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:20260422T212731Z UID:AGNES/1 DESCRIPTION:Title: Ko daira dimensions of some moduli spaces of hyperkähler fourfolds\nby J ack Petok (Darthmouth) as part of Algebraic Geometry NorthEastern Series ( AGNES)\n\n\nAbstract\nThe Noether-Lefschetz locus in a moduli space of K3^ [2]-fourfolds parametrizes fourfolds with Picard rank at least 2. Followin g Hassett’s work on cubic fourfolds\, Debarre\, Iliev\, and Manivel show ed that the Noether-Lefschetz locus in the moduli space of degree 2 K3^[2] -fourfolds is a countable union of special divisors indexed by discriminan t d. In this talk\, we compute the Kodaira dimensions of these special div isors for all but finitely many discriminants\; in particular\, we show th e divisors for discriminants greater than 224 are all of general type.\n LOCATION:https://researchseminars.org/talk/AGNES/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Rachel Webb (Berkeley) DTSTART:20211023T143000Z DTEND:20211023T145000Z DTSTAMP:20260422T212731Z UID:AGNES/2 DESCRIPTION:Title: Th e moduli of maps has a canonical obstruction theory\nby Rachel Webb (B erkeley) as part of Algebraic Geometry NorthEastern Series (AGNES)\n\n\nAb stract\nI will explain why the moduli of maps from tame twisted curves to a fairly general algebraic stack carries a canonical obstruction theory. A key ingredient is the construction of a dualizing sheaf and trace map for families of tame twisted curves.\n LOCATION:https://researchseminars.org/talk/AGNES/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Max Weinreich (Brown) DTSTART:20211023T150000Z DTEND:20211023T152000Z DTSTAMP:20260422T212731Z UID:AGNES/3 DESCRIPTION:Title: Th e pentagram map\nby Max Weinreich (Brown) as part of Algebraic Geometr y NorthEastern Series (AGNES)\n\n\nAbstract\nThe pentagram map was introdu ced by Schwartz as a dynamical system on polygons in the real projective p lane. The map sends a polygon to the shape formed by intersecting certain diagonals. This simple operation turns out to define a discrete integrable system\, meaning roughly that\, after a birational change of coordinates\ , it is a translation on a family of real tori. We will explain how the re al\, complex\, and finite field dynamics of the pentagram map are all rela ted by the following generalization: the pentagram map is birational to a translation on a family of Jacobian varieties.\n LOCATION:https://researchseminars.org/talk/AGNES/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Claudia Yun (Brown) DTSTART:20211023T153000Z DTEND:20211023T155000Z DTSTAMP:20260422T212731Z UID:AGNES/4 DESCRIPTION:Title: Ho mology representations of compactified configurations on graphs\nby Cl audia Yun (Brown) as part of Algebraic Geometry NorthEastern Series (AGNES )\n\n\nAbstract\nThe $n$-th ordered configuration space of a graph paramet rizes ways of placing $n$ distinct and labelled particles on that graph. T he homology of the one-point compactification of such configuration space is equipped with commuting actions of a symmetric group and the outer auto morphism group of a free group. We give a cellular decomposition of these configuration spaces on which the actions are realized cellularly and thus construct an efficient free resolution for their homology representations . Using the Peter-Weyl Theorem for symmetric groups\, we consider each irr educible $S_n$-representation individually\, vastly simplifying the calcul ation of these homology representations from the free resolution. As our m ain application\, we obtain computer calculations of the top weight ration al cohomology of the moduli spaces $\\mathcal{M}_{2\,n}$\, equivalently th e rational homology of the tropical moduli spaces $\\Delta_{2\,n}$\, as a representation of $S_n$ acting by permuting point labels for all $n\\leq 1 0$. This is joint work with Christin Bibby\, Melody Chan\, and Nir Gadish. \n LOCATION:https://researchseminars.org/talk/AGNES/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Ryan Contreras (Boston College) DTSTART:20211023T180000Z DTEND:20211023T182000Z DTSTAMP:20260422T212731Z UID:AGNES/5 DESCRIPTION:Title: Pl ane $\\mathbb{A}^1$-curves on the complement of strange rational curves\nby Ryan Contreras (Boston College) as part of Algebraic Geometry NorthE astern Series (AGNES)\n\n\nAbstract\nA plane curve is called strange if it s tangent line at any smooth point passes through a fixed point\, called t he strange point. We study $\\mathbb{A}^1$-curves on the complement of a r ational strange curve of degree $p$ in characteristic $p$. We prove the co nnectedness of the moduli spaces of $\\mathbb{A}^1$-curves with a given de gree\, classify their irreducible components\, and exhibit the inseparable $\\mathbb{A}^1$-connectedness of the complement using $\\mathbb{A}^1$-cur ves parameterized by each irreducible component. I'm going to explain how the key to these results are the strangeness of all $\\mathbb{A}^1$-curves .\n LOCATION:https://researchseminars.org/talk/AGNES/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Frei (Rice) DTSTART:20211023T183000Z DTEND:20211023T185000Z DTSTAMP:20260422T212731Z UID:AGNES/6 DESCRIPTION:Title: Re duction of Brauer classes on K3 surfaces\nby Sarah Frei (Rice) as part of Algebraic Geometry NorthEastern Series (AGNES)\n\n\nAbstract\nFor a ve ry general polarized K3 surface over the rational numbers\, it is a conseq uence of the Tate conjecture that the Picard rank jumps upon reduction mod ulo any prime. This jumping in the Picard rank is countered by a drop in t he size of the Brauer group. In this talk\, I will report on joint work wi th Brendan Hassett and Anthony Várilly-Alvarado\, in which we consider th e following: Given a non-trivial Brauer class on a very general polarized K3 surface over Q\, how often does this class become trivial upon reductio n modulo various primes? This has implications for the rationality of redu ctions of cubic fourfolds as well as reductions of twisted derived equival ent K3 surfaces.\n LOCATION:https://researchseminars.org/talk/AGNES/6/ END:VEVENT BEGIN:VEVENT SUMMARY:John Kopper (Penn State) DTSTART:20211023T190000Z DTEND:20211023T192000Z DTSTAMP:20260422T212731Z UID:AGNES/7 DESCRIPTION:Title: Am ple stable vector bundles on rational surfaces\nby John Kopper (Penn S tate) as part of Algebraic Geometry NorthEastern Series (AGNES)\n\n\nAbstr act\nA theorem of Fulton says that ample vector bundles cannot be classifi ed numerically. However\, ampleness is open in families\, and so producing 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 deformation s. Le Potier suggests exploiting this fact and classifying those Chern cha racters for which the general stable bundle is ample (provided\, say\, the moduli space is irreducible). I will discuss recent progress on this prob lem on the minimal rational surfaces. I will give a complete classificatio n of those Chern characters for which the general stable bundle is both am ple and globally generated. I will also explain an "asymptotic" version of this result for bundles that aren't globally generated. This is joint wor k with Jack Huizenga.\n LOCATION:https://researchseminars.org/talk/AGNES/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Joaquín Moraga (Princeton) DTSTART:20211023T193000Z DTEND:20211023T200000Z DTSTAMP:20260422T212731Z UID:AGNES/8 DESCRIPTION:Title: Re ductive quotient of klt singularities\nby Joaquín Moraga (Princeton) as part of Algebraic Geometry NorthEastern Series (AGNES)\n\n\nAbstract\nI n this talk\, I will explain recent progress towards the understanding of quotients of smooth points by the action of reductive groups. The main res ult is that these quotients belong to the singularities of the minimal mod el program. Some applications of this result to moduli theory will be expl ained.\n LOCATION:https://researchseminars.org/talk/AGNES/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Levi Heath (Colorado State) DTSTART:20211024T140000Z DTEND:20211024T142000Z DTSTAMP:20260422T212731Z UID:AGNES/9 DESCRIPTION:Title: Qu antum Serre duality for quasimaps\nby Levi Heath (Colorado State) as p art of Algebraic Geometry NorthEastern Series (AGNES)\n\n\nAbstract\nLet X be a smooth variety or orbifold and let Z be a complete intersection in X defined by a section of a vector bundle E over X. Originally proposed by Givental\, quantum Serre duality refers to a precise relationship between the Gromov--Witten invariants of Z and those of the dual vector bundle E^ \\vee. In this talk\, we present recent results proving a quantum Serre du ality statement for quasimap invariants. In shifting focus to quasimaps\, 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://researchseminars.org/talk/AGNES/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Nawaz Sultani (Michigan) DTSTART:20211024T143000Z DTEND:20211024T145000Z DTSTAMP:20260422T212731Z UID:AGNES/10 DESCRIPTION:Title: G romov-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 Gromov-Wit ten (GW) invariants are often computed using the Quantum Lefshetz Hyperpla ne theorem\, which relates the invariants to those of the ambient space. H owever\, even in the genus 0 theory\, the convexity condition often fails when the target is an orbifold\, and so Quantum Lefshetz is no longer guar anteed. In this talk\, I will showcase a method to compute these invariant s\, despite the failure of Quantum Lefshetz\, for orbifold complete inters ections in stack quotients of the form [V // G]. This talk will be based o n joint work with Felix Janda (Notre Dame) and Yang Zhou (Harvard)\, and u pcoming work with Rachel Webb (Berkeley).\n LOCATION:https://researchseminars.org/talk/AGNES/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Wern Yeong (Notre Dame) DTSTART:20211024T150000Z DTEND:20211024T152000Z DTSTAMP:20260422T212731Z UID:AGNES/11 DESCRIPTION:Title: A lgebraic hyperbolicity of very general hypersurfaces in products of projec tive spaces\nby Wern Yeong (Notre Dame) as part of Algebraic Geometry NorthEastern Series (AGNES)\n\n\nAbstract\nA complex algebraic variety is said to be hyperbolic if it contains no entire curves\, which are non-cons tant holomorphic images of the complex line. Demailly introduced algebraic hyperbolicity as an algebraic version of this property\, and it has since been well-studied as a means for understanding Kobayashi’s conjecture\, which says that a generic hypersurface in dimensional projective space is hyperbolic whenever its degree is large enough. In this talk\, we study t he algebraic hyperbolicity of very general hypersurfaces of high bi-degree s in Pm x Pn and completely classify them by their bi-degrees\, except for a few cases in P3 x P1. We present three techniques to do that\, which bu ild on past work by Ein\, Voisin\, Pacienza\, Coskun and Riedl\, and other s. As another application of these techniques\, we simplify a proof of Voi sin (1988) of the algebraic hyperbolicity of generic high-degree projectiv e hypersurfaces.\n LOCATION:https://researchseminars.org/talk/AGNES/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Aline Zanardini (Leiden) DTSTART:20211024T153000Z DTEND:20211024T155000Z DTSTAMP:20260422T212731Z UID:AGNES/12 DESCRIPTION:Title: T he moduli space of rational elliptic surfaces of index two\nby Aline Z anardini (Leiden) as part of Algebraic Geometry NorthEastern Series (AGNES )\n\n\nAbstract\nElliptic surfaces are ubiquitous in Mathematics. Examples include Enriques surfaces\, Dolgachev surfaces\, and all surfaces of Koda ira dimension one. In this talk we will focus on those elliptic surfaces w hich are rational and that have exactly one multiple fiber of multiplicity two. These are called rational elliptic surfaces of index two. Our goal w ill be to describe how to construct their moduli space when the choice of a bisection is part of the classification problem. This is based on work i n progress joint with Rick Miranda.\n LOCATION:https://researchseminars.org/talk/AGNES/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Samir Canning + Hannah Larson (UCSD + Stanford) DTSTART:20211024T180000Z DTEND:20211024T182000Z DTSTAMP:20260422T212731Z UID:AGNES/13 DESCRIPTION:Title: C how rings of Hurwitz spaces and moduli spaces of curves\nby Samir Cann ing + Hannah Larson (UCSD + Stanford) as part of Algebraic Geometry NorthE astern Series (AGNES)\n\n\nAbstract\nWe outline our results from a series of papers about the Chow rings of Hurwitz moduli spaces and the moduli spa ces of curves. We will introduce the notion of tautological classes for bo th moduli spaces. We then will explain how our study of the tautological a nd Chow rings of Hurwitz moduli spaces leads to new results about the Chow rings of the moduli spaces of curves.\n LOCATION:https://researchseminars.org/talk/AGNES/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Kai Huang (MIT) DTSTART:20211024T183000Z DTEND:20211024T185000Z DTSTAMP:20260422T212731Z UID:AGNES/14 DESCRIPTION:Title: K -stability of Log Fano Cone Singularities\nby Kai Huang (MIT) as part of Algebraic Geometry NorthEastern Series (AGNES)\n\n\nAbstract\nWe genera lize the valuative criterion for K-stability of Fano varieties to log Fano cone singularities. We also show the higher rank finite generation conjec ture for log Fano cone singularities\, which implies the Yau-Tian-Donaldso n Conjecture for Sasakian-Einstein metric.\n LOCATION:https://researchseminars.org/talk/AGNES/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Lena Ji (Michigan) DTSTART:20211024T190000Z DTEND:20211024T192000Z DTSTAMP:20260422T212731Z UID:AGNES/15 DESCRIPTION:Title: T he Noether–Lefschetz theorem in arbitrary characteristic\nby Lena Ji (Michigan) as part of Algebraic Geometry NorthEastern Series (AGNES)\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 restri ction map from the divisor class group on P^3 to S is an isomorphism. In t his talk\, we will show a Noether–Lefschetz result for varieties over fi elds of arbitrary characteristic. The proof uses the relative Jacobian of a curve fibration\, and it also works for singular varieties (for Weil div isors).\n LOCATION:https://researchseminars.org/talk/AGNES/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Fumiaki Suzuki (UCLA) DTSTART:20211024T193000Z DTEND:20211024T200000Z DTSTAMP:20260422T212731Z UID:AGNES/16 DESCRIPTION:Title: A n O-acyclic variety of even index\nby Fumiaki Suzuki (UCLA) as part of Algebraic Geometry NorthEastern Series (AGNES)\n\n\nAbstract\nI will cons truct a family of Enriques surfaces parametrized by P^1 such that any mult i-section has even degree over the base P^1. Over the function field of a complex curve\, this gives the first example of an O-acyclic variety (H^i( X\,O)=0 for i>0) whose index is not equal to one\, and an affirmative answ er to a question of Colliot-Thélène and Voisin. I will also discuss appl ications to related problems\, including the integral Hodge conjecture and Murre’s question on universality of the Abel-Jacobi maps. This is joint work with John Christian Ottem.\n LOCATION:https://researchseminars.org/talk/AGNES/16/ END:VEVENT END:VCALENDAR