BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jack Petok (Darthmouth) DTSTART:20211023T140000Z DTEND:20211023T142000Z DTSTAMP:20260404T094653Z UID:AGNES/1 DESCRIPTION:Title: Kodaira dimensions of some moduli spaces of hyperkähler fourfolds\nby Jack Petok (Darthmouth) as part of Algebraic Geometry NorthEastern S eries (AGNES)\n\n\nAbstract\nThe Noether-Lefschetz locus in a moduli space of K3^[2]-fourfolds parametrizes fourfolds with Picard rank at least 2. F ollowing Hassett’s work on cubic fourfolds\, Debarre\, Iliev\, and Maniv el showed that the Noether-Lefschetz locus in the moduli space of degree 2 K3^[2]-fourfolds is a countable union of special divisors indexed by disc riminant d. In this talk\, we compute the Kodaira dimensions of these spec ial divisors for all but finitely many discriminants\; in particular\, we show the divisors for discriminants greater than 224 are all of general ty pe.\n LOCATION:https://stable.researchseminars.org/talk/AGNES/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Rachel Webb (Berkeley) DTSTART:20211023T143000Z DTEND:20211023T145000Z DTSTAMP:20260404T094653Z UID:AGNES/2 DESCRIPTION:Title: The moduli of maps has a canonical obstruction theory\nby Rachel Webb (Berkeley) as part of Algebraic Geometry NorthEastern Series (AGNES)\ n\n\nAbstract\nI will explain why the moduli of maps from tame twisted cur ves to a fairly general algebraic stack carries a canonical obstruction th eory. A key ingredient is the construction of a dualizing sheaf and trace map for families of tame twisted curves.\n LOCATION:https://stable.researchseminars.org/talk/AGNES/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Max Weinreich (Brown) DTSTART:20211023T150000Z DTEND:20211023T152000Z DTSTAMP:20260404T094653Z UID:AGNES/3 DESCRIPTION:Title: The pentagram map\nby Max Weinreich (Brown) as part of Algebraic Geometry NorthEastern Series (AGNES)\n\n\nAbstract\nThe pentagram map was introduced by Schwartz as a dynamical system on polygons in the real proje ctive plane. The map sends a polygon to the shape formed by intersecting c ertain diagonals. This simple operation turns out to define a discrete int egrable system\, meaning roughly that\, after a birational change of coord inates\, it is a translation on a family of real tori. We will explain how the real\, complex\, and finite field dynamics of the pentagram map are a ll related by the following generalization: the pentagram map is birationa l to a translation on a family of Jacobian varieties.\n LOCATION:https://stable.researchseminars.org/talk/AGNES/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Claudia Yun (Brown) DTSTART:20211023T153000Z DTEND:20211023T155000Z DTSTAMP:20260404T094653Z UID:AGNES/4 DESCRIPTION:Title: Homology representations of compactified configurations on graphs \nby Claudia Yun (Brown) as part of Algebraic Geometry NorthEastern Series (AGNES)\n\n\nAbstract\nThe $n$-th ordered configuration space of a graph parametrizes ways of placing $n$ distinct and labelled particles on that g raph. The homology of the one-point compactification of such configuration space is equipped with commuting actions of a symmetric group and the out er automorphism group of a free group. We give a cellular decomposition of these configuration spaces on which the actions are realized cellularly a nd thus construct an efficient free resolution for their homology represen tations. Using the Peter-Weyl Theorem for symmetric groups\, we consider e ach irreducible $S_n$-representation individually\, vastly simplifying the calculation of these homology representations from the free resolution. A s our main application\, we obtain computer calculations of the top weight rational cohomology of the moduli spaces $\\mathcal{M}_{2\,n}$\, equivale ntly the rational homology of the tropical moduli spaces $\\Delta_{2\,n}$\ , as a representation of $S_n$ acting by permuting point labels for all $n \\leq 10$. This is joint work with Christin Bibby\, Melody Chan\, and Nir Gadish.\n LOCATION:https://stable.researchseminars.org/talk/AGNES/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Ryan Contreras (Boston College) DTSTART:20211023T180000Z DTEND:20211023T182000Z DTSTAMP:20260404T094653Z UID:AGNES/5 DESCRIPTION:Title: Plane $\\mathbb{A}^1$-curves on the complement of strange rational cu rves\nby Ryan Contreras (Boston College) as part of Algebraic Geometry NorthEastern Series (AGNES)\n\n\nAbstract\nA plane curve is called strang e if its tangent line at any smooth point passes through a fixed point\, c alled the strange point. We study $\\mathbb{A}^1$-curves on the complement of a rational strange curve of degree $p$ in characteristic $p$. We prove the connectedness of the moduli spaces of $\\mathbb{A}^1$-curves with a g iven degree\, classify their irreducible components\, and exhibit the inse parable $\\mathbb{A}^1$-connectedness of the complement using $\\mathbb{A} ^1$-curves parameterized by each irreducible component. I'm going to expla in how the key to these results are the strangeness of all $\\mathbb{A}^1$ -curves.\n LOCATION:https://stable.researchseminars.org/talk/AGNES/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Frei (Rice) DTSTART:20211023T183000Z DTEND:20211023T185000Z DTSTAMP:20260404T094653Z UID:AGNES/6 DESCRIPTION:Title: Reduction of Brauer classes on K3 surfaces\nby Sarah Frei (Rice) as part of Algebraic Geometry NorthEastern Series (AGNES)\n\n\nAbstract\nF or a very general polarized K3 surface over the rational numbers\, it is a consequence of the Tate conjecture that the Picard rank jumps upon reduct ion modulo any prime. This jumping in the Picard rank is countered by a dr op in the size of the Brauer group. In this talk\, I will report on joint work with Brendan Hassett and Anthony Várilly-Alvarado\, in which we cons ider the following: Given a non-trivial Brauer class on a very general pol arized K3 surface over Q\, how often does this class become trivial upon r eduction modulo various primes? This has implications for the rationality of reductions of cubic fourfolds as well as reductions of twisted derived equivalent K3 surfaces.\n LOCATION:https://stable.researchseminars.org/talk/AGNES/6/ END:VEVENT BEGIN:VEVENT SUMMARY:John Kopper (Penn State) DTSTART:20211023T190000Z DTEND:20211023T192000Z DTSTAMP:20260404T094653Z UID:AGNES/7 DESCRIPTION:Title: Ample stable vector bundles on rational surfaces\nby John Kopper (Penn State) as part of Algebraic Geometry NorthEastern Series (AGNES)\n\n \nAbstract\nA theorem of Fulton says that ample vector bundles cannot be c lassified numerically. However\, ampleness is open in families\, and so pr oducing a single ample bundle typically implies the existence of many more . If a bundle is both stable and ample\, then it has stable and ample defo rmations. Le Potier suggests exploiting this fact and classifying those Ch ern characters for which the general stable bundle is ample (provided\, sa y\, the moduli space is irreducible). I will discuss recent progress on th is problem on the minimal rational surfaces. I will give a complete classi fication of those Chern characters for which the general stable bundle is both ample and globally generated. I will also explain an "asymptotic" ver sion of this result for bundles that aren't globally generated. This is jo int work with Jack Huizenga.\n LOCATION:https://stable.researchseminars.org/talk/AGNES/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Joaquín Moraga (Princeton) DTSTART:20211023T193000Z DTEND:20211023T200000Z DTSTAMP:20260404T094653Z UID:AGNES/8 DESCRIPTION:Title: Reductive quotient of klt singularities\nby Joaquín Moraga (Prin ceton) as part of Algebraic Geometry NorthEastern Series (AGNES)\n\n\nAbst ract\nIn this talk\, I will explain recent progress towards the understand ing of quotients of smooth points by the action of reductive groups. The m ain result is that these quotients belong to the singularities of the mini mal model program. Some applications of this result to moduli theory will be explained.\n LOCATION:https://stable.researchseminars.org/talk/AGNES/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Levi Heath (Colorado State) DTSTART:20211024T140000Z DTEND:20211024T142000Z DTSTAMP:20260404T094653Z UID:AGNES/9 DESCRIPTION:Title: Quantum Serre duality for quasimaps\nby Levi Heath (Colorado Stat e) as part of Algebraic Geometry NorthEastern Series (AGNES)\n\n\nAbstract \nLet X be a smooth variety or orbifold and let Z be a complete intersecti on in X defined by a section of a vector bundle E over X. Originally prop osed by Givental\, quantum Serre duality refers to a precise relationship between the Gromov--Witten invariants of Z and those of the dual vector bu ndle E^\\vee. In this talk\, we present recent results proving a quantum S erre duality statement for quasimap invariants. In shifting focus to quasi maps\, we obtain a comparison that is simpler and which also holds for non -convex complete intersections. This is joint work with Mark Shoemaker.\n LOCATION:https://stable.researchseminars.org/talk/AGNES/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Nawaz Sultani (Michigan) DTSTART:20211024T143000Z DTEND:20211024T145000Z DTSTAMP:20260404T094653Z UID:AGNES/10 DESCRIPTION:Title: Gromov-Witten invariants of some non-convex complete intersections\nby Nawaz Sultani (Michigan) as part of Algebraic Geometry NorthEastern Series (AGNES)\n\n\nAbstract\nFor convex complete intersections\, the Gro mov-Witten (GW) invariants are often computed using the Quantum Lefshetz H yperplane theorem\, which relates the invariants to those of the ambient s pace. However\, even in the genus 0 theory\, the convexity condition often fails when the target is an orbifold\, and so Quantum Lefshetz is no long er guaranteed. In this talk\, I will showcase a method to compute these in variants\, despite the failure of Quantum Lefshetz\, for orbifold complete intersections in stack quotients of the form [V // G]. This talk will be based on joint work with Felix Janda (Notre Dame) and Yang Zhou (Harvard)\ , and upcoming work with Rachel Webb (Berkeley).\n LOCATION:https://stable.researchseminars.org/talk/AGNES/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Wern Yeong (Notre Dame) DTSTART:20211024T150000Z DTEND:20211024T152000Z DTSTAMP:20260404T094653Z UID:AGNES/11 DESCRIPTION:Title: Algebraic hyperbolicity of very general hypersurfaces in products of projective spaces\nby Wern Yeong (Notre Dame) as part of Algebraic Ge ometry NorthEastern Series (AGNES)\n\n\nAbstract\nA complex algebraic vari ety is said to be hyperbolic if it contains no entire curves\, which are n on-constant holomorphic images of the complex line. Demailly introduced al gebraic hyperbolicity as an algebraic version of this property\, and it ha s since been well-studied as a means for understanding Kobayashi’s conje cture\, which says that a generic hypersurface in dimensional projective s pace is hyperbolic whenever its degree is large enough. In this talk\, we study the algebraic hyperbolicity of very general hypersurfaces of high bi -degrees in Pm x Pn and completely classify them by their bi-degrees\, exc ept for a few cases in P3 x P1. We present three techniques to do that\, w hich build on past work by Ein\, Voisin\, Pacienza\, Coskun and Riedl\, an d others. As another application of these techniques\, we simplify a proof of Voisin (1988) of the algebraic hyperbolicity of generic high-degree pr ojective hypersurfaces.\n LOCATION:https://stable.researchseminars.org/talk/AGNES/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Aline Zanardini (Leiden) DTSTART:20211024T153000Z DTEND:20211024T155000Z DTSTAMP:20260404T094653Z UID:AGNES/12 DESCRIPTION:Title: The moduli space of rational elliptic surfaces of index two\nby Aline Zanardini (Leiden) as part of Algebraic Geometry NorthEastern Series (AGNES)\n\n\nAbstract\nElliptic surfaces are ubiquitous in Mathematics. E xamples include Enriques surfaces\, Dolgachev surfaces\, and all surfaces of Kodaira dimension one. In this talk we will focus on those elliptic sur faces which are rational and that have exactly one multiple fiber of multi plicity two. These are called rational elliptic surfaces of index two. Our goal will be to describe how to construct their moduli space when the cho ice of a bisection is part of the classification problem. This is based on work in progress joint with Rick Miranda.\n LOCATION:https://stable.researchseminars.org/talk/AGNES/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Samir Canning + Hannah Larson (UCSD + Stanford) DTSTART:20211024T180000Z DTEND:20211024T182000Z DTSTAMP:20260404T094653Z UID:AGNES/13 DESCRIPTION:Title: Chow rings of Hurwitz spaces and moduli spaces of curves\nby Sam ir Canning + Hannah Larson (UCSD + Stanford) as part of Algebraic Geometry NorthEastern Series (AGNES)\n\n\nAbstract\nWe outline our results from a series of papers about the Chow rings of Hurwitz moduli spaces and the mod uli spaces of curves. We will introduce the notion of tautological classes for both moduli spaces. We then will explain how our study of the tautolo gical and Chow rings of Hurwitz moduli spaces leads to new results about t he Chow rings of the moduli spaces of curves.\n LOCATION:https://stable.researchseminars.org/talk/AGNES/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Kai Huang (MIT) DTSTART:20211024T183000Z DTEND:20211024T185000Z DTSTAMP:20260404T094653Z UID:AGNES/14 DESCRIPTION:Title: K-stability of Log Fano Cone Singularities\nby Kai Huang (MIT) a s part of Algebraic Geometry NorthEastern Series (AGNES)\n\n\nAbstract\nWe generalize the valuative criterion for K-stability of Fano varieties to l og Fano cone singularities. We also show the higher rank finite generation conjecture for log Fano cone singularities\, which implies the Yau-Tian-D onaldson Conjecture for Sasakian-Einstein metric.\n LOCATION:https://stable.researchseminars.org/talk/AGNES/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Lena Ji (Michigan) DTSTART:20211024T190000Z DTEND:20211024T192000Z DTSTAMP:20260404T094653Z UID:AGNES/15 DESCRIPTION:Title: The Noether–Lefschetz theorem in arbitrary characteristic\nby Lena Ji (Michigan) as part of Algebraic Geometry NorthEastern Series (AGNE S)\n\n\nAbstract\nThe classical Noether–Lefschetz theorem says that for a very general surface S of degree 4 in P^3 over the complex numbers\, the restriction map from the divisor class group on P^3 to S is an isomorphis m. In this talk\, we will show a Noether–Lefschetz result for varieties over fields of arbitrary characteristic. The proof uses the relative Jacob ian of a curve fibration\, and it also works for singular varieties (for W eil divisors).\n LOCATION:https://stable.researchseminars.org/talk/AGNES/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Fumiaki Suzuki (UCLA) DTSTART:20211024T193000Z DTEND:20211024T200000Z DTSTAMP:20260404T094653Z UID:AGNES/16 DESCRIPTION:Title: An O-acyclic variety of even index\nby Fumiaki Suzuki (UCLA) as part of Algebraic Geometry NorthEastern Series (AGNES)\n\n\nAbstract\nI wi ll construct a family of Enriques surfaces parametrized by P^1 such that a ny multi-section has even degree over the base P^1. Over the function fiel d of a complex curve\, this gives the first example of an O-acyclic variet y (H^i(X\,O)=0 for i>0) whose index is not equal to one\, and an affirmati ve answer to a question of Colliot-Thélène and Voisin. I will also discu ss applications to related problems\, including the integral Hodge conject ure and Murre’s question on universality of the Abel-Jacobi maps. This i s joint work with John Christian Ottem.\n LOCATION:https://stable.researchseminars.org/talk/AGNES/16/ END:VEVENT END:VCALENDAR