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:20260422T212937Z UID:madisonmoduliweekendonline/1 DESCRIPTION:Title: Vertex algebras of CohFT- type\nby Angela Gibney (R utgers University) as part of Madison Moduli Weekend\n\n\nAbstract\nRepres entations of vertex algebras of CohFT-type can be used to construct vector bundles of coinvariants and conformal blocks on moduli spaces of stable p ointed curves. As I'll explain in the talk\, the name comes from the fact that such bundles define semisimple cohomological field theories. I'll pr esent motivation for why one may be interested in such bundles and their c lasses\, as well as a few examples.\n LOCATION:https://researchseminars.org/talk/madisonmoduliweekendonline/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Changho Han (University of Georgia) DTSTART:20200926T163000Z DTEND:20200926T165000Z DTSTAMP:20260422T212937Z UID:madisonmoduliweekendonline/2 DESCRIPTION:Title: Compact moduli of lattice polarized $K3$ surfaces with $\\mathbb{Z}/3\\mathbb{Z}$ group actions\nby Changho Han (University o f Georgia) as part of Madison Moduli Weekend\n\n\nAbstract\nObserve that a ny construction of "meaningful" compactification of moduli spaces of objec ts involve enlarging the class of objects in consideration. For example\, Deligne and Mumford introduced the notion of stable curves in order to com pactify the moduli of smooth curves of genus g\, and Satake used the perio ds from Hodge theory to compactify the same moduli space. After a brief re view of the elliptic curve case (how those notions are the same)\, I will generalize into looking at various compactifications of Kondo's moduli spa ce of lattice polarized $K3$ surfaces (which are of degree 6) with non sym plectic $\\mathbb{Z}/3\\mathbb{Z}$ group action\, then describe the birati onal relations between those different compactifications. The main advanta ge of this approach is that we obtain an explicit classification of degene rate $K3$ surfaces\, which is used to find geometric meaning of points par ametrized by Hodge-theoretic compactifications. This comes from a joint wo rks with Anand Deopurkar and a joint work in progress with Valery Alexeev\ , Anand Deopurkar\, and Philip Engel.\n LOCATION:https://researchseminars.org/talk/madisonmoduliweekendonline/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Laure Flapan (Michigan State University) DTSTART:20200926T172000Z DTEND:20200926T182000Z DTSTAMP:20260422T212937Z UID:madisonmoduliweekendonline/3 DESCRIPTION:Title: Fano manifolds and hyperkahler manifolds\nby Laure Flapan (Michigan State University) as part of Madison Moduli Weekend\n\n\n Abstract\nFor many Fano manifolds whose cohomology looks like that of a K3 surface\, there are known geometric constructions of corresponding hyperk ahler manifolds. In this talk\, we discuss a reverse procedure by which\, given a hyperkahler manifold\, one can geometrically construct a correspon ding Fano manifold. This is joint work with E. Macrì\, K. O’Grady\, and G. Saccà.\n LOCATION:https://researchseminars.org/talk/madisonmoduliweekendonline/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Wanlin Li (MIT) DTSTART:20200926T182000Z DTEND:20200926T184000Z DTSTAMP:20260422T212937Z UID:madisonmoduliweekendonline/4 DESCRIPTION:Title: The Section Conjecture at the Boundary of $\\mathcal{M} _g$\nby Wanlin Li (MIT) as part of Madison Moduli Weekend\n\n\nAbstrac t\nGrothendieck's section conjecture predicts that rational points on a sm ooth projective curve of genus $g\\ge 2$ correspond to splittings of the a rithmetic fundamental group sequence. We construct infinitely many curves in each genus where this sequence does not split and so these curves satis fy the section conjecture. The main inputs to our result are the construct ion of two cohomology classes which provide obstruction to splitting and t he computation of the order of their Gysin images on various boundary comp onents of $\\mathcal{M}_g$. This is joint work in progress with Daniel Lit t\, Nick Salter\, and Padmavathi Srinivasan.​\n LOCATION:https://researchseminars.org/talk/madisonmoduliweekendonline/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Ananth Shankar (University of Wisconsin-Madison) DTSTART:20200926T193000Z DTEND:20200926T195000Z DTSTAMP:20260422T212937Z UID:madisonmoduliweekendonline/5 DESCRIPTION:Title: Finiteness results for Hecke orbits over local fields\nby Ananth Shankar (University of Wisconsin-Madison) as part of Madison Moduli Weekend\n\n\nAbstract\nI will talk about a finiteness result for r eductions of Hecke orbits of abelian varieties defined over finite extensi ons of $\\mathbb{Q}_p$. This is joint work with Mark Kisin\, Joshua Lam an d Padmavathi Srinivasan.\n LOCATION:https://researchseminars.org/talk/madisonmoduliweekendonline/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Max Lieblich (University of Washington) DTSTART:20200926T200000Z DTEND:20200926T210000Z DTSTAMP:20260422T212937Z UID:madisonmoduliweekendonline/6 DESCRIPTION:Title: Moduli spaces in computer vision\nby Max Lieblich ( University of Washington) as part of Madison Moduli Weekend\n\n\nAbstract\ nI will discuss some moduli spaces that naturally arise in computer vision . While these spaces were traditionally studied using classical projective geometry\, a modern functorial approach yields stronger results. I’ll t alk a bit about the rich history of interactions between photogrammetry an d projective geometry and how modern algebraic geometry helps us understan d these connections in new a fruitful ways. I’ll also discuss a key open problem on these moduli spaces that has potentially important practical i mplications.\n LOCATION:https://researchseminars.org/talk/madisonmoduliweekendonline/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Lightning Talks DTSTART:20200926T210000Z DTEND:20200926T213000Z DTSTAMP:20260422T212937Z UID:madisonmoduliweekendonline/7 DESCRIPTION:Title: View website for details\nby Lightning Talks as par t of Madison Moduli Weekend\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/madisonmoduliweekendonline/7/ END:VEVENT BEGIN:VEVENT SUMMARY:David Zureick-Brown (Emory Univeristy) DTSTART:20200927T153000Z DTEND:20200927T163000Z DTSTAMP:20260422T212937Z UID:madisonmoduliweekendonline/8 DESCRIPTION:Title: Canonical rings of stacky curves\nby David Zureick- Brown (Emory Univeristy) as part of Madison Moduli Weekend\n\n\nAbstract\n We give a generalization to stacks of the classical (1920's) theorem of Pe tri - we give a presentation for the canonical ring of a stacky curve. Thi s is motivated by the following application: we give an explicit presentat ion for the ring of modular forms for a Fuchsian group with cofinite area\ , which depends on the signature of the group. This is joint work with Joh n Voight.\n LOCATION:https://researchseminars.org/talk/madisonmoduliweekendonline/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Weiyan Chen (University of Minnesota) DTSTART:20200927T163000Z DTEND:20200927T165000Z DTSTAMP:20260422T212937Z UID:madisonmoduliweekendonline/9 DESCRIPTION:Title: Choosing points on plane cubic curves: rigidity and fle xibility\nby Weiyan Chen (University of Minnesota) as part of Madison Moduli Weekend\n\n\nAbstract\nEvery smooth plane cubic curve has 9 inflect ion points\, 27 sextactic points\, and 72 points of type nine. Motivated b y these classical algebro-geometric constructions\, we study the following topological question: Is it possible to continuously choose $n$ distinct unordered points on each smooth plane cubic curve for a given natural numb er $n$? We show that the answer is no unless $n$ is a multiple of 9. We al so show that such choices are rigid when $\\frac{n}{9}$ is small\, and fle xible when $\\frac{n}{9}$ is large. Part of the talk is on work joint with Ishan Banerjee.\n LOCATION:https://researchseminars.org/talk/madisonmoduliweekendonline/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Antieau (Northwestern University) DTSTART:20200927T172000Z DTEND:20200927T182000Z DTSTAMP:20260422T212937Z UID:madisonmoduliweekendonline/10 DESCRIPTION:Title: On the Brauer group of the moduli stack of elliptic cu rves\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\, generated by the Hodge bundle of the universal family of elliptic curves. After giv ing background on Brauer groups and on the moduli of elliptic curves\, I w ill talk about work with Lennart Meier\, which computes the Brauer group o f the moduli stack over various arithmetic base schemes and shows in parti cular that the Brauer group of the integral moduli stack vanishes. This ta lk will focus on the concrete computational and arithmetic aspects of the proof.\n LOCATION:https://researchseminars.org/talk/madisonmoduliweekendonline/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Alicia Lamarche (University of Utah) DTSTART:20200927T182000Z DTEND:20200927T184000Z DTSTAMP:20260422T212937Z UID:madisonmoduliweekendonline/11 DESCRIPTION:Title: Derived Categories and Arithmetic\nby Alicia Lamar che (University of Utah) as part of Madison Moduli Weekend\n\n\nAbstract\n In this talk\, we will explore the extent to which the derived category of coherent sheaves can be used to answer rationality questions about a vari ety defined over an arbitrary field. In particular\, we will give some exa mples of using the machinery of the derived category in an arithmetic sett ing. We will also discuss recent results of joint work with Matthew Ballar d\, Alex Duncan\, and Patrick McFaddin concerning the behavior of the deri ved category under twisting by a torsor.\n LOCATION:https://researchseminars.org/talk/madisonmoduliweekendonline/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Kobin (UCSC) DTSTART:20200927T193000Z DTEND:20200927T195000Z DTSTAMP:20260422T212937Z UID:madisonmoduliweekendonline/12 DESCRIPTION:Title: Stacky Curves in characteristic $p$\nby Andrew Kob in (UCSC) as part of Madison Moduli Weekend\n\n\nAbstract\nAs stacks conti nue to become an essential part of a modern algebraic geometer’s toolbox \, researchers look to their local structure as a guide to their nature. O ver the complex numbers\, this local structure is called a complex orbifol d\, or ‘orbit space of a manifold’ under a cyclic group action. In thi s talk\, I will survey the classification of stacky curves in characterist ic 0 and introduce a new construction\, called an Artin–Schreier root st ack\, which allows for similar classification results in characteristic $p $.\n LOCATION:https://researchseminars.org/talk/madisonmoduliweekendonline/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Lightning Talks DTSTART:20200927T200000Z DTEND:20200927T210000Z DTSTAMP:20260422T212937Z UID:madisonmoduliweekendonline/13 DESCRIPTION:Title: View website for details\nby Lightning Talks as pa rt of Madison Moduli Weekend\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/madisonmoduliweekendonline/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Libby Taylor (Stanford University) DTSTART:20200927T210000Z DTEND:20200927T213000Z DTSTAMP:20260422T212937Z UID:madisonmoduliweekendonline/14 DESCRIPTION:Title: Derived equivalences for stacky genus 1 curves\nby Libby Taylor (Stanford University) as part of Madison Moduli Weekend\n\n\ nAbstract\nWe will study the question of when two stacky genus 1 curves ov er a field have equivalent derived categories. Stacky genus 1 curves occur as connected components of the Picard stack of a genus 1 curve. Some ques tions we will answer: when are two genus 1 curves derived equivalent? Can we make derived equivalences explicit? And how do we connect derived equi valences to moduli problems?\n LOCATION:https://researchseminars.org/talk/madisonmoduliweekendonline/14/ END:VEVENT END:VCALENDAR