Z UID:agstanford/61 DESCRIPTION:Title: Quadratic forms on rings and the homotopy limit problem\nby Denis Nardin (Regensburg) as part of Stanford algebraic geometry seminar\ n\n\nAbstract\nHermitian K-theory is an invariant of rings (or\, more gene rally\, schemes) constructed using the behaviour of quadratic forms. In re cent years significant progress has been made in the study of it for rings where 2 is not invertible. In this talk I will give an introduction to th e subject from a modern perspective\, using as a guide work in progress on the homotopy limit problem\, which essentially is asking how much informa tion we can recover from just knowing the algebraic K-theory of the ring.\ n LOCATION:https://master.researchseminars.org/talk/agstanford/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Joaquín Moraga (Princeton University) DTSTART:20211008T190000Z DTEND:20211008T200000Z DTSTAMP:20260419T185122Z UID:agstanford/62 DESCRIPTION:Title: ​​Toroidalization principles for klt singularities\nby Joaquín Moraga (Princeton University) as part of Stanford algebraic geome try seminar\n\n\nAbstract\nIn this talk\, I will discuss some recent progr ess on toroidalization principles for klt singularities. These toroidaliz ations allow us to prove theorems about the topology of klt singularities and about their minimal log discrepancies. If time permits\, I will also explain the relationship between these toroidalization principles and the termination of flips.\n LOCATION:https://master.researchseminars.org/talk/agstanford/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Maddie Weinstein (Stanford University) DTSTART:20211015T190000Z DTEND:20211015T200000Z DTSTAMP:20260419T185122Z UID:agstanford/64 DESCRIPTION:Title: Algebraic Geometry of Curvature and Matrices with Partitioned E igenvalues\nby Maddie Weinstein (Stanford University) as part of Stanf ord algebraic geometry seminar\n\n\nAbstract\nThis talk is a combined disc ussion of an upcoming paper with Paul Breiding and Kristian Ranestad on th e enumerative geometry of the curvature of algebraic varieties and a past paper called Real Symmetric Matrices with Partitioned Eigenvalues. Curvatu re is an important concept in differential geometry. We approach curvature from the perspective of algebraic geometry\, studying the critical curvat ure locus of an algebraic variety. A curvature feature known as an umbilic al point occurs when the eigenvalues of the second fundamental form coinci de. This leads us to a discussion of the real algebraic variety of matrice s with eigenvalue multiplicities determined by a partition.\n LOCATION:https://master.researchseminars.org/talk/agstanford/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Han-Bom Moon (Fordham/Stanford) DTSTART:20210917T190000Z DTEND:20210917T200000Z DTSTAMP:20260419T185122Z UID:agstanford/65 DESCRIPTION:Title: Derived category of moduli of vector bundles\nby Han-Bom Mo on (Fordham/Stanford) as part of Stanford algebraic geometry seminar\n\n\n Abstract\nI will present recent progress on the structure of the derived c ategory of the moduli space of stable vector bundles on a curve. This talk is based on ongoing joint work with Kyoung-Seog Lee.\n LOCATION:https://master.researchseminars.org/talk/agstanford/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Arnav Tripathy (Stanford University) DTSTART:20211001T190000Z DTEND:20211001T200000Z DTSTAMP:20260419T185122Z UID:agstanford/66 DESCRIPTION:Title: Line bundles in equivariant elliptic cohomology\nby Arnav T ripathy (Stanford University) as part of Stanford algebraic geometry semin ar\n\n\nAbstract\nGiven a compact Lie group G acting on a space X\, the G- equivariant elliptic cohomology of X is naturally a scheme Ell_G(X) (with a map down to the moduli space of G-bundles on elliptic curves). Given a G -equivariant vector bundle V on X\, one obtains an interesting line bundle Thom(V) on Ell_G(X). Both topologists and string theorists have predicted that given two vector bundles V_1\, V_2 whose first Chern classes both va nish and whose second Chern classes agree\, the resulting line bundles Tho m(V_1) and Thom(V_2) should agree in Pic(Ell_G(X)). I'll describe how the theory of pushforwards in topology gives rise to this subtle question in a lgebraic geometry\, and I hope to indicate in broad strokes the proof of t his conjecture. This is joint work with D. Berwick-Evans.\n LOCATION:https://master.researchseminars.org/talk/agstanford/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Mohammed Abouzaid (Columbia University) DTSTART:20211105T190000Z DTEND:20211105T200000Z DTSTAMP:20260419T185122Z UID:agstanford/67 DESCRIPTION:Title: What can symplectic topology tell us about algebraic varieties? \nby Mohammed Abouzaid (Columbia University) as part of Stanford algeb raic geometry seminar\n\nLecture held in 383-N.\n\nAbstract\nI will begin by briefly recalling the relationship between\ncomplex projective algebrai c geometry and symplectic topology\, which\ngoes through Kaehler manifolds . I will then survey results from the\nend of the last century\, largely d ue to Seidel and McDuff\, about the\nsymplectic topology of Hamiltonian fi brations over the 2-sphere\, and\ntheir consequences for smooth projective maps over the projective\nline. Finally\, I will indicate some recent adv ances in this area\,\nincluding the use of methods of Floer homotopy theor y to\nrefine our knowledge about the topology of these spaces.\n LOCATION:https://master.researchseminars.org/talk/agstanford/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Kai Behrend (UBC) DTSTART:20211112T200000Z DTEND:20211112T210000Z DTSTAMP:20260419T185122Z UID:agstanford/68 DESCRIPTION:Title: Donaldson-Thomas theory of the quantum Fermat quintic\nby K ai Behrend (UBC) as part of Stanford algebraic geometry seminar\n\n\nAbstr act\nWe study non-commutative projective varieties in the sense of Artin-Z hang\, which are given by non-commutative homogeneous coordinate rings\, w hich are finite over their centre. We construct moduli spaces of stable m odules for these\, and construct a symmetric obstruction theory in the CY3 -case. This gives deformation invariants of Donaldson-Thomas type. The si mplest example is the Fermat quintic in quantum projective space\, where t he coordinates commute up to carefully chosen 5th roots of unity. We explo re the moduli theory of finite length modules\, which mixes features of th e Hilbert scheme of commutative 3-folds\, and the representation theory of quivers with potential. This is mostly work of Yu-Hsiang Liu\, with cont ributions by myself and Atsushi Kanazawa.\n LOCATION:https://master.researchseminars.org/talk/agstanford/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Renzo Cavalieri (Colorado State University) DTSTART:20211119T200000Z DTEND:20211119T210000Z DTSTAMP:20260419T185122Z UID:agstanford/69 DESCRIPTION:Title: The integral Chow ring of $M_{0}(\\mathbb{P}^r\,d)$\nby Ren zo Cavalieri (Colorado State University) as part of Stanford algebraic geo metry seminar\n\n\nAbstract\nWe give an efficient presentation of the Chow ring with integral coefficients of the open part of the moduli space of r ational maps of odd degree to projective space. A less fancy description o f this space has its closed points correspond to equivalence classes of $( r+1)$-tuples of degree $d$ polynomials in one variable with no common posi tive degree factor. We identify this space as a $GL(2\,\\mathbb{C})$ quoti ent of an open set in a projective space\, and then obtain a (highly redun dant) presentation by considering an envelope of the complement. A combina torial analysis then leads us to eliminating a large number of relations\, and to express the remaining ones in generating function form for all dim ensions. The upshot of this work is to observe the rich combinatorial stru cture contained in the Chow rings of these moduli spaces as the degree and the target dimension vary. This is joint work with Damiano Fulghesu.\n\nT he synchronous discussion for Renzo Cavalieri’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/2021-11-19-rc (and will be dele ted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Noah Olander (Columbia University) DTSTART:20211210T200000Z DTEND:20211210T210000Z DTSTAMP:20260419T185122Z UID:agstanford/70 DESCRIPTION:Title: Semiorthogonal decompositions and dimension\nby Noah Olande r (Columbia University) as part of Stanford algebraic geometry seminar\n\n \nAbstract\nA conjecture of Orlov predicts that we can recover the dimensi on of a smooth quasi-projective variety from its derived category via the Rouquier dimension. We explain the meaning of the conjecture and some thin gs we know about it\, then we explain the proof of a weakened version. We use this to prove a fact predicted by Orlov’s conjecture: If the derived category of X appears as a component of a semiorthogonal decomposition o f the derived category of Y (X\,Y smooth proper varieties) then the dimens ion of X is at most the dimension of Y.\n\nThe synchronous discussion for Noah Olander’s talk is taking place not in zoom-chat\, but at https://ti nyurl.com/2021-12-10-no (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Louis Esser (UCLA) DTSTART:20211203T200000Z DTEND:20211203T210000Z DTSTAMP:20260419T185122Z UID:agstanford/71 DESCRIPTION:Title: Varieties of general type with doubly exponential asymptotics\nby Louis Esser (UCLA) as part of Stanford algebraic geometry seminar\n \n\nAbstract\nBy a theorem of Hacon–McKernan\, Takayama\, and Tsuji\, fo r every $n$ there is a constant $r_n$ for which every smooth variety $X$ o f dimension $n$ of general type has birational pluricanonical maps $|mK_X| $ for $m \\geq r_n$. In joint work with Burt Totaro and Chengxi Wang (see https://arxiv.org/abs/2109.13383)\, we show that the constants $r_n$ grow at least doubly exponentially. Conjecturally\, it's expected that the op timal bound is in fact doubly exponential. We do this by finding weighted projective hypersurfaces of general type with extreme behavior: this incl udes examples of very small volume and many vanishing plurigenera. We als o consider the analogous questions for other classes of varieties and prov ide some conjecturally optimal examples. For instance\, we conjecture the terminal Fano variety of minimal volume and the canonical Calabi-Yau vari ety of minimal volume in each dimension.\n\nThe synchronous discussion for Louis Esser’s talk is taking place not in zoom-chat\, but at https://ti nyurl.com/2021-12-03-le (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Ziquan Zhuang (MIT) DTSTART:20211217T200000Z DTEND:20211217T210000Z DTSTAMP:20260419T185122Z UID:agstanford/72 DESCRIPTION:Title: Properness of the K-moduli space\nby Ziquan Zhuang (MIT) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nK-stability is an algebraic condition that characterizes the existence of Kahler-Einstei n metrics on Fano varieties. Recently there has been a lot of work on the construction of the K-moduli space\, i.e. a good moduli space parametrizin g K-polystable Fano varieties. Motivated by results in differential geomet ry\, it is conjectured that this K-moduli space is proper and projective. In this talk\, I'll discuss some recent progress in birational geometry th at leads to a full solution of this conjecture. Based on joint work with Y uchen Liu and Chenyang Xu.\n\nThe synchronous discussion for Ziquan Zhuang ’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/20 21-12-17-zz (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Chelsea Walton (Rice) DTSTART:20220121T200000Z DTEND:20220121T210000Z DTSTAMP:20260419T185122Z UID:agstanford/73 DESCRIPTION:Title: Representation theory of elliptic algebras\nby Chelsea Walt on (Rice) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nIn this talk\, I will discuss how to use algebro-geometric and Poisson geome tric methods to study the representation theory of noncommutative algebras that are ‘close’ to being commutative. Such algebras will include the 3- and the 4-dimensional Sklyanin algebras\, which are noncommutative ana logues of polynomial algebras whose behavior is governed by a certain elli ptic curve. This will be based on joint work with Xingting Wang and Milen Yakimov available in PLMS (2019) and Selecta Math (2021). I also aim to ke ep the presentation as down-to-earth as possible so that everybody will ha ve fun.\n\nThe synchronous discussion for Chelsea Walton’s talk is takin g place not in zoom-chat\, but at https://tinyurl.com/2022-01-21-cw (and w ill be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Emily Clader (SFSU) DTSTART:20220114T200000Z DTEND:20220114T210000Z DTSTAMP:20260419T185122Z UID:agstanford/74 DESCRIPTION:Title: Permutohedral complexes and rational curves with cyclic action< /a>\nby Emily Clader (SFSU) as part of Stanford algebraic geometry seminar \n\n\nAbstract\nAlthough the moduli space of genus-zero curves is not tori c\, it shares an intriguing amount of the combinatorial structure that a t oric variety would enjoy. In fact\, by adjusting the moduli problem sligh tly\, one finds a moduli space that is indeed toric\, known as Losev-Manin space. The associated polytope is the permutohedron\, which also encodes the group-theoretic structure of the symmetric group. Batyrev and Blume generalized this story by constructing a type-B version of Losev-Manin spa ce\, whose associated polytope is a signed permutohedron that relates to t he group of signed permutations. In joint work with C. Damiolini\, D. Hua ng\, S. Li\, and R. Ramadas\, we carry out the next stage of generalizatio n\, defining a family of moduli spaces of rational curves with Z_r action encoded by an associated "permutohedral complex" for a more general comple x reflection group\, which specializes when r=2 to Batyrev and Blume's mod uli space.\n\nThe synchronous discussion for Emily Clader’s talk is taki ng place not in zoom-chat\, but at https://tinyurl.com/2022-01-14-ec (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Madeline Brandt (Brown) DTSTART:20220204T200000Z DTEND:20220204T210000Z DTSTAMP:20260419T185122Z UID:agstanford/75 DESCRIPTION:Title: Top Weight Cohomology of $A_g$\nby Madeline Brandt (Brown) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nI will discu ss a recent project in computing the top weight cohomology of the moduli s pace $A_g$ of principally polarized abelian varieties of dimension $g$ for small values of $g$. This piece of the cohomology is controlled by the co mbinatorics of the boundary strata of a compactification of $A_g$. Thus\, it can be computed combinatorially. This is joint work with Juliette Bruce \, Melody Chan\, Margarida Melo\, Gwyneth Moreland\, and Corey Wolfe.\n\nT he synchronous discussion for Madeline Brandt’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/2022-02-04-mb (and will be dele ted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Allen Knutson (Cornell) DTSTART:20220128T200000Z DTEND:20220128T210000Z DTSTAMP:20260419T185122Z UID:agstanford/76 DESCRIPTION:Title: Resolutions of Richardson varieties\, stable curves\, and dual simplicial spheres\nby Allen Knutson (Cornell) as part of Stanford alg ebraic geometry seminar\n\n\nAbstract\nThe combinatorics of a simple norma l crossings divisor determines a "dual" simplicial complex. Kollár and Xu showed that when this divisor is anticanonical\, the simplicial complex h as the rational homology of a sphere. I'll construct two resolutions-of-si ngularities of Richardson varieties (a slight generalization of Schubert v arieties)\, one using Bott-Samelson manifolds\, the other (requiring no ch oices!) using circle-equivariant stable curves. In each case the dual simp licial complex is actually homeomorphic to a sphere.\n LOCATION:https://master.researchseminars.org/talk/agstanford/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Enrica Mazzon (University of Michigan) DTSTART:20220218T200000Z DTEND:20220218T210000Z DTSTAMP:20260419T185122Z UID:agstanford/77 DESCRIPTION:Title: Higher Fano manifolds\nby Enrica Mazzon (University of Mich igan) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nFano m anifolds are complex projective manifolds having positive first Chern clas s. The positivity condition on the first Chern class has far-reaching geom etric and arithmetic implications. For instance\, Fano manifolds are cover ed by rational curves\, and families of Fano manifolds over one-dimensiona l bases always admit holomorphic sections. In recent years\, there has bee n a great effort towards defining suitable higher analogues of the Fano co ndition. Higher Fano manifolds are expected to enjoy stronger versions of several of the nice properties of Fano manifolds. For instance\, they shou ld be covered by higher dimensional rational varieties\, and families of h igher Fano manifolds over higher-dimensional bases should admit meromorphi c sections (modulo Brauer obstruction). In this talk\, I will discuss a po ssible notion of higher Fano manifolds in terms of positivity of higher Ch ern characters\, and discuss special geometric features of these manifolds .\n\nThe synchronous discussion for Enrica Mazzon’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/2022-02-18-em (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Yi Hu (University of Arizona) DTSTART:20220225T200000Z DTEND:20220225T210000Z DTSTAMP:20260419T185122Z UID:agstanford/78 DESCRIPTION:Title: Resolution of Singularities in Arbitrary Characteristics\nb y Yi Hu (University of Arizona) as part of Stanford algebraic geometry sem inar\n\n\nAbstract\nLet X be an integral affine or projective scheme over a perfect field of an arbitrary characteristic. Then\, X admits a resoluti on. That is\, there exists a smooth scheme Y and a projective birational m orphism from Y onto X.\n\nThe synchronous discussion for Yi Hu’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/2022-02-25-yh (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/78/ END:VEVENT BEGIN:VEVENT SUMMARY:Ana Balibanu (Harvard) DTSTART:20220304T200000Z DTEND:20220304T210000Z DTSTAMP:20260419T185122Z UID:agstanford/79 DESCRIPTION:Title: Regular centralizers and the wonderful compactification\nby Ana Balibanu (Harvard) as part of Stanford algebraic geometry seminar\n\n \nAbstract\nThe universal centralizer of a complex semisimple adjoint grou p G is the family of regular centralizers in G\, parametrized by the regul ar conjugacy classes. It has a natural symplectic structure which is inher ited from the cotangent bundle of G. I will construct a smooth\, log-sympl ectic relative compactification of this family using the wonderful compact ification of G. Its compactified centralizer fibers are isomorphic to Hess enberg varieties\, and its symplectic leaves are indexed by root system co mbinatorics. I will also explain how to produce a multiplicative analogue of this construction\, by moving from the Poisson to the quasi-Poisson set ting.\n\nThe synchronous discussion for Ana Balibanu’s talk is taking pl ace not in zoom-chat\, but at https://tinyurl.com/2022-03-04-ab (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/79/ END:VEVENT BEGIN:VEVENT SUMMARY:Omid Amini (École Polytechnique) DTSTART:20220311T200000Z DTEND:20220311T210000Z DTSTAMP:20260419T185122Z UID:agstanford/80 DESCRIPTION:Title: Geometry of hybrid curves and their moduli spaces\, with a view toward applications\nby Omid Amini (École Polytechnique) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nThe talk will be an int roduction to the mathematics of geometric objects called hybrid curves and their moduli spaces\, which mix features from higher rank non-Archimedean \, tropical and complex geometries. Some applications to questions around the asymptotic geometry of Riemann surfaces close to the boundary of their moduli spaces will be discussed.\n\nBased on joint works with Noema Nicol ussi.\n\nThe synchronous discussion for Omid Amini’s talk is taking plac e not in zoom-chat\, but at https://tinyurl.com/2022-03-11-oa (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/80/ END:VEVENT BEGIN:VEVENT SUMMARY:Tony Yue Yu (Caltech) DTSTART:20220318T190000Z DTEND:20220318T200000Z DTSTAMP:20260419T185122Z UID:agstanford/81 DESCRIPTION:Title: Non-archimedean Quantum K-theory and Gromov-Witten invariants\nby Tony Yue Yu (Caltech) as part of Stanford algebraic geometry semina r\n\n\nAbstract\nMotivated by mirror symmetry and the enumeration of curve s with boundaries\, it is desirable to develop a theory of Gromov-Witten i nvariants in the setting of non-archimedean geometry. I will explain our r ecent works in this direction. Our approach differs from the classical one in algebraic geometry via perfect obstruction theory. Instead\, we build on our previous works on the foundation of derived non-archimedean geometr y\, the representability theorem and Gromov compactness. We obtain numeric al invariants by passing to K-theory or motivic cohomology. We prove a lis t of natural geometric relations between the stacks of stable maps\, direc tly at the derived level\, with respect to elementary operations on graphs \, namely\, products\, cutting edges\, forgetting tails and contracting ed ges. They imply the corresponding properties of numerical invariants. The derived approach produces highly intuitive statements and functorial proof s. Furthermore\, its flexibility allows us to impose not only simple incid ence conditions for marked points\, but also incidence conditions with mul tiplicities. Joint work with M Porta.\n\nThe synchronous discussion for To ny Yue Yu’s talk is taking place not in zoom-chat\, but at https://tiny url.com/2022-03-18-ty (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/81/ END:VEVENT BEGIN:VEVENT SUMMARY:Hunter Spink (Stanford) DTSTART:20220325T190000Z DTEND:20220325T200000Z DTSTAMP:20260419T185122Z UID:agstanford/82 DESCRIPTION:Title: A new Chern character for "classical Lie type" combinatorics\nby Hunter Spink (Stanford) as part of Stanford algebraic geometry semin ar\n\n\nAbstract\nFor X of “classical Lie type” (formally such that X has a GKM torus action where all characters are of the form t_i\, t_i+t_j\ , and t_i-t_j for various i\,j)\, we adapt for combinatorial applications the (equivariant) Hirzebruch-Riemann-Roch framework which computes Euler c haracteristics of vector bundles via cohomological computations\, extendin g previous joint work in type A with Andrew Berget\, Chris Eur\, and Denni s Tseng.\n\nThis framework directly relates the structure sheaf of Schuber t varieties to Grothendieck polynomials\, produces formulas (some of them new) relating the number of lattice points and volumes for type A and B ge neralized permutahedrons\, and when applied to ample equivariant vector bu ndles on toric varieties is a key component in recent progress on establis hing and unifying results on the log-concavity of sequences associated to matroids and delta-matroids.\n\n[This is joint work with Chris Eur\, Alex Fink\, and Matthew Larson.]\n\nThe synchronous discussion for Hunter Spink ’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/20 22-03-25-hs (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/82/ END:VEVENT BEGIN:VEVENT SUMMARY:Kiran Kedlaya (UC San Diego) DTSTART:20220415T190000Z DTEND:20220415T200000Z DTSTAMP:20260419T185122Z UID:agstanford/84 DESCRIPTION:Title: Angle ranks of abelian varieties\nby Kiran Kedlaya (UC San Diego) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nThe a ngle rank of an abelian variety over a finite field (or a CM abelian varie ty over C) quantifies the extent to which the Tate conjecture (or the Hodg e conjecture) holds "for trivial reasons"\; cases where this does not happ en tend to be rare in practice. Picking up a thread from some old (1980s a nd 1990s) results of Tankeev and Lenstra-Zarhin\, we show that in many cas es\, the Tate conjecture is forced to hold by the Newton polygon of the ab elian variety or the Galois group of the Frobenius eigenvalues. Joint work with Taylor Dupuy and David Zureick-Brown.\n\nThe synchronous discussion for Kiran Kedlaya’s talk is taking place not in zoom-chat\, but at https ://tinyurl.com/2022-04-15-kk (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/84/ END:VEVENT BEGIN:VEVENT SUMMARY:Michail Savvas (UT Austin) DTSTART:20220408T190000Z DTEND:20220408T200000Z DTSTAMP:20260419T185122Z UID:agstanford/85 DESCRIPTION:Title: Reduction of stabilizers and generalized Donaldson-Thomas invar iants\nby Michail Savvas (UT Austin) as part of Stanford algebraic geo metry seminar\n\n\nAbstract\nStarting with a sufficiently nice Artin stack \, we explain a canonical blowup procedure that produces a Deligne-Mumford stack\, resolving the locus of points with infinite automorphism group. T his construction can be applied to moduli stacks parametrizing semistable sheaves or complexes on Calabi-Yau threefolds. We show that their stabiliz er reductions admit natural virtual fundamental cycles\, allowing us to de fine generalized Donaldson-Thomas invariants which act as counts of these objects. Everything in this talk is (maybe not so) secretly expected to be the shadow of a corresponding phenomenon in derived algebraic geometry\, giving a new\, derived perspective on Donaldson-Thomas invariants.\n\nBase d on joint work with Young-Hoon Kiem and Jun Li and joint work in progress with Jeroen Hekking and David Rydh.\n\nThe synchronous discussion for Mic hail Savvas’ talk is taking place not in zoom-chat\, but at https://tiny url.com/2022-04-08-ms (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/85/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniele Agostini (Max Planck Institute (Leipzig)) DTSTART:20220513T190000Z DTEND:20220513T200000Z DTSTAMP:20260419T185122Z UID:agstanford/86 DESCRIPTION:Title: Singular curves\, degenerate theta functions and KP solutions\nby Daniele Agostini (Max Planck Institute (Leipzig)) as part of Stanfo rd algebraic geometry seminar\n\n\nAbstract\nSmooth algebraic curves give rise to solutions to the KP equation\, which models waves in shallow water \, via Riemann's theta function. Singular curves produce solutions as wel l\, but the theta function in this case becomes degenerate. I will presen t some results and questions in this direction\, focusing on soliton and rational solutions.\n\nThe synchronous discussion for Daniele Agostini’s talk is taking place not in zoom-chat\, but at https://tinyurl.com/2022-0 5-13-da (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/86/ END:VEVENT BEGIN:VEVENT SUMMARY:Soheyla Feyzbakhsh (Imperial College London) DTSTART:20220527T190000Z DTEND:20220527T200000Z DTSTAMP:20260419T185122Z UID:agstanford/87 DESCRIPTION:Title: Hyperkahler varieties as Brill-Noether loci on curves\nby S oheyla Feyzbakhsh (Imperial College London) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nConsider the moduli space $M_C(r\; K_C)$ o f stable rank r vector bundles on a curve $C$ with canonical determinant\, and let $h$ be the maximum number of linearly independent global sections of these bundles. If $C$ embeds in a K3 surface $X$ as a generator of $Pi c(X)$ and the genus of $C$ is sufficiently high\, I will show the Brill-No ether locus $BN_C \\subset M_C(r\; K_C)$ of bundles with $h$ global sectio ns is a smooth projective Hyperkahler manifold\, isomorphic to a moduli sp ace of stable vector bundles on $X$. The main technique is to apply wall-c rossing with respect to Bridgeland stability conditions on K3 surfaces.\n\ nThe synchronous discussion for Soheyla Feyzbakhsh’s talk is taking plac e not in zoom-chat\, but at https://tinyurl.com/2022-05-27-sf (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/87/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniil Rudenko (University of Chicago) DTSTART:20220506T190000Z DTEND:20220506T200000Z DTSTAMP:20260419T185122Z UID:agstanford/89 DESCRIPTION:Title: Rational Elliptic Surfaces and Trigonometry of Non-Euclidean Te trahedra\nby Daniil Rudenko (University of Chicago) as part of Stanfor d algebraic geometry seminar\n\n\nAbstract\nI will explain how to construc t a rational elliptic\nsurface out of every non-Euclidean tetrahedra. This surface\n"remembers" the trigonometry of the tetrahedron: the length of e dges\,\ndihedral angles and the volume can be naturally computed in terms of\nthe surface. The main property of this construction is self-duality:\n the surfaces obtained from the tetrahedron and its dual coincide. This\nle ads to some unexpected relations between angles and edges of the tetrahedr on. For instance\, the cross-ratio of the exponents of the spherical angle s coincides with the cross-ratio of the exponents of the perimeters of it s faces. The construction is based on relating mixed Hodge structures\, as sociated to the tetrahedron and the corresponding surface.\n\nThe synchron ous discussion for Daniil Rudenko’s talk is taking place not in zoom-cha t\, but at https://tinyurl.com/2022-05-06-dr (and will be deleted after ~3 -7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/89/ END:VEVENT BEGIN:VEVENT SUMMARY:Tony Feng (MIT) DTSTART:20220520T190000Z DTEND:20220520T200000Z DTSTAMP:20260419T185122Z UID:agstanford/90 DESCRIPTION:Title: Enumerative arithmetic geometry and automorphic forms\nby T ony Feng (MIT) as part of Stanford algebraic geometry seminar\n\n\nAbstrac t\nThe problem of counting vectors with given length in a lattice turns ou t to have much more structure than initially expected\, and is connected w ith the theory of so-called automorphic forms. A geometric analogue of thi s problem is to count global sections of vector bundles on a curve over a finite field. The generating functions for such counts are special automor phic forms called theta series. In joint work with Zhiwei Yun and Wei Zhan g\, we find a family of generalizations of such counting problems in the e numerative geometry of arithmetic moduli spaces\, which lead to generating functions that we call higher theta series. I will explain theorems and c onjectures around these higher theta series.\n\nThe synchronous discussion for Tony Feng’s talk is taking place not in zoom-chat\, but at https:// tinyurl.com/2022-05-20-tf (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/90/ END:VEVENT BEGIN:VEVENT SUMMARY:Siddarth Kannan (Brown University) DTSTART:20220401T190000Z DTEND:20220401T200000Z DTSTAMP:20260419T185122Z UID:agstanford/91 DESCRIPTION:Title: Moduli of relative stable maps to $\\mathbf{P}^1$: cut-and-past e invariants\nby Siddarth Kannan (Brown University) as part of Stanfor d algebraic geometry seminar\n\n\nAbstract\nI will give an introduction to the moduli space of genus zero rubber stable maps to $\\mathbf{P}^1$\, re lative to 0 and infinity\, with fixed ramification profiles. Then I will d iscuss two recent results on the topology of these moduli spaces. The firs t concerns a chamber structure for the classes of these moduli spaces in t he Grothendieck ring of varieties. The second gives a recursive algorithm for the calculation of the Euler characteristic\, in the case where the ma ps are fully ramified over zero\, and unramified over infinity. If time pe rmits\, I will also discuss some potential future directions.\n\nThe synch ronous discussion for Siddarth Kannan’s talk is taking place not in zoom -chat\, but at https://tinyurl.com/2022-04-01-sk (and will be deleted afte r ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/91/ END:VEVENT BEGIN:VEVENT SUMMARY:David Anderson (Ohio State) DTSTART:20220429T190000Z DTEND:20220429T200000Z DTSTAMP:20260419T185122Z UID:agstanford/92 DESCRIPTION:Title: The direct sum morphism in (equivariant) Schubert calculus\ nby David Anderson (Ohio State) as part of Stanford algebraic geometry sem inar\n\n\nAbstract\nDirect sum of subspaces defines a map on Grassmannians \, which\, after taking an appropriate limit\, leads to a product-like str ucture on the infinite Grassmannian. The corresponding cohomology pullbac k coincides with a famous co-product on the ring of symmetric functions. I’ll describe torus-equivariant extensions of this setup\, along with po sitivity results for structure constants\, and some open questions. This story partially extends work by Thomas-Yong\, Knutson-Lederer\, and Lam-Le e-Shimozono\, and connects to joint work with W. Fulton. (No special know ledge of Schubert calculus -- equivariant or not -- will be assumed.)\n LOCATION:https://master.researchseminars.org/talk/agstanford/92/ END:VEVENT BEGIN:VEVENT SUMMARY:Hunter Spink (Stanford) DTSTART:20220902T190000Z DTEND:20220902T200000Z DTSTAMP:20260419T185122Z UID:agstanford/93 DESCRIPTION:Title: Examples of o-minimality in algebraic geometry\nby Hunter S pink (Stanford) as part of Stanford algebraic geometry seminar\n\n\nAbstra ct\nIn this introductory talk\, we will define o-minimality (a way of augm enting algebraic geometry with functions like $e^x$\, $\\sin$\, $\\cos$\, etc.)\, and show:\n\n(1) The number of solutions to a system of polynomial s equations is bounded by a function of the sizes of the supports of the e quations\, independent of the sizes of the exponents.\n\n(2) For an irredu cible polynomial $f(x\,y)$ not of the form $ax^iy^j+bx^ky^l$ there are onl y finitely many solutions to $f(x\,y)=0$ with $x$\, $y$ roots of unity.\n LOCATION:https://master.researchseminars.org/talk/agstanford/93/ END:VEVENT BEGIN:VEVENT SUMMARY:Adeel Khan (Academia Sinica) DTSTART:20220909T190000Z DTEND:20220909T200000Z DTSTAMP:20260419T185122Z UID:agstanford/94 DESCRIPTION:Title: An invitation to motivic sheaves (part 1)\nby Adeel Khan (A cademia Sinica) as part of Stanford algebraic geometry seminar\n\n\nAbstra ct\nThese lectures will be an introduction to Voevodsky's theory of motivi c sheaves. In the first lecture we will try to understand what the theory is supposed to look like\, according to Beilinson's 1985 conjectures. To better appreciate these we will briefly review some of the ideas that inf luenced him\, such as Grothendieck's theory of pure motives and Deligne's theory of mixed Hodge structures (i.e.\, why motives?)\, and the six funct or formalism on l-adic sheaves (i.e.\, why sheaves?). In the second lectu re\, we will begin looking into Voevodsky's work on actually constructing categories of motivic sheaves\, as well as the connection with invariants like Chow groups and algebraic K-theory.\n\nDespite the seemingly forbiddi ng nature of the topic\, these lectures are intended for an audience with familiarity with basic algebraic geometry\, but no familiarity with any of the advanced topics being addressed.\n\nThe synchronous discussion for Ad eel Khan’s talk is taking place not in zoom-chat\, but at https://tinyur l.com/2022-09-09-ak (and will be deleted after ~2 weeks).\n LOCATION:https://master.researchseminars.org/talk/agstanford/94/ END:VEVENT BEGIN:VEVENT SUMMARY:Adeel Khan (Academia Sinica) DTSTART:20220916T190000Z DTEND:20220916T200000Z DTSTAMP:20260419T185122Z UID:agstanford/95 DESCRIPTION:Title: An invitation to motivic sheaves (part 2)\nby Adeel Khan (A cademia Sinica) as part of Stanford algebraic geometry seminar\n\n\nAbstra ct\nThese lectures will be an introduction to Voevodsky's theory of motivi c sheaves. In the first lecture we will try to understand what the theory is supposed to look like\, according to Beilinson's 1985 conjectures. To better appreciate these we will briefly review some of the ideas that inf luenced him\, such as Grothendieck's theory of pure motives and Deligne's theory of mixed Hodge structures (i.e.\, why motives?)\, and the six funct or formalism on l-adic sheaves (i.e.\, why sheaves?). In the second lectu re\, we will begin looking into Voevodsky's work on actually constructing categories of motivic sheaves\, as well as the connection with invariants like Chow groups and algebraic K-theory.\n\nDespite the seemingly forbiddi ng nature of the topic\, these lectures are intended for an audience with familiarity with basic algebraic geometry\, but no familiarity with any of the advanced topics being addressed.\n\nThe synchronous discussion for Ad eel Khan’s talk is taking place not in zoom-chat\, but at https://tinyur l.com/2022-09-16-ak (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/95/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Emerton (University of Chicago) DTSTART:20221028T190000Z DTEND:20221028T200000Z DTSTAMP:20260419T185122Z UID:agstanford/96 DESCRIPTION:Title: Stacks in the arithmetic Langlands program\nby Matthew Emer ton (University of Chicago) as part of Stanford algebraic geometry seminar \n\nLecture held in Room 383-N.\n\nAbstract\nRecent years have seen the in troduction of geometric ideas\, formerly the sole province of the geometri c Langlands program\, into the arithmetic Langlands program as well. In pa rticular\, stacks of Langlands parameters have taken a central place in th e arithmetic theory.\n\nIn this talk I will discuss some aspects of these stacks\, with an emphasis on their interesting geometric features. Much o f the work I’ll report on will be joint with Toby Gee. Some will also b e joint with Xinwen Zhu.\n LOCATION:https://master.researchseminars.org/talk/agstanford/96/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacob Tsimerman (University of Toronto) DTSTART:20221111T200000Z DTEND:20221111T210000Z DTSTAMP:20260419T185122Z UID:agstanford/97 DESCRIPTION:Title: Abelian Varieties not Isogenous to Jacobians\nby Jacob Tsim erman (University of Toronto) as part of Stanford algebraic geometry semin ar\n\nLecture held in Room 383-N.\n\nAbstract\nKatz and Oort raised the fo llowing question: Given an algebraically closed field k\, and a positive i nteger g>3\, does there exist an abelian variety over k not isogenous to a Jacobian over k? There has been much progress on this question\, with sev eral proofs now existing over $\\overline{\\mathbb{Q}}$. We discuss recent work with Ananth Shankar\, answering this question in the affirmative ove r $\\overline{\\mathbb{F}_q(T)}$. Our method introduces new types of local obstructions\, and can be used to give another proof over $\\overline{\\m athbb{Q}}$.\n LOCATION:https://master.researchseminars.org/talk/agstanford/97/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierrick Bousseau (University of Georgia) DTSTART:20221118T200000Z DTEND:20221118T210000Z DTSTAMP:20260419T185122Z UID:agstanford/98 DESCRIPTION:Title: Fock–Goncharov Dual Cluster Varieties and Gross–Siebert Mir rors\nby Pierrick Bousseau (University of Georgia) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nCluster varieties are algebraic varieties obtained by gluing together complex tori using explicit biratio nal transformations. They play an important role in algebra and geometric representation theory\, and have the peculiarity to come in pairs (A\,X). On the other hand\, in the context of mirror symmetry\, associated with an y log Calabi–Yau variety is its mirror dual\, which can be constructed u sing the enumerative geometry of rational curves in the framework of the G ross–Siebert program. I will explain how to bridge the theory of cluster varieties with the algebro-geometric framework of Gross–Siebert mirror symmetry and show that the mirror to the X-cluster variety is a degenerati on of the Fock–Goncharov dual A-cluster variety and vice versa. To do th is\, we investigate how the cluster scattering diagram of Gross–Hacking –Keel–Kontsevich compares with the canonical scattering diagram define d by Gross–Siebert to construct mirror duals in arbitrary dimensions. Th is is joint work with Hulya Arguz.\n\nThe synchronous discussion for Pierr ick Bousseau’s talk is taking place not in zoom-chat\, but at https://ti nyurl.com/2022-11-18-pb (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/98/ END:VEVENT BEGIN:VEVENT SUMMARY:Matt Larson (Stanford) DTSTART:20221021T190000Z DTEND:20221021T200000Z DTSTAMP:20260419T185122Z UID:agstanford/99 DESCRIPTION:Title: The local motivic monodromy conjecture for simplicial nondegene rate singularities\nby Matt Larson (Stanford) as part of Stanford alge braic geometry seminar\n\nLecture held in 383-N.\n\nAbstract\nThe monodrom y conjecture predicts a relationship between the motivic zeta function of a hypersurface V(f)\, which governs the number of solutions to f = 0 (mod p^n) if f has integer coefficients and p is a sufficiently large prime\, a nd the eigenvalues of the monodromy action on the cohomology of the Milnor fiber\, which is a topological invariant of the complex hypersurface. Whe n f is nondegenerate with respect to its Newton polyhedron\, which is true for "generic" polynomials\, there are combinatorial formulas for both the motivic zeta function and the eigenvalue of monodromy. I will describe re cent results (joint with S. Payne and A. Stapledon) which prove a version of the monodromy conjecture for nondegenerate polynomials which have a sim plicial Newton polyhedron.\n LOCATION:https://master.researchseminars.org/talk/agstanford/99/ END:VEVENT BEGIN:VEVENT SUMMARY:Chengxi Wang (UCLA) DTSTART:20221202T200000Z DTEND:20221202T210000Z DTSTAMP:20260419T185122Z UID:agstanford/100 DESCRIPTION:Title: Calabi-Yau varieties of large index\nby Chengxi Wang (UCLA ) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nA projecti ve variety $X$ is called Calabi-Yau if its canonical divisor is $\\mathbb{ Q}$-linearly equivalent to zero. The smallest positive integer $m$ with $m K_X$ linearly equivalent to zero is called the index of $X$. Using ideas f rom mirror symmetry\, we construct Calabi-Yau varieties with index growing doubly exponentially with dimension. We conjecture they are the largest i ndex in each dimension based on evidence in low dimensions. We also give C alabi-Yau varieties with large orbifold Betti numbers or small minimal log discrepancy. Joint work with Louis Esser and Burt Totaro.\n\nThe synchron ous discussion for Chengxi Wang’s talk is taking place not in zoom-chat\ , but at https://tinyurl.com/2022-12-02-cw (and will be deleted after ~3-7 days).\n LOCATION:https://master.researchseminars.org/talk/agstanford/100/ END:VEVENT BEGIN:VEVENT SUMMARY:Patricio Gallardo Candela (UC Riverside) DTSTART:20230224T200000Z DTEND:20230224T210000Z DTSTAMP:20260419T185122Z UID:agstanford/101 DESCRIPTION:Title: A perspective on explicit compactifications of the moduli spac e of surfaces and pairs\nby Patricio Gallardo Candela (UC Riverside) a s part of Stanford algebraic geometry seminar\n\nLecture held in Room 383- N.\n\nAbstract\nIn this talk\, we will discuss techniques for explicitly d escribing the degenerations parametrized by the KSBA moduli space of surfa ces and log pairs of general type. We will focus on specific examples\, su ch as certain Horikawa surfaces and cubic surfaces\, and how our technique s have been applied to them. These results were obtained in joint work wit h L. Schaffler\, G. Pearlstein\, Z. Zhang\, and M. Kerr.\n LOCATION:https://master.researchseminars.org/talk/agstanford/101/ END:VEVENT BEGIN:VEVENT SUMMARY:Will Sawin (Columbia) DTSTART:20230120T200000Z DTEND:20230120T210000Z DTSTAMP:20260419T185122Z UID:agstanford/102 DESCRIPTION:Title: Quantitative $\\ell$-adic sheaf theory\nby Will Sawin (Col umbia) as part of Stanford algebraic geometry seminar\n\nLecture held in R oom 383-N.\n\nAbstract\nSheaf cohomology is a powerful tool both in algebr aic \ngeometry and its applications to other fields. Often\, one wants to \nprove bounds for the dimension of sheaf cohomology groups. Katz gave \nb ounds for the dimension of the étale cohomology groups of a variety \nin terms of its defining equations (degree\, number of equations\, \nnumber o f variables). But the utility of sheaf cohomology arises less \nfrom the a bility to compute the cohomology of varieties and more from \nthe toolbox of functors that let us construct new sheaves from old\, \nwhich we often apply in quite complicated sequences. In joint work \nwith Arthur Forey\, Javier Fresán\, and Emmanuel Kowalski\, we prove \nbounds for the dimensi ons of étale cohomology groups which are \ncompatible with the six functo rs formalism (and other functors \nbesides) in the sense that we define th e “complexity” of a sheaf and \ncontrol how much the complexity can gr ow when we apply one of these \noperations.\n LOCATION:https://master.researchseminars.org/talk/agstanford/102/ END:VEVENT BEGIN:VEVENT SUMMARY:Shiji Lyu (Princeton) DTSTART:20230310T200000Z DTEND:20230310T210000Z DTSTAMP:20260419T185122Z UID:agstanford/103 DESCRIPTION:Title: Behavior of some invariants in characteristic $p$\nby Shij i Lyu (Princeton) as part of Stanford algebraic geometry seminar\n\nLectur e held in Room 383-N.\n\nAbstract\nThere are many numerical invariants of a ring in characteristic $p$ measuring its singularity. In this talk\, we will discuss two classical ones\, Hilbert-Kunz multiplicity and the $F$-si gnature\, and a rather recent one\, the $F$-rational signature. We will di scuss several properties of these invariants\, including semi-continuity a nd behavior under smooth extensions.\n LOCATION:https://master.researchseminars.org/talk/agstanford/103/ END:VEVENT BEGIN:VEVENT SUMMARY:Ming Hao Quek (Brown University) DTSTART:20230519T190000Z DTEND:20230519T200000Z DTSTAMP:20260419T185122Z UID:agstanford/105 DESCRIPTION:Title: Around the motivic monodromy conjecture for non-degenerate hyp ersurfaces\nby Ming Hao Quek (Brown University) as part of Stanford al gebraic geometry seminar\n\nLecture held in Room 383-N.\n\nAbstract\nI wil l discuss my ongoing effort to comprehend\, from a geometric viewpoint\, t he motivic monodromy conjecture for a "generic" complex multivariate polyn omial $f$\, namely any polynomial $f$ that is non-degenerate with respect to its Newton polyhedron. This conjecture\, due to Igusa and Denef--Loeser \, states that for every pole $s$ of the motivic zeta function associated to $f$\, $\\exp(2\\pi is)$ is a "monodromy eigenvalue" associated to $f$. On the other hand\, the non-degeneracy condition on $f$ ensures that the s ingularity theory of $f$ is governed\, up to a certain extent\, by faces o f the Newton polyhedron of $f$. The extent to which the former is governed by the latter is one key aspect of the conjecture\, and will be the main focus of my talk.\n LOCATION:https://master.researchseminars.org/talk/agstanford/105/ END:VEVENT BEGIN:VEVENT SUMMARY:Dusty Ross (San Francisco State) DTSTART:20230127T200000Z DTEND:20230127T210000Z DTSTAMP:20260419T185122Z UID:agstanford/106 DESCRIPTION:Title: Putting the “volume” back in “volume polynomials”\ nby Dusty Ross (San Francisco State) as part of Stanford algebraic geometr y seminar\n\nLecture held in Room 383-N.\n\nAbstract\nRecent developments in tropical geometry and matroid theory have led to the study of “volume polynomials” associated to tropical varieties\, the coefficients of whi ch record all possible degrees of top powers of tropical divisors. In this talk\, I’ll discuss a volume-theoretic interpretation of volume polynom ials of tropical fans\; namely\, they measure volumes of polyhedral comple xes obtained by truncating the tropical fan with normal hyperplanes. I’l l also discuss how this volume-theoretic interpretation inspires a general framework for studying an analogue of the Alexandrov-Fenchel inequalities for degrees of divisors on tropical fans. Parts of this work are joint wi th Anastasia Nathanson\, Lauren Nowak\, and Patrick O’Melveny.\n LOCATION:https://master.researchseminars.org/talk/agstanford/106/ END:VEVENT BEGIN:VEVENT SUMMARY:Hernan Iriarte (UT Austin) DTSTART:20230203T200000Z DTEND:20230203T210000Z DTSTAMP:20260419T185122Z UID:agstanford/107 DESCRIPTION:Title: Weak continuity on the variation of Newton Okounkov bodies \nby Hernan Iriarte (UT Austin) as part of Stanford algebraic geometry sem inar\n\nLecture held in Room 383-N.\n\nAbstract\nWe start by presenting ne w tools and results suitable for\nthe study of valuations of higher rank o n function fields of algebraic\nvarieties. This will be based on a study o f higher rank quasi-monomial\nvaluations taking values in the lexicographi cally ordered group R^k.\nThis gives us a space of higher rank valuations that we endow with a\nweak "tropical" topology. In this setting\, we show that the Newton\nOkounkov bodies of a given line bundle vary continuously with respect\nto the valuation. We explain how this result fits in the lit erature\nand how it gives us a restriction in the existence of mutations o f\nNewton Okounkov bodies. Joint work with Omid Amini.\n LOCATION:https://master.researchseminars.org/talk/agstanford/107/ END:VEVENT BEGIN:VEVENT SUMMARY:Aaron Landesman (MIT) DTSTART:20230210T200000Z DTEND:20230210T210000Z DTSTAMP:20260419T185122Z UID:agstanford/108 DESCRIPTION:Title: Splitting types of finite monodromy vector bundles\nby Aar on Landesman (MIT) as part of Stanford algebraic geometry seminar\n\nLectu re held in Room 383-N.\n\nAbstract\nGiven a finite degree $d$ cover of cur ves $f: X \\to \\mathbb P^1$\, we study $f_* \\mathscr O_X$\, which is a r ank $d$ vector bundle on $\\mathbb P^1$\, hence\ncan be written as a direc t sum of line bundles \n$f_* \\mathscr O_X \\simeq \\oplus_{i=1}^d \\maths cr O(a_i)$.\nNaively\, one might expect that if the cover above is general \, this vector bundle is balanced\, meaning that the $a_i$'s are as close to each other as possible.\nWhile this is not quite true\, we explain what can be said about these splitting types\, by studying how they change as we deform the cover. This is based on joint work with Daniel Litt.\n\nThe ideas cropping up here were also instrumental in resolving\nconjectures of Esnault-Kerz and Budur-Wang regarding the density of geometric local\nsys tems in the moduli space of local systems.\n LOCATION:https://master.researchseminars.org/talk/agstanford/108/ END:VEVENT BEGIN:VEVENT SUMMARY:Eric Larson (Brown University) DTSTART:20230421T190000Z DTEND:20230421T200000Z DTSTAMP:20260419T185122Z UID:agstanford/109 DESCRIPTION:Title: Interpolation for Brill--Noether Curves\nby Eric Larson (B rown University) as part of Stanford algebraic geometry seminar\n\nLecture held in Room 383-N.\n\nAbstract\nIn this talk\, we determine when there i s a Brill--Noether curve of given degree and given genus that passes throu gh a given number of general points in any projective space.\n LOCATION:https://master.researchseminars.org/talk/agstanford/109/ END:VEVENT BEGIN:VEVENT SUMMARY:Hannah Larson (Harvard/Berkeley) DTSTART:20230505T190000Z DTEND:20230505T200000Z DTSTAMP:20260419T185122Z UID:agstanford/110 DESCRIPTION:Title: The embedding theorem in Hurwitz--Brill--Noether theory\nb y Hannah Larson (Harvard/Berkeley) as part of Stanford algebraic geometry seminar\n\nLecture held in Room 383-N.\n\nAbstract\nBrill--Noether theory studies the maps of general curves to projective spaces. The embedding the orem of Eisenbud and Harris states that a general degree $d$ map $C \\righ tarrow \\mathbb{P}^r$ is an embedding when $r \\geq 3$. Hurwitz--Brill--No ether theory starts with a curve $C$ already equipped with a fixed map $C \\rightarrow \\mathbb{P}^1$ (which often forces $C$ to be special) and stu dies the maps of $C$ to other projective spaces. In this setting\, the app ropriate analogue of the invariants $d$ and $r$ is a finer invariant calle d the splitting type. Our embedding theorem determines the splitting types $\\vec{e}$ such that a general map of splitting type $\\vec{e}$ is an emb edding. This is joint work with Kaelin Cook--Powel\, Dave Jensen\, Eric La rson\, and Isabel Vogt.\n LOCATION:https://master.researchseminars.org/talk/agstanford/110/ END:VEVENT BEGIN:VEVENT SUMMARY:Allen Knutson (Cornell) DTSTART:20230120T214500Z DTEND:20230120T224500Z DTSTAMP:20260419T185122Z UID:agstanford/111 DESCRIPTION:Title: Generic pipe dreams and the commuting scheme\nby Allen Knu tson (Cornell) as part of Stanford algebraic geometry seminar\n\nLecture h eld in Room 383-N.\n\nAbstract\nConsider the equations XY=YX on a pair of matrices. Do these generate a prime ideal\, or\, are there secret equation s that pairs of commuting matrices satisfy? Mel Hochster asked this in '84 and noone has answered it (past small matrix size). I'll degenerate this scheme into pieces indexed by "generic pipe dreams"\, thereby giving a for mula for its degree as a sum of powers of 2\, and use an associated formul a to derive both the ordinary and bumpless pipe dream formulae for Schuber t polynomials. This work is joint with Paul Zinn-Justin.\n\nThis is the se cond algebraic geometry seminar of the day. We will zip out to buy lunch in between\, and enjoy lunchtime theater with this talk.\n LOCATION:https://master.researchseminars.org/talk/agstanford/111/ END:VEVENT BEGIN:VEVENT SUMMARY:Chih-Wei Chang (UT Austin) DTSTART:20230217T200000Z DTEND:20230217T210000Z DTSTAMP:20260419T185122Z UID:agstanford/112 DESCRIPTION:Title: The Iitaka dimensions of toric vector bundles\nby Chih-Wei Chang (UT Austin) as part of Stanford algebraic geometry seminar\n\nLectu re held in Room 383-N.\n\nAbstract\nIn this talk\, we will start by briefl y reviewing the notion of the Iitaka dimension for vector bundles\, introd uced by E. C. Mistretta and S. Urbinati. Then we will discuss how to compu te it in the toric geometry setting by studying the map defined by the glo bal sections of a toric vector bundle. We then demonstrate how to use this to construct some interesting examples.\n LOCATION:https://master.researchseminars.org/talk/agstanford/112/ END:VEVENT BEGIN:VEVENT SUMMARY:Isabel Vogt (Brown University) DTSTART:20230414T190000Z DTEND:20230414T200000Z DTSTAMP:20260419T185122Z UID:agstanford/113 DESCRIPTION:Title: Curve classes on conic bundles threefolds and applications to rationality\nby Isabel Vogt (Brown University) as part of Stanford alg ebraic geometry seminar\n\n\nAbstract\nIn this talk I'll discuss joint wor k with Sarah Frei\, Lena Ji\, Soumya Sankar and Bianca Viray on the proble m of determining when a geometrically rational variety is birational to pr ojective space over its field of definition. Hassett--Tschinkel and Benoi st--Wittenberg recently refined the classical intermediate Jacobian obstru ction of Clemens--Griffiths by considering torsors under the intermediate Jacobian of a geometrically rational threefold. By work of Hassett--Tschi nkel\, Benoist--Wittenberg and Kuznetsov--Prokhorov\, this obstruction is strong enough to characterize rationality of geometrically rational Fano t hreefolds of geometric Picard rank 1. Moving into higher Picard rank\, we compute this obstruction for conic bundles over $\\mathbf{P}^2$. As a con sequence of our work\, when the ground field is the real numbers\, we show that neither the topological obstruction nor the refined intermediate Jac obian obstruction is sufficient to determine rationality.\n LOCATION:https://master.researchseminars.org/talk/agstanford/113/ END:VEVENT BEGIN:VEVENT SUMMARY:Helene Esnault (Freie Universität Berlin) DTSTART:20230428T190000Z DTEND:20230428T200000Z DTSTAMP:20260419T185122Z UID:agstanford/114 DESCRIPTION:Title: Crystallinity properties of complex rigid local systems [not o nline]\nby Helene Esnault (Freie Universität Berlin) as part of Stanf ord algebraic geometry seminar\n\nLecture held in 383-N.\n\nAbstract\nJoin t work in progress with Michael Groechenig\n\n We prove in all generality that on a smooth complex quasi-projective variety $X$\, Rigid connection s yield $F$-isocrystals on almost all good reductions $X_{\\mathbb F_q}$ and that rigid local systems yield crystalline local systems on $X_K$ for $K$ the field of fractions of the Witt vectors of a finite field $\\mathb b F_q$\, for almost all $X_{\\mathbb F_q}$. This improves our earlier work where\, if $X$ was not projective\, we assumed a strong cohomological con dition (which is fulfilled for Shimura varieties of real rank $\\geq 2$)\, \n and we obtained only infinitely many $\\mathbb F_q$ of growing charact eristic. While the earlier proof was via characteristic $p$\, the new one is purely $p$-adic and uses $p$-adic topology.\n\n We shall discuss the pr ojective case during the lecture.\n LOCATION:https://master.researchseminars.org/talk/agstanford/114/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Chen (Columbia University) DTSTART:20230310T220000Z DTEND:20230310T230000Z DTSTAMP:20260419T185122Z UID:agstanford/115 DESCRIPTION:Title: Fano hypersurfaces and differential forms via positive charact eristic\nby Nathan Chen (Columbia University) as part of Stanford alge braic geometry seminar\n\nLecture held in 383-N.\n\nAbstract\nHolomorphic forms are an important birational invariant for studying the geometry of a variety. In characteristic 0\, Fano varieties do not have any holomorphic forms. Surprisingly\, Kollár showed that in positive characteristic cert ain (singular) Fano varieties admit many global (n-1)-forms\, and he combi ned this with a specialization method to prove nonrationality of many comp lex Fano hypersurfaces. In this talk\, we will revisit this construction a nd use it to address several related questions for Fano hypersurfaces in c ertain ranges: (1) how can one further measure their nonrationality\, (2) what are their possible rational endomorphisms\, and (3) is their biration al automorphism group infinite or finite? Parts of this will be joint with David Stapleton as well as with Lena Ji-Stapleton.\n LOCATION:https://master.researchseminars.org/talk/agstanford/115/ END:VEVENT BEGIN:VEVENT SUMMARY:Melody Chan (Brown University) DTSTART:20230602T190000Z DTEND:20230602T200000Z DTSTAMP:20260419T185122Z UID:agstanford/117 DESCRIPTION:Title: The weight 0 compactly supported Euler characteristic of modul i spaces of marked hyperelliptic curves\nby Melody Chan (Brown Univers ity) as part of Stanford algebraic geometry seminar\n\nLecture held in 383 -N.\n\nAbstract\nJoint work with Madeline Brandt and Siddarth Kannan. We use moduli spaces of $G$-admissible covers and tropical geometry to give a sum-over-graphs formula for the weight-0 compactly supported Euler charac teristic of the moduli spaces $H_{g\,n}$ of $n$-marked hyperelliptic curve s of genus $g$\, as a virtual representation of $S_n$. Computer calculati ons then enable fully explicit formulas for the above in small genus. My aim is to make this talk accessible to anyone with passing familiarity wit h $M_g$ and its Deligne-Mumford compactification.\n LOCATION:https://master.researchseminars.org/talk/agstanford/117/ END:VEVENT BEGIN:VEVENT SUMMARY:Ben Church (Stanford University) DTSTART:20230609T190000Z DTEND:20230609T200000Z DTSTAMP:20260419T185122Z UID:agstanford/118 DESCRIPTION:Title: Frames of 1-forms on varieties and maps to abelian varieties\nby Ben Church (Stanford University) as part of Stanford algebraic geom etry seminar\n\nLecture held in 383-N.\n\nAbstract\nA fruitful question in complex algebraic geometry is how much the global 1-forms on a variety co nstrains its geometry. The foundational work of Popa and Schnell shows tha t if a variety admits a nowhere vanishing 1-form then it cannot be general type. We build off this theorem to consider varieties X admitting a frame of g everywhere independent 1-forms. This property heavily constrains the birational type of X. Under additional hypotheses that ensure X is "as ge neral type as possible\," we prove that X is a smooth isotrivial fibration over an abelian variety. Our methods also verify certain conjectures abou t the existence and structure of smooth maps to abelian varieties for sour ce varieties with large Kodaira dimensions. This is joint work with Nathan Chen and Feng Hao.\n LOCATION:https://master.researchseminars.org/talk/agstanford/118/ END:VEVENT BEGIN:VEVENT SUMMARY:Sung Gi Park (Harvard University) DTSTART:20231020T183000Z DTEND:20231020T193000Z DTSTAMP:20260419T185122Z UID:agstanford/119 DESCRIPTION:Title: Kodaira dimension and hyperbolicity for smooth families of var ieties\nby Sung Gi Park (Harvard University) as part of Stanford algeb raic geometry seminar\n\nLecture held in 383-N.\n\nAbstract\nIn this talk\ , I will discuss the behavior of positivity\, hyperbolicity\, and Kodaira dimension under smooth morphisms of complex quasi-projective manifolds. Th is includes a vast generalization of a classical result: a fibration from a projective surface of non-negative Kodaira dimension to a projective lin e has at least three singular fibers. Furthermore\, I will explain a proof of Popa's conjecture on the superadditivity of the log Kodaira dimension over bases of dimension at most three. These theorems are applications of the main technical result\, namely the logarithmic base change theorem.\n LOCATION:https://master.researchseminars.org/talk/agstanford/119/ END:VEVENT BEGIN:VEVENT SUMMARY:Izzet Coskun (University of Illinois at Chicago) DTSTART:20231027T183000Z DTEND:20231027T193000Z DTSTAMP:20260419T185122Z UID:agstanford/120 DESCRIPTION:Title: The cohomology of a general stable sheaf on a K3 surface\n by Izzet Coskun (University of Illinois at Chicago) as part of Stanford al gebraic geometry seminar\n\nLecture held in 383-N.\n\nAbstract\nClassical Brill-Noether theory studies the cohomology jumping loci for line bundles on curves. On surfaces\, even the generic cohomology of a sheaf in a modul i space may be hard to determine. In this talk\, I will explain how to com pute the cohomology of a general stable sheaf on a K3 surface using Bridge land stability. If time permits\, I will discuss the case of abelian surfa ces. This is joint work with Howard Nuer and Kota Yoshioka.\n LOCATION:https://master.researchseminars.org/talk/agstanford/120/ END:VEVENT BEGIN:VEVENT SUMMARY:Renzo Cavalieri (Colorado State University) DTSTART:20231117T193000Z DTEND:20231117T203000Z DTSTAMP:20260419T185122Z UID:agstanford/121 DESCRIPTION:Title: A log/tropical take on Hurwitz numbers\nby Renzo Cavalieri (Colorado State University) as part of Stanford algebraic geometry semina r\n\nLecture held in 383-N.\n\nAbstract\nI will present some joint work wi th Hannah Markwig and Dhruv Ranganathan\, in which we interpret double Hur witz numbers as intersection numbers of the double ramification cycle with a logarithmic boundary class on the moduli space of curves. This approach removes the "need" for a branch morphism and therefore allows the general ization to related enumerative problems on moduli spaces of pluricanonical divisors - which have a natural combinatorial structure coming from thei r tropical interpretation. I will discuss some generalizations springing o ut from this approach that are currently being pursued in joint work with Hannah Markwig and Johannes Schmitt.\n LOCATION:https://master.researchseminars.org/talk/agstanford/121/ END:VEVENT BEGIN:VEVENT SUMMARY:Angela Gibney (University of Pennsylvania) DTSTART:20231208T193000Z DTEND:20231208T203000Z DTSTAMP:20260419T185122Z UID:agstanford/122 DESCRIPTION:Title: Vertex operator algebras and moduli spaces\nby Angela Gibn ey (University of Pennsylvania) as part of Stanford algebraic geometry sem inar\n\nLecture held in 383-N.\n\nAbstract\nVertex operator algebras (VOAs ) are generalizations of commutative associative algebras and of Lie algeb ras. As I will illustrate\, there are a number of interesting examples of VOAs that come from moduli spaces\, and striking instances where the VOA f ormalism has been used to solve problems about these moduli spaces. There are natural algebraic structures on moduli of curves derived from represe ntations of more general VOAs. I’ll describe some open questions about t he VOAs\, and about the moduli spaces of curves which these structures hav e been used to investigate.\n LOCATION:https://master.researchseminars.org/talk/agstanford/122/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Temkin (HUJI) DTSTART:20231002T213000Z DTEND:20231002T223000Z DTSTAMP:20260419T185122Z UID:agstanford/123 DESCRIPTION:Title: Wild ramification and geometry of valuations (joint algebraic geometry and number theory seminar)\nby Michael Temkin (HUJI) as part of Stanford algebraic geometry seminar\n\nLecture held in 383-N.\n\nAbstra ct\nWild ramification is known to be a major obstacle to solving various q uestions in positive characteristic\, including resolution of singularitie s\, compactifying Hurwitz spaces\, etc.\, and the very terminology suggest s that we are dealing with something not so controllable. Nevertheless\, i n valuative geometries\, such as Berkovich or adic\, some wild ramificatio n phenomena that originally look chaotic do get very conceptual explanatio ns. In my talk I will give a few examples with the different function of a ramified covering being the main player.\n\n(At 2 pm in advance\, there w ill be an informal pre-talk giving an introduction to non-archimedean geom etry.)\n LOCATION:https://master.researchseminars.org/talk/agstanford/123/ END:VEVENT BEGIN:VEVENT SUMMARY:Matt Satriano (University of Waterloo) DTSTART:20231201T193000Z DTEND:20231201T203000Z DTSTAMP:20260419T185122Z UID:agstanford/124 DESCRIPTION:Title: Beyond twisted maps: crepant resolutions of log terminal singu larities and a motivic McKay correspondence\nby Matt Satriano (Univers ity of Waterloo) as part of Stanford algebraic geometry seminar\n\nLecture held in 383-N.\n\nAbstract\nCrepant resolutions have inspired connections between birational geometry\, derived categories\, representation theory\ , and motivic integration. In this talk\, we prove that every variety with log-terminal singularities admits a crepant resolution by a smooth stack. We additionally prove a motivic McKay correspondence for stack-theoretic resolutions. Finally\, we show how our work naturally leads to a generaliz ation of twisted mapping spaces. No prior knowledge of stacks will be assu med. This is joint work with Jeremy Usatine.\n LOCATION:https://master.researchseminars.org/talk/agstanford/124/ END:VEVENT BEGIN:VEVENT SUMMARY:Eugene Gorsky (UC Davis) DTSTART:20231013T190000Z DTEND:20231013T200000Z DTSTAMP:20260419T185122Z UID:agstanford/125 DESCRIPTION:Title: Braid varieties\nby Eugene Gorsky (UC Davis) as part of St anford algebraic geometry seminar\n\nLecture held in 383-N.\n\nAbstract\nI will introduce and discuss a remarkable class of algebraic varieties\, ca lled braid varieties. These include all open Richardson and positroid vari eties\, and are closely related to augmentation varieties for Legendrian l inks. The topology of braid varieties is related to various link invariant s such as HOMFLY polynomial and Khovanov-Rozansky homology\, while their c oordinate ring has a cluster structure.\n\nThe talk is based on joint work s with Roger Casals\, Mikhail Gorsky\, Ian Le\, Linhui Shen and Jose Simen tal.\n LOCATION:https://master.researchseminars.org/talk/agstanford/125/ END:VEVENT BEGIN:VEVENT SUMMARY:Louis Esser (Princeton) DTSTART:20231020T210000Z DTEND:20231020T220000Z DTSTAMP:20260419T185122Z UID:agstanford/126 DESCRIPTION:Title: Symmetries of Fano varieties\nby Louis Esser (Princeton) a s part of Stanford algebraic geometry seminar\n\nLecture held in 383-N.\n\ nAbstract\nA landmark result of Birkar\, Prokhorov\, and Shramov shows tha t automorphism groups of Fano (or more generally rationally connected) var ieties over C of a fixed dimension are uniformly Jordan. This means in pa rticular that there is some upper bound on the size of symmetric groups ac ting faithfully on rationally connected varieties of fixed dimension. We give the first effective asymptotic bound on these symmetric group actions \, as well as optimal bounds in all dimensions for special classes\, such as Fano weighted complete intersections and toric varieties. Finally\, we show that klt Fano fourfolds with maximal symmetric actions are bounded\, establishing a link between boundedness and large group actions. This tal k is based on joint work with Lena Ji and Joaquín Moraga.\n LOCATION:https://master.researchseminars.org/talk/agstanford/126/ END:VEVENT BEGIN:VEVENT SUMMARY:Federico Scavia (UCLA) DTSTART:20231110T193000Z DTEND:20231110T203000Z DTSTAMP:20260419T185122Z UID:agstanford/127 DESCRIPTION:Title: Massey products in Galois cohomology\nby Federico Scavia ( UCLA) as part of Stanford algebraic geometry seminar\n\nLecture held in 38 3-N.\n\nAbstract\nBorn as part of algebraic topology\, Massey products hav e now made a surprising appearance in Galois cohomology. The Massey Vanish ing Conjecture of Minac and Tan predicts that all Massey products in the G alois cohomology of a field vanish as soon as they are defined. This conje cture is motivated by the Profinite Inverse Galois Problem: which profinit e groups are absolute Galois groups? I will describe recent progress on th e Massey Vanishing Conjecture\, joint with Alexander Merkurjev.\n LOCATION:https://master.researchseminars.org/talk/agstanford/127/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Temkin (HUJI) DTSTART:20231005T233000Z DTEND:20231006T003000Z DTSTAMP:20260419T185122Z UID:agstanford/128 DESCRIPTION:Title: Distinguished Lecture: Filling a few holes in the classical re solution of singularities\nby Michael Temkin (HUJI) as part of Stanfor d algebraic geometry seminar\n\nLecture held in TBA.\n\nAbstract\n"...in t his field\, almost everything is already discovered\, and all that remains is to fill a few unimportant holes." Philipp von Jolly in his recommendat ion to Max Planck not to go into physics.\n\nSince 2015 I am taking part i n a long project (more precisely\, a series of projects) with Dan Abramovi ch and Jarek Wlodarczyk on resolution of singularities in characteristic z ero -- a field which was (and sometimes still is) considered as accomplish ed up to a few unimportant holes. To our surprise it turned out that there were (and still are) quite a few fundamental things to discover in this c lassical and thoroughly explored field\, and the new discoveries even prov ide a more conceptual view on what was known before we started our project . It is impossible to compress all results of this journey in one talk\, b ut I will try to outline a unified view on most of our discoveries in thes e projects. If time permits in the end I will also say a couple of words a bout our new project in progress with Andre Belotto -- still in characteri stic zero...\n LOCATION:https://master.researchseminars.org/talk/agstanford/128/ END:VEVENT BEGIN:VEVENT SUMMARY:Ziquan Zhuang (Johns Hopkins University) DTSTART:20240119T200000Z DTEND:20240119T210000Z DTSTAMP:20260419T185122Z UID:agstanford/129 DESCRIPTION:Title: Stability of klt singularities\nby Ziquan Zhuang (Johns Ho pkins University) as part of Stanford algebraic geometry seminar\n\nLectur e held in 383-N.\n\nAbstract\nA theorem of Donaldson and Sun asserts that the metric tangent cone of a smoothable Kähler–Einstein Fano variety un derlies some algebraic structure\, and they conjecture that the metric tan gent cone only depends on the algebraic structure of the singularity. Late r Li and Xu extend this speculation and conjecture that every klt singular ity has a canonical “stable” degeneration induced by the valuation tha t minimizes the normalized volume. I’ll talk about some recent work with Chenyang Xu on the solution of these conjectures. If time permits\, I wil l also discuss some further implications on the boundedness of singulariti es.\n LOCATION:https://master.researchseminars.org/talk/agstanford/129/ END:VEVENT BEGIN:VEVENT SUMMARY:Junliang Shen (Yale University) DTSTART:20240126T200000Z DTEND:20240126T210000Z DTSTAMP:20260419T185122Z UID:agstanford/130 DESCRIPTION:Title: Geometry of the P=W conjecture and beyond\nby Junliang She n (Yale University) as part of Stanford algebraic geometry seminar\n\nLect ure held in 383-N.\n\nAbstract\nGiven a compact Riemann surface\, nonabeli an Hodge theory relates topological and algebro-geometric objects associat ed to it. Specifically\, complex representations of the fundamental group are in correspondence with algebraic vector bundles\, equipped with an ext ra structure called a Higgs field. This gives a transcendental matching be tween two very different moduli spaces associated with the Riemann surface : the character variety (parameterizing representations of the fundamental group) and the Hitchin moduli space (parameterizing Higgs bundles). In 20 10\, de Cataldo\, Hausel\, and Migliorini proposed the P=W conjecture\, wh ich gives a precise link between the topology of the Hitchin space and the Hodge theory of the character variety\, imposing surprising constraints o n each side. I will introduce the conjecture\, review its recent proofs\, and discuss how the geometry hidden behind the P=W phenomenon is connected to other branches of mathematics.\n LOCATION:https://master.researchseminars.org/talk/agstanford/130/ END:VEVENT BEGIN:VEVENT SUMMARY:Farbod Shokrieh (University of Washington) DTSTART:20240223T200000Z DTEND:20240223T210000Z DTSTAMP:20260419T185122Z UID:agstanford/131 DESCRIPTION:Title: Heights\, abelian varieties\, and tropical geometry\nby Fa rbod Shokrieh (University of Washington) as part of Stanford algebraic ge ometry seminar\n\nLecture held in 383-N.\n\nAbstract\nI will describe some connections between arithmetic geometry of abelian varieties\, non-archim edean/tropical geometry\, and combinatorics. For a principally polarized a belian variety\, we show an identity relating the Faltings height and the Néron--Tate height (of a symmetric effective divisor defining the polariz ation) which involves invariants arising from non-archimedean/tropical geo metry. If time permits\, we also give formulas for (non-archimedean) canon ical local heights in terms of tropical invariants. (Based on joint work w ith Robin de Jong)\n LOCATION:https://master.researchseminars.org/talk/agstanford/131/ END:VEVENT BEGIN:VEVENT SUMMARY:Weite Pi (Yale University) DTSTART:20240412T190000Z DTEND:20240412T200000Z DTSTAMP:20260419T185122Z UID:agstanford/132 DESCRIPTION:Title: Cohomology rings of the moduli of one-dimensional sheaves on t he projective plane\nby Weite Pi (Yale University) as part of Stanford algebraic geometry seminar\n\nLecture held in 383-N.\n\nAbstract\nThe mod uli spaces of one-dimensional sheaves on the projective plane have been st udied through their connections to enumerative geometry and representation theory. In this talk\, I will explain a systematic approach to study thei r cohomology rings\, using notably tautological relations of geometric ori gin. Our study leads to a conjecture that describes a highly nontrivial pe rverse filtration (which carries important enumerative data) on the cohomo logy in terms of explicit ring generators. This can be viewed as an analog ue of the P=W conjecture in a compact and Fano setting. Based on joint wor k with Y. Kononov\, W. Lim\, M. Moreira\, and J. Shen.\n LOCATION:https://master.researchseminars.org/talk/agstanford/132/ END:VEVENT BEGIN:VEVENT SUMMARY:Matt Baker (Georgia Tech) DTSTART:20240405T190000Z DTEND:20240405T200000Z DTSTAMP:20260419T185122Z UID:agstanford/133 DESCRIPTION:Title: Representations of rigid matroids\nby Matt Baker (Georgia Tech) as part of Stanford algebraic geometry seminar\n\nLecture held in 38 3-N.\n\nAbstract\nWe give a new proof\, along with some generalizations\, of a folklore theorem - attributed to Laurent Lafforgue - that a rigid mat roid (i.e.\, a matroid whose base polytope is indecomposable) has only fin itely many projective equivalence classes of representations over any give n field. A key ingredient in the proof is a generalization of the category of commutative rings which we call *bands*.\n LOCATION:https://master.researchseminars.org/talk/agstanford/133/ END:VEVENT BEGIN:VEVENT SUMMARY:Rosie Shen (Harvard University) DTSTART:20240315T190000Z DTEND:20240315T200000Z DTSTAMP:20260419T185122Z UID:agstanford/134 DESCRIPTION:Title: Du Bois singularities\, rational singularities\, and beyond\nby Rosie Shen (Harvard University) as part of Stanford algebraic geomet ry seminar\n\nLecture held in 383-N.\n\nAbstract\nWe survey some extension s of the classical notions of Du Bois and rational singularities\, known a s the k-Du Bois and k-rational singularities. By now\, these notions are w ell-understood for local complete intersections (lci). We explain the diff iculties beyond the lci case\, and propose new definitions in general to m ake further progress in the theory. This is joint work with Matthew Satria no\, Sridhar Venkatesh and Anh Duc Vo.\n LOCATION:https://master.researchseminars.org/talk/agstanford/134/ END:VEVENT BEGIN:VEVENT SUMMARY:Joaquin Moraga (UCLA) DTSTART:20240531T190000Z DTEND:20240531T200000Z DTSTAMP:20260419T185122Z UID:agstanford/135 DESCRIPTION:Title: Higher-dimensional Fano varieties\nby Joaquin Moraga (UCLA ) as part of Stanford algebraic geometry seminar\n\nLecture held in 383-N. \n\nAbstract\nFano varieties are one of the three building blocks of algeb raic varieties. In this talk\, we will discuss how to describe a general n -dimensional Fano variety. Although there is no consensus on how to answer to this question\, we will explore some new invariants motivated by combi natorics and toric geometry that may lead to a first approximation of an a nswer.\n LOCATION:https://master.researchseminars.org/talk/agstanford/135/ END:VEVENT BEGIN:VEVENT SUMMARY:Hannah Larson (Berkeley\, Clay Mathematical Institute) DTSTART:20240524T193000Z DTEND:20240524T203000Z DTSTAMP:20260419T185122Z UID:agstanford/136 DESCRIPTION:Title: The Chow ring of the universal Picard stack over the hyperelli ptic locus\nby Hannah Larson (Berkeley\, Clay Mathematical Institute) as part of Stanford algebraic geometry seminar\n\nLecture held in 383-N.\n \nAbstract\nI'll start by defining the Chow ring\, which is an important i nvariant of a scheme (or stack). Next\, I will define the Picard variety a nd Picard stack of a curve\, and then introduce their universal versions $ J^d_g$ and $\\mathscr{J}^d_g$ over the moduli space of curves $M_g$. Recen tly\, progress has been made studying the Chow ring of $M_g$ in low genus by stratifying the moduli space by gonality (the minimal degree of a map t o $\\mathbb{P}^1$). The smallest piece in this stratification is the hyper elliptic locus. Motivated by this\, I'll present several results about the restriction of $\\mathscr{J}^d_g$ to the hyperelliptic locus\, denoted $\ \mathscr{J}^d_{2\,g}$. These include a presentation of the rational Chow r ing of $\\mathscr{J}^d_{2\,g}$. I also determine the integral Picard group of $\\mathscr{J}^d_{2\,g}$\, completing (and extending to the $PGL_2$-equ ivariant case) prior work of Erman and Wood.\n\nNotice unusual time so Ele ny Ionel can attend!\n LOCATION:https://master.researchseminars.org/talk/agstanford/136/ END:VEVENT BEGIN:VEVENT SUMMARY:Matt Kerr (Washington University in St. Louis) DTSTART:20240503T190000Z DTEND:20240503T200000Z DTSTAMP:20260419T185122Z UID:agstanford/137 DESCRIPTION:Title: Hypergeometric families and Beilinson’s conjectures (pre-tal k)\nby Matt Kerr (Washington University in St. Louis) as part of Stanf ord algebraic geometry seminar\n\nLecture held in 383-N.\n\nAbstract\nI wi ll describe the construction of motivic cohomology classes on hypergeometr ic families of Calabi-Yau 3-folds using Hadamard convolutions. One can vi ew this as a “higher” version of the Mordell-Weil group for families o f elliptic curves\, giving rise to sections of “higher” Jacobian bundl es which produce solutions to certain inhomogeneous Picard-Fuchs equations . This is part of a joint project with Vasily Golyshev which aims to nume rically verify Beilinson’s conjectures in some new cases.\n\n(Matt Kerr kindly offered to give an introductory pre-talk on hypergeometric variatio ns of hodge structures (VHS). So part 1\, 12-1 pm\, will be a friendly pre-talk\, and part 2\, 2:30-3:30 pm\, will be the friendly talk itself.)\ n LOCATION:https://master.researchseminars.org/talk/agstanford/137/ END:VEVENT BEGIN:VEVENT SUMMARY:Jakub Witaszek (Princeton) DTSTART:20240419T190000Z DTEND:20240419T200000Z DTSTAMP:20260419T185122Z UID:agstanford/138 DESCRIPTION:Title: Singularities in mixed characteristic via the Riemann-Hilbert correspondence\nby Jakub Witaszek (Princeton) as part of Stanford alge braic geometry seminar\n\nLecture held in 383-N.\n\nAbstract\nIn my talk\, I will start by reviewing how various properties of characteristic zero s ingularities can be understood topologically by ways of the Riemann-Hilber t correspondence. After that\, I will explain how similar ideas can be app lied in the study of mixed characteristic singularities. This is based on a joint work with Bhargav Bhatt\, Linquan Ma\, Zsolt Patakfalvi\, Karl Sch wede\, Kevin Tucker\, and Joe Waldron.\n LOCATION:https://master.researchseminars.org/talk/agstanford/138/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Chen (Columbia University) DTSTART:20240311T224500Z DTEND:20240311T234500Z DTSTAMP:20260419T185122Z UID:agstanford/139 DESCRIPTION:Title: An overview of measures of irrationality\nby Nathan Chen ( Columbia University) as part of Stanford algebraic geometry seminar\n\nLec ture held in 384-I (unusual date and location).\n\nAbstract\nThe classical question of determining which varieties are rational has led to a huge am ount of interest and activity. On the other hand\, one can consider a comp lementary perspective - given a smooth projective variety whose nonrationa lity is known\, how "irrational" is it? I will survey what is currently kn own\, with an emphasis on surfaces and open problems.\n LOCATION:https://master.researchseminars.org/talk/agstanford/139/ END:VEVENT BEGIN:VEVENT SUMMARY:Dhruv Goel (Harvard University) DTSTART:20240312T200000Z DTEND:20240312T210000Z DTSTAMP:20260419T185122Z UID:agstanford/140 DESCRIPTION:Title: Chow Classes of Varieties of Secant and Tangent Lines\nby Dhruv Goel (Harvard University) as part of Stanford algebraic geometry sem inar\n\nLecture held in 384-H.\n\nAbstract\n(special Student Algebraic Geo metry Seminar\; note unusual time and location)\n\nGiven a nondegenerate s mooth variety $X\\subset\\mathbb{P}^n$\, let $\\mathcal{S}(X)$ (resp. $\\m athcal{T}(X)$) be the subvariety of the Grassmannian $\\mathbb{G}(1\, n)=\ \mathrm{Gr}(2\, n+1)$ of lines in $\\mathbb{P}^n$ consisting of secant (re sp. tangent) lines to X. I will give closed-form formulae for the classes of $\\mathcal{S}(X)$ and $\\mathcal{T}(X)$ in the Chow ring of $\\mathbb{G }(1\, n)$ in terms of the “higher degrees” of the embedding\, by a sim ple application of the Excess Intersection Formula on a flag variety. Usin g these formulae\, one can recover classical results about the degree of t he subvariety $\\mathrm{Sec}(X)$ (resp. $\\mathrm{Tan}(X)$) of $\\mathbb{P }^n$ swept out by the lines in $\\mathcal{S}(X)$ (resp. $\\mathcal{T}(X)$) \, when it has the expected dimension. Finally\, I will suggest potential extensions of these techniques to varieties of trisecant or bitangent line s.\n LOCATION:https://master.researchseminars.org/talk/agstanford/140/ END:VEVENT BEGIN:VEVENT SUMMARY:Hunter Spink (University of Toronto) DTSTART:20240315T213000Z DTEND:20240315T223000Z DTSTAMP:20260419T185122Z UID:agstanford/141 DESCRIPTION:Title: A new divided difference\, with applications to Schubert polyn omials\nby Hunter Spink (University of Toronto) as part of Stanford al gebraic geometry seminar\n\nLecture held in 380-W (unusual room!).\n\nAbst ract\nI will talk about a new algebra of operations on polynomials which h as the property \n$T_iT_j=T_jT_{i+1}$ for $i>j$ and a family of polynomial s dual to them called forest polynomials. This family of operations plays the exact role for quasisymmetric polynomials and forest polynomials as th e divided difference operations play for symmetric polynomials and Schuber t polynomials. (Joint with Philippe Nadeau and Vasu Tewari)\n LOCATION:https://master.researchseminars.org/talk/agstanford/141/ END:VEVENT BEGIN:VEVENT SUMMARY:Mura Yakerson (Oxford) DTSTART:20240419T213000Z DTEND:20240419T223000Z DTSTAMP:20260419T185122Z UID:agstanford/142 DESCRIPTION:Title: Motivic Adams conjecture\nby Mura Yakerson (Oxford) as par t of Stanford algebraic geometry seminar\n\nLecture held in 383-N.\n\nAbst ract\nThe well-known Adams conjecture in topology is a theorem about compa ctifications of real vector bundles on CW-complexes\, which has important implications for analyzing stable homotopy groups of spheres. In the talk we will discuss an algebro-geometric version of this statement\, which tac kles algebraic vector bundles on smooth algebraic varieties. This is joint work with Alexey Ananyevskiy\, Elden Elmanto and Oliver Röndigs.\n LOCATION:https://master.researchseminars.org/talk/agstanford/142/ END:VEVENT BEGIN:VEVENT SUMMARY:Matt Kerr (Washington University in St. Louis) DTSTART:20240503T213000Z DTEND:20240503T223000Z DTSTAMP:20260419T185122Z UID:agstanford/143 DESCRIPTION:Title: Hypergeometric families and Beilinson’s conjectures (main ta lk)\nby Matt Kerr (Washington University in St. Louis) as part of Stan ford algebraic geometry seminar\n\nLecture held in 383-N.\n\nAbstract\nI w ill describe the construction of motivic cohomology classes on hypergeomet ric families of Calabi-Yau 3-folds using Hadamard convolutions. One can v iew this as a “higher” version of the Mordell-Weil group for families of elliptic curves\, giving rise to sections of “higher” Jacobian bund les which produce solutions to certain inhomogeneous Picard-Fuchs equation s. This is part of a joint project with Vasily Golyshev which aims to num erically verify Beilinson’s conjectures in some new cases.\n\n(Matt Kerr kindly offered to give an introductory pre-talk on hypergeometric variati ons of hodge structures (VHS). So part 1\, 12-1 pm\, will be a friendly pre-talk\, and part 2\, 2:30-3:30 pm\, will be the friendly talk itself.) \n LOCATION:https://master.researchseminars.org/talk/agstanford/143/ END:VEVENT BEGIN:VEVENT SUMMARY:Hannah Larson (Berkeley\, Clay Mathematical Institute) DTSTART:20240523T233000Z DTEND:20240524T003000Z DTSTAMP:20260419T185122Z UID:agstanford/144 DESCRIPTION:Title: Yormark Distinguished Lecture: Cohomology of moduli spaces of curves\nby Hannah Larson (Berkeley\, Clay Mathematical Institute) as part of Stanford algebraic geometry seminar\n\nLecture held in 383-N.\n\nA bstract\nThe moduli space M_g of genus g curves (or Riemann surfaces) is a central object of study in algebraic geometry. Its cohomology is importan t in many fields. For example\, the cohomology of M_g is the same as the c ohomology of the mapping class group\, and is also related to spaces of mo dular forms. Using its properties as a moduli space\, Mumford defined a di stinguished subring of the cohomology of M_g called the tautological ring. The definition of the tautological ring was later extended to the compact ification M_g-bar and the moduli spaces with marked points M_{g\,n}-bar. W hile the full cohomology ring of M_{g\,n}-bar is quite mysterious\, the ta utological subring is relatively well understood\, and conjecturally compl etely understood. In this talk\, I'll ask the question: which cohomology g roups H^k(M_{g\,n}-bar) are tautological? And when they are not\, how can we better understand them? This is joint work with Samir Canning and Sam P ayne.\n LOCATION:https://master.researchseminars.org/talk/agstanford/144/ END:VEVENT BEGIN:VEVENT SUMMARY:Dori Bejleri (University of Maryland) DTSTART:20240531T213000Z DTEND:20240531T223000Z DTSTAMP:20260419T185122Z UID:agstanford/145 DESCRIPTION:Title: Moduli of boundary polarized Calabi-Yau pairs\nby Dori Bej leri (University of Maryland) as part of Stanford algebraic geometry semin ar\n\nLecture held in 383-N.\n\nAbstract\nThe theories of KSBA stability a nd K-stability furnish compact moduli spaces of general type pairs and Fan o pairs respectively. However\, much less is known about the moduli theory of Calabi-Yau pairs. In this talk I will present an approach to construct ing a moduli space of Calabi-Yau pairs which should interpolate between KS BA and K-stable moduli via wall-crossing. I will explain how this approac h can be used to construct projective moduli spaces of plane curve pairs. This is based on joint work with K. Ascher\, H. Blum\, K. DeVleming\, G. I nchiostro\, Y. Liu\, X. Wang.\n LOCATION:https://master.researchseminars.org/talk/agstanford/145/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Halpern-Leistner (Cornell) DTSTART:20240524T213000Z DTEND:20240524T223000Z DTSTAMP:20260419T185122Z UID:agstanford/146 DESCRIPTION:Title: Infinite dimensional geometric invariant theory and gauged Gro mov-Witten theory\nby Daniel Halpern-Leistner (Cornell) as part of Sta nford algebraic geometry seminar\n\nLecture held in 380-X (unusual room!). \n\nAbstract\nHarder-Narasimhan (HN) theory gives a structure theorem for principal G bundles on a smooth projective curve. A bundle is either semis table\, or it admits a canonical filtration whose associated graded bundle is semistable in a graded sense. After reviewing recent advances in exten ding HN theory to arbitrary algebraic stacks\, I will discuss work with An dres Fernandez Herrero applying this general machinery to the stack of map s from a curve C to a quotient stack X/G\, where G is a reductive group an d X is an affine G-scheme. Our main immediate application is to compute ge nerating functions for K-theoretic gauged Gromov-Witten invariants. The me thod we develop to analyze this moduli problem is an infinite dimensional analog of geometric invariant theory\, which is potentially applicable to a much broader range of moduli problems.\n LOCATION:https://master.researchseminars.org/talk/agstanford/146/ END:VEVENT BEGIN:VEVENT SUMMARY:Ziquan Zhuang (Johns Hopkins) DTSTART:20241011T190000Z DTEND:20241011T200000Z DTSTAMP:20260419T185122Z UID:agstanford/147 DESCRIPTION:Title: Boundedness of singularities and discreteness of local volumes \nby Ziquan Zhuang (Johns Hopkins) as part of Stanford algebraic geome try seminar\n\nLecture held in 383-N.\n\nAbstract\nThe local volume of a K awamata log terminal (klt) singularity is an invariant that plays a centra l role in the local theory of K-stability. By the stable degeneration theo rem\, every klt singularity has a volume preserving degeneration to a K-se mistable Fano cone singularity. I will talk about a joint work with Chenya ng Xu on the boundedness of Fano cone singularities when the volume is bou nded away from zero. This implies that local volumes only accumulate aroun d zero in any given dimension.\n LOCATION:https://master.researchseminars.org/talk/agstanford/147/ END:VEVENT BEGIN:VEVENT SUMMARY:Jordan Ellenberg (University of Wisconsin) DTSTART:20240723T220000Z DTEND:20240723T230000Z DTSTAMP:20260419T185122Z UID:agstanford/148 DESCRIPTION:Title: Smyth’s conjecture and a non-deterministic Hasse principle\nby Jordan Ellenberg (University of Wisconsin) as part of Stanford alge braic geometry seminar\n\nLecture held in 383-N.\n\nAbstract\nSmyth asked in the 1980s which linear relations with integral coefficients $a_1 x_1 + ... + a_r x_r$ could hold when $x_1$\, ...\, $x_r$ are Galois conjugates. He found a necessary condition\, which he conjectured was sufficient. Su rprisingly\, this problem\, which appears to be about algebraic number the ory\, ends up touching on many different areas. I’ll explain how to exp ress this problem in terms of eigenvalues of linear combinations of permut ation matrices\, and finally how to solve it by means of a “non-determin istic Hasse principle\,” in which we solve Diophantine equations but tak e our variables to be rational-valued random variables rather than determi nistic rational numbers. There will be almost no advanced math beyond the definition of the p-adic numbers in this talk\, but we will at one point use Brianchon’s theorem on ellipses inscribed in hexagons.\n LOCATION:https://master.researchseminars.org/talk/agstanford/148/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Kuronya (Goethe-Universität Frankfurt) DTSTART:20240909T190000Z DTEND:20240909T200000Z DTSTAMP:20260419T185122Z UID:agstanford/149 DESCRIPTION:Title: Lattice polygons and finite generation of certain valuation se migroups\nby Alex Kuronya (Goethe-Universität Frankfurt) as part of S tanford algebraic geometry seminar\n\nLecture held in 383-I (unusual room) .\n\nAbstract\nThe main theme of the talk is the combinatorics of lattice polygons and its relationship to the geometry of the associated toric surf aces. Our point of view is to measure the complexity of lattice polygons v ia the complexity of geometric objects to which they give rise. For the la tter\, we will focus on convex geometric finiteness properties such as the polyhedrality of the cone of curves or the finite generation of valuation semigroups coming from Newton-Okounkov theory. The latter is a central (a nd wide open) question in combinatorial algebraic geometry with strong ti es to representation theory.\n\nAlthough the talk is in algebraic geometry \, various parts of it will be understandable without much specialized kno wledge from algebraic geometry. This is an account of joint work with Klau s Altmann\, Christian Haase\, Karin Schaller\, and Lena Walter.\n LOCATION:https://master.researchseminars.org/talk/agstanford/149/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierrick Bousseau (University of Georgia) DTSTART:20241101T190000Z DTEND:20241101T200000Z DTSTAMP:20260419T185122Z UID:agstanford/150 DESCRIPTION:Title: Generalized Block-Göttsche polynomials and Welschinger invari ants\nby Pierrick Bousseau (University of Georgia) as part of Stanford algebraic geometry seminar\n\nLecture held in 383-N.\n\nAbstract\nUsing t ropical geometry\, Block-Göttsche defined polynomials with the remarkable property to interpolate between Gromov-Witten counts of complex curves an d Welschinger counts of real curves in toric del Pezzo surfaces. I will de scribe a generalization of Block-Göttsche polynomials to arbitrary\, not- necessarily toric\, rational surfaces and propose a conjectural relation w ith refined Donaldson-Thomas invariants. This is joint work in progress wi th Hulya Arguz.\n LOCATION:https://master.researchseminars.org/talk/agstanford/150/ END:VEVENT BEGIN:VEVENT SUMMARY:Ludmil Katzarkov (Miami) DTSTART:20241122T200000Z DTEND:20241122T210000Z DTSTAMP:20260419T185122Z UID:agstanford/151 DESCRIPTION:Title: New birational invariants\nby Ludmil Katzarkov (Miami) as part of Stanford algebraic geometry seminar\n\nLecture held in 383-N.\n\nA bstract\nIn this talk we will introduce new birational invariants.\nMany e xamples of obstruction to rationality and G rationality will be\nconsidere d.\n LOCATION:https://master.researchseminars.org/talk/agstanford/151/ END:VEVENT BEGIN:VEVENT SUMMARY:Christopher Hacon (University of Utah) DTSTART:20241204T220000Z DTEND:20241204T230000Z DTSTAMP:20260419T185122Z UID:agstanford/152 DESCRIPTION:Title: (Distinguished Lecture) Algebraic geometry vs Kahler geometry< /a>\nby Christopher Hacon (University of Utah) as part of Stanford algebra ic geometry seminar\n\nLecture held in 383-N.\n\nAbstract\nAlgebraic geome try and analytic geometry are two closely related subjects with many impor tant interactions that have spurred major progress in both areas. In this talk we will highlight some of these connections with an emphasis on recen t progress\, future directions\, and open questions.\n LOCATION:https://master.researchseminars.org/talk/agstanford/152/ END:VEVENT BEGIN:VEVENT SUMMARY:Ben Church (Stanford) DTSTART:20250124T200000Z DTEND:20250124T210000Z DTSTAMP:20260419T185122Z UID:agstanford/153 DESCRIPTION:Title: Curves on complete intersections and measures of irrationality \nby Ben Church (Stanford) as part of Stanford algebraic geometry semi nar\n\nLecture held in 383-N.\n\nAbstract\nGiven a projective variety $X$\ , it is always covered by curves obtained by taking the intersection with a linear subspace. We study whether there exist curves on $X$ that have sm aller numerical invariants than those of the linear slices. If $X$ is a ge neral complete intersection of large degrees\, we show that there are no c urves on $X$ of smaller degree\, nor are there curves of asymptotically sm aller gonality. This verifies a folklore conjecture on the degrees of subv arieties of complete intersections as well as a conjecture of Bastianelli- -De Poi--Ein--Lazarsfeld--Ullery on measures of irrationality for complete intersections. This is joint work with Nathan Chen and Junyan Zhao.\n LOCATION:https://master.researchseminars.org/talk/agstanford/153/ END:VEVENT BEGIN:VEVENT SUMMARY:Frank Sottile (Texas A&M University) DTSTART:20250314T190000Z DTEND:20250314T200000Z DTSTAMP:20260419T185122Z UID:agstanford/154 DESCRIPTION:Title: Galois groups in Enumerative Geometry\nby Frank Sottile (T exas A&M University) as part of Stanford algebraic geometry seminar\n\nLec ture held in 383-N.\n\nAbstract\nIn 1870 Jordan explained how Galois theor y can be applied\n to problems from enumerative geometry\, with the group\ n encoding intrinsic structure of the problem. Earlier\n Hermite showed t he equivalence of Galois groups with\n geometric monodromy groups\, and in 1979 Harris initiated the\n modern study of Galois groups of enumerative problems. He\n posited that a Galois group should be `as large as possibl e'\n in that it will be the largest group preserving internal\n symmetry i n the geometric problem.\n\n I will describe this background and discuss some work of\n many to compute\, study\, and use Galois groups of geometr ic\n problems\, including those that arise in applications of\n algebraic geometry.\n LOCATION:https://master.researchseminars.org/talk/agstanford/154/ END:VEVENT END:VCALENDAR