Algebraic geometry seminar

from Thursday
June 01, 2017 to Sunday
December 31, 2017
 Show events for: All Events AGNES Algebraic geometry seminar Algebraic models in geometry seminar Am.Math.Soc. (AMS) Chapter Seminar Analysis Student Seminar Capsule Research Talks Colloquium Commencement Ceremony Comprehensive Exams Dynamical Systems Seminar Equivalence Method and Exterior Differential Systems Seminar First and Second Year Student Seminar Friday Summer Meeting Geometric Analysis Learning Seminar Geometry/Topology Seminar Grad / Postdoc Professional Development Seminar Graduate Student Seminar Graduate Topology Seminar Grant Proposal Panel Hodge Theory, Moduli and Representation Theory Holiday Party Joint Columbia-CUNY-Stony Brook General Relativity Seminar Math Club Math Day 2016 Math in Jeans Mathematical Writing Seminar Mathematics Education Colloquium Mathematics Summer Camp Mini Course / Dynamics Learning Seminar Mini-School in Geometry Minicourse in Real Enumerative Geometry New Graduate Students NY General Relativity Seminar RTG Colloquium RTG Seminar RTG Student Geometry Seminar Seminar in Topology and Symplectic Geometry Seminar on algebraic structures in physics Simons Colloquium Simons Lectures Series Singular metrics and direct images Special Algebra / Algebraic Geometry Seminar Special Analysis Seminar Special Colloquium Special Geometry/Topology Seminar Special Lectures Special Seminar in Algebraic Geometry Special Topology Seminar Student Algebraic Geometry Seminar Student Gauge Theory Seminar Student Seminar on Differential Geometry and Analysis Summer Workshop in Topology and Geometry Symplectic Geometry Reading Seminar Symplectic Geometry Seminar Thesis Defense Topology and Symplectic Geometry / Math of Gauge Fields seminar Women in Mathematics Instructions for subscribing to Stony Brook Math Department Calendars

 WednesdaySeptember 06, 20174:00 PM - 5:30 PM Math Tower P-131 Rob Silversmith, SCGP Gromov-Witten invariants of symmetric products of projective spaceThrough 3 general points and 6 general lines in $P^3$, there are exactly 190 twisted cubics; 190 is a (genus-zero) Gromov-Witten invariant of $P^3$. I will introduce Gromov-Witten invariants of a smooth complex projective variety X, and discuss how a torus action on X can help us compute its Gromov-Witten invariants. In the case when X is a toric variety, Kontsevich used this method to compute any Gromov-Witten invariant of X. Givental and Lian-Liu-Yau used Kontsevich’s computation to prove a mirror theorem, which states that genus-zero Gromov-Witten invariants of X have an interesting rigid structure, which had been previously predicted by physicists. I will discuss the difficulties that arise when X is not toric. In particular, I will talk about the nontoric orbifold $X=Sym^d(P^r)$, the symmetric product of projective space. By studying the equivariant geometry of $Sym^d(P^r)$, I extended the strategies of Givental/Lian-Liu-Yau to prove a mirror theorem for $Sym^d(P^r)$.

 WednesdaySeptember 13, 20174:00 PM - 5:30 PM Math Tower P-131 Francois Greer, Stony Brook University Elliptic Fibrations and Noether-Lefschetz TheoryThe mirror symmetry philosophy suggests that the Gromov-Witten series of an elliptic fibration should be a modular form. Using the theta correspondence from automorphic forms and the Hodge theory of surfaces, we give a proof of this statement for genus 0 and base degree 1, and compute the series explicitly in many examples. Time permitting, we will discuss some ideas on how to generalize to all genera and base degrees.

 WednesdaySeptember 20, 20174:00 PM - 5:30 PM Math Tower P-131 Philip Engel, Harvard Algebraic/symplectic K3 dictionarySingular integral-affine structures on the sphere arise in connection to K3 surface in two distinct ways: Algebraically, as the dual complex of the central fiber of a degenerating family, and symplectically, as the base of a Lagrangian torus fibration. The Teichmuller space of such structures thus provides a dictionary between algebraic and symplectic moduli. Joint work with Simion Filip proves various structure results on the Teichmuller space of integral-affine structures on S^2---it is itself a separated 44-dimensional integral-affine manifold, with a natural 24 dimensional foliation, whose leaf space maps to the positive cone in R^{2,18}. Heuristically, any extension of the universal family of polarized K3 surfaces to a toroidal compactification would necessarily correspond to a section of the foliation over a certain hyperplane in R^{2,18}. Thus, the existence of such a section constructed by hyperKahler rotation evinces a program to extend the universal family.

 WednesdayOctober 04, 20174:00 PM - 5:30 PM Math Tower P-131 Luca Schaffler, University of Massachusetts, Amherst The KSBA compactification of the moduli space of $D_{1,6}$-polarized Enriques surfacesIn this talk we describe the moduli compactification by stable pairs (also known as KSBA compactification) of a 4-dimensional family of Enriques surfaces, which arise as the bidouble covers of the blow up of the projective plane at three general points branched along a configuration of three pairs of lines. The chosen divisor is an appropriate multiple of the ramification locus. Using the theory of stable toric pairs we are able to study the degenerations parametrized by the boundary and its stratification. We relate this compactification to the Baily-Borel compactification of the same family of Enriques surfaces. Part of the boundary of this stable pairs compactification has a toroidal behavior, another part is isomorphic to the Baily-Borel compactification, and what remains is a mixture of these two. To conclude, we construct an explicit Looijenga semitoric compactification of this 4-dimensional family which we conjecture is isomorphic to the KSBA compactification studied.

 WednesdayOctober 11, 20174:00 PM - 5:30 PM Math Tower P-131 Xudong Zheng, J. Hopkins University The Hilbert scheme of points on singular surfacesThe Hilbert scheme of points on a quasi-projective variety parametrizes its zero-dimensional subschemes. When the variety is a singular surface, the geometry of the Hilbert scheme should reflect the singularity of the underlying surface. I will present a sufficient condition for the Hilbert scheme to be irreducible in terms of the singularity of the surface, namely, the surface has only Kleinian singularities, via a purely algebraic approach. I will also report work in progress on some geometric consequences following their irreducibility.

 MondayOctober 16, 20174:00 PM - 5:00 PM Math Tower P-131 Daniele Agostini, Visiting Stony Brook University Asymptotic syzygies and higher order embeddings.The syzygies of an algebraic variety are the algebraic relations between its equations, and they often encode surprising geometric informations about the variety. For example, recently Ein and Lazarsfeld proved that one can read the gonality of a curve off the syzygies of an embedding of very high degree. I will present a partial extension of this result in higher dimensions, especially in the case of surfaces.

 WednesdayOctober 18, 20174:00 PM - 5:00 PM Math Tower P-131 Harold Blum, U. Michigan, Ann Arbor Valuations, Singularities, and K-stabilityLet L be a line bundle on a projective variety X. We use valuations to measure the singularities of the linear system |mL| as m goes to infinity. Specifically, we consider the global log canonical threshold, also known as Tian’s alpha invariant, and the stability thresholds of L. The stability threshold generalizes an invariant recently introduced by Kento Fujita and Yuji Odaka. When X is a Fano variety, we show that the stability threshold detects the K-(semi)stability of X. This talk is based on joint work with Mattias Jonsson.

 WednesdayOctober 25, 20174:00 PM - 5:30 PM Math Tower P-131 Sebastian Casalaina-Martin, U. of Colorado,. Boulder TBATBA

 WednesdayNovember 01, 20174:00 PM - 5:30 PM Math Tower P-131 Inna Zakharevich, Cornell TBA

 WednesdayNovember 08, 20174:00 PM - 5:30 PM Math Tower P-131 Fedor Bogomolov, NYU TBATBA

 WednesdayNovember 15, 20174:00 PM - 5:30 PM Math Tower P-131 Nicolas Addington, U. Oregon TBATBA

 WednesdayNovember 22, 20174:00 PM - 5:30 PM Math Tower P-131 Happy TKSgiving!, Happy TKSgiving! Happy TKSgiving!Happy TKSgiving!

 WednesdayNovember 29, 20174:00 PM - 5:30 PM Math Tower P-131 Christian Schnell, Stony Brook University TBATBA

 WednesdayDecember 06, 20174:00 PM - 5:30 PM Math Tower P-131 Davesh Maulik, MIT TBATBA

 Show events for: All Events AGNES Algebraic geometry seminar Algebraic models in geometry seminar Am.Math.Soc. (AMS) Chapter Seminar Analysis Student Seminar Capsule Research Talks Colloquium Commencement Ceremony Comprehensive Exams Dynamical Systems Seminar Equivalence Method and Exterior Differential Systems Seminar First and Second Year Student Seminar Friday Summer Meeting Geometric Analysis Learning Seminar Geometry/Topology Seminar Grad / Postdoc Professional Development Seminar Graduate Student Seminar Graduate Topology Seminar Grant Proposal Panel Hodge Theory, Moduli and Representation Theory Holiday Party Joint Columbia-CUNY-Stony Brook General Relativity Seminar Math Club Math Day 2016 Math in Jeans Mathematical Writing Seminar Mathematics Education Colloquium Mathematics Summer Camp Mini Course / Dynamics Learning Seminar Mini-School in Geometry Minicourse in Real Enumerative Geometry New Graduate Students NY General Relativity Seminar RTG Colloquium RTG Seminar RTG Student Geometry Seminar Seminar in Topology and Symplectic Geometry Seminar on algebraic structures in physics Simons Colloquium Simons Lectures Series Singular metrics and direct images Special Algebra / Algebraic Geometry Seminar Special Analysis Seminar Special Colloquium Special Geometry/Topology Seminar Special Lectures Special Seminar in Algebraic Geometry Special Topology Seminar Student Algebraic Geometry Seminar Student Gauge Theory Seminar Student Seminar on Differential Geometry and Analysis Summer Workshop in Topology and Geometry Symplectic Geometry Reading Seminar Symplectic Geometry Seminar Thesis Defense Topology and Symplectic Geometry / Math of Gauge Fields seminar Women in Mathematics Instructions for subscribing to Stony Brook Math Department Calendars