BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Angela Gibney (Rutgers University) DTSTART:20200926T153000Z DTEND:20200926T163000Z DTSTAMP:20260404T094701Z UID:madisonmoduliweekendonline/1 DESCRIPTION:Title: Vertex algebras of CohFT- type\nby Angela Gi bney (Rutgers University) as part of Madison Moduli Weekend\n\n\nAbstract\ nRepresentations of vertex algebras of CohFT-type can be used to construct vector bundles of coinvariants and conformal blocks on moduli spaces of s table pointed curves. As I'll explain in the talk\, the name comes from th e fact that such bundles define semisimple cohomological field theories. I'll present motivation for why one may be interested in such bundles and their classes\, as well as a few examples.\n LOCATION:https://stable.researchseminars.org/talk/madisonmoduliweekendonli ne/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Changho Han (University of Georgia) DTSTART:20200926T163000Z DTEND:20200926T165000Z DTSTAMP:20260404T094701Z UID:madisonmoduliweekendonline/2 DESCRIPTION:Title: Compact moduli of lattice polarized $K3$ surface s with $\\mathbb{Z}/3\\mathbb{Z}$ group actions\nby Changho Han (Unive rsity of Georgia) as part of Madison Moduli Weekend\n\n\nAbstract\nObserve that any construction of "meaningful" compactification of moduli spaces o f objects involve enlarging the class of objects in consideration. For exa mple\, Deligne and Mumford introduced the notion of stable curves in order to compactify the moduli of smooth curves of genus g\, and Satake used th e periods from Hodge theory to compactify the same moduli space. After a b rief review of the elliptic curve case (how those notions are the same)\, I will generalize into looking at various compactifications of Kondo's mod uli space of lattice polarized $K3$ surfaces (which are of degree 6) with non symplectic $\\mathbb{Z}/3\\mathbb{Z}$ group action\, then describe the birational relations between those different compactifications. The main advantage of this approach is that we obtain an explicit classification of degenerate $K3$ surfaces\, which is used to find geometric meaning of poi nts parametrized by Hodge-theoretic compactifications. This comes from a j oint works with Anand Deopurkar and a joint work in progress with Valery A lexeev\, Anand Deopurkar\, and Philip Engel.\n LOCATION:https://stable.researchseminars.org/talk/madisonmoduliweekendonli ne/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Laure Flapan (Michigan State University) DTSTART:20200926T172000Z DTEND:20200926T182000Z DTSTAMP:20260404T094701Z UID:madisonmoduliweekendonline/3 DESCRIPTION:Title: Fano manifolds and hyperkahler manifolds\nby Laure Flapan (Michigan State University) as part of Madison Moduli Weeken d\n\n\nAbstract\nFor many Fano manifolds whose cohomology looks like that of a K3 surface\, there are known geometric constructions of corresponding hyperkahler manifolds. In this talk\, we discuss a reverse procedure by w hich\, given a hyperkahler manifold\, one can geometrically construct a co rresponding Fano manifold. This is joint work with E. Macrì\, K. O’Grad y\, and G. Saccà.\n LOCATION:https://stable.researchseminars.org/talk/madisonmoduliweekendonli ne/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Wanlin Li (MIT) DTSTART:20200926T182000Z DTEND:20200926T184000Z DTSTAMP:20260404T094701Z UID:madisonmoduliweekendonline/4 DESCRIPTION:Title: The Section Conjecture at the Boundary of $\\mat hcal{M}_g$\nby Wanlin Li (MIT) as part of Madison Moduli Weekend\n\n\n Abstract\nGrothendieck's section conjecture predicts that rational points on a smooth projective curve of genus $g\\ge 2$ correspond to splittings o f the arithmetic fundamental group sequence. We construct infinitely many curves in each genus where this sequence does not split and so these curve s satisfy the section conjecture. The main inputs to our result are the co nstruction of two cohomology classes which provide obstruction to splittin g and the computation of the order of their Gysin images on various bounda ry components of $\\mathcal{M}_g$. This is joint work in progress with Dan iel Litt\, Nick Salter\, and Padmavathi Srinivasan.​\n LOCATION:https://stable.researchseminars.org/talk/madisonmoduliweekendonli ne/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Ananth Shankar (University of Wisconsin-Madison) DTSTART:20200926T193000Z DTEND:20200926T195000Z DTSTAMP:20260404T094701Z UID:madisonmoduliweekendonline/5 DESCRIPTION:Title: Finiteness results for Hecke orbits over local f ields\nby Ananth Shankar (University of Wisconsin-Madison) as part of Madison Moduli Weekend\n\n\nAbstract\nI will talk about a finiteness resul t for reductions of Hecke orbits of abelian varieties defined over finite extensions of $\\mathbb{Q}_p$. This is joint work with Mark Kisin\, Joshua Lam and Padmavathi Srinivasan.\n LOCATION:https://stable.researchseminars.org/talk/madisonmoduliweekendonli ne/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Max Lieblich (University of Washington) DTSTART:20200926T200000Z DTEND:20200926T210000Z DTSTAMP:20260404T094701Z UID:madisonmoduliweekendonline/6 DESCRIPTION:Title: Moduli spaces in computer vision\nby Max Lie blich (University of Washington) as part of Madison Moduli Weekend\n\n\nAb stract\nI will discuss some moduli spaces that naturally arise in computer vision. While these spaces were traditionally studied using classical pro jective geometry\, a modern functorial approach yields stronger results. I ’ll talk a bit about the rich history of interactions between photogramm etry and projective geometry and how modern algebraic geometry helps us un derstand these connections in new a fruitful ways. I’ll also discuss a k ey open problem on these moduli spaces that has potentially important prac tical implications.\n LOCATION:https://stable.researchseminars.org/talk/madisonmoduliweekendonli ne/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Lightning Talks DTSTART:20200926T210000Z DTEND:20200926T213000Z DTSTAMP:20260404T094701Z UID:madisonmoduliweekendonline/7 DESCRIPTION:Title: View website for details\nby Lightning Talks as part of Madison Moduli Weekend\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/madisonmoduliweekendonli ne/7/ END:VEVENT BEGIN:VEVENT SUMMARY:David Zureick-Brown (Emory Univeristy) DTSTART:20200927T153000Z DTEND:20200927T163000Z DTSTAMP:20260404T094701Z UID:madisonmoduliweekendonline/8 DESCRIPTION:Title: Canonical rings of stacky curves\nby David Z ureick-Brown (Emory Univeristy) as part of Madison Moduli Weekend\n\n\nAbs tract\nWe give a generalization to stacks of the classical (1920's) theore m of Petri - we give a presentation for the canonical ring of a stacky cur ve. This is motivated by the following application: we give an explicit pr esentation for the ring of modular forms for a Fuchsian group with cofinit e area\, which depends on the signature of the group. This is joint work w ith John Voight.\n LOCATION:https://stable.researchseminars.org/talk/madisonmoduliweekendonli ne/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Weiyan Chen (University of Minnesota) DTSTART:20200927T163000Z DTEND:20200927T165000Z DTSTAMP:20260404T094701Z UID:madisonmoduliweekendonline/9 DESCRIPTION:Title: Choosing points on plane cubic curves: rigidity and flexibility\nby Weiyan Chen (University of Minnesota) as part of M adison Moduli Weekend\n\n\nAbstract\nEvery smooth plane cubic curve has 9 inflection points\, 27 sextactic points\, and 72 points of type nine. Moti vated by these classical algebro-geometric constructions\, we study the fo llowing topological question: Is it possible to continuously choose $n$ di stinct unordered points on each smooth plane cubic curve for a given natur al number $n$? We show that the answer is no unless $n$ is a multiple of 9 . We also show that such choices are rigid when $\\frac{n}{9}$ is small\, and flexible when $\\frac{n}{9}$ is large. Part of the talk is on work joi nt with Ishan Banerjee.\n LOCATION:https://stable.researchseminars.org/talk/madisonmoduliweekendonli ne/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Antieau (Northwestern University) DTSTART:20200927T172000Z DTEND:20200927T182000Z DTSTAMP:20260404T094701Z UID:madisonmoduliweekendonline/10 DESCRIPTION:Title: On the Brauer group of the moduli stack of elli ptic curves\nby Benjamin Antieau (Northwestern University) as part of Madison Moduli Weekend\n\n\nAbstract\nMumford proved that the Picard group of the moduli stack of elliptic curves is a finite group of order 12\, ge nerated by the Hodge bundle of the universal family of elliptic curves. Af ter giving background on Brauer groups and on the moduli of elliptic curve s\, I will talk about work with Lennart Meier\, which computes the Brauer group of the moduli stack over various arithmetic base schemes and shows i n particular that the Brauer group of the integral moduli stack vanishes. This talk will focus on the concrete computational and arithmetic aspects of the proof.\n LOCATION:https://stable.researchseminars.org/talk/madisonmoduliweekendonli ne/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Alicia Lamarche (University of Utah) DTSTART:20200927T182000Z DTEND:20200927T184000Z DTSTAMP:20260404T094701Z UID:madisonmoduliweekendonline/11 DESCRIPTION:Title: Derived Categories and Arithmetic\nby Alici a Lamarche (University of Utah) as part of Madison Moduli Weekend\n\n\nAbs tract\nIn this talk\, we will explore the extent to which the derived cate gory of coherent sheaves can be used to answer rationality questions about a variety defined over an arbitrary field. In particular\, we will give s ome examples of using the machinery of the derived category in an arithmet ic setting. We will also discuss recent results of joint work with Matthew Ballard\, Alex Duncan\, and Patrick McFaddin concerning the behavior of t he derived category under twisting by a torsor.\n LOCATION:https://stable.researchseminars.org/talk/madisonmoduliweekendonli ne/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Kobin (UCSC) DTSTART:20200927T193000Z DTEND:20200927T195000Z DTSTAMP:20260404T094701Z UID:madisonmoduliweekendonline/12 DESCRIPTION:Title: Stacky Curves in characteristic $p$\nby And rew Kobin (UCSC) as part of Madison Moduli Weekend\n\n\nAbstract\nAs stack s continue to become an essential part of a modern algebraic geometer’s toolbox\, researchers look to their local structure as a guide to their na ture. Over the complex numbers\, this local structure is called a complex orbifold\, or ‘orbit space of a manifold’ under a cyclic group action. In this talk\, I will survey the classification of stacky curves in chara cteristic 0 and introduce a new construction\, called an Artin–Schreier root stack\, which allows for similar classification results in characteri stic $p$.\n LOCATION:https://stable.researchseminars.org/talk/madisonmoduliweekendonli ne/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Lightning Talks DTSTART:20200927T200000Z DTEND:20200927T210000Z DTSTAMP:20260404T094701Z UID:madisonmoduliweekendonline/13 DESCRIPTION:Title: View website for details\nby Lightning Talk s as part of Madison Moduli Weekend\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/madisonmoduliweekendonli ne/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Libby Taylor (Stanford University) DTSTART:20200927T210000Z DTEND:20200927T213000Z DTSTAMP:20260404T094701Z UID:madisonmoduliweekendonline/14 DESCRIPTION:Title: Derived equivalences for stacky genus 1 curves< /a>\nby Libby Taylor (Stanford University) as part of Madison Moduli Weeke nd\n\n\nAbstract\nWe will study the question of when two stacky genus 1 cu rves over a field have equivalent derived categories. Stacky genus 1 curve s occur as connected components of the Picard stack of a genus 1 curve. So me questions we will answer: when are two genus 1 curves derived equivalen t? Can we make derived equivalences explicit? And how do we connect deriv ed equivalences to moduli problems?\n LOCATION:https://stable.researchseminars.org/talk/madisonmoduliweekendonli ne/14/ END:VEVENT END:VCALENDAR