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 Seminar Analysis 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 Postdoc Geometry/Dynamics Seminar Postdoc 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 Algebraic representatives and intermediate Jacobians over perfect fieldsIntermediate Jacobians and Abel--Jacobi maps provide a powerful tool for the study of complex projective manifolds. In positive characteristic, over algebraically closed fields, algebraic representatives and regular homomorphisms provide a replacement for the intermediate Jacobian and Abel--Jacobi map. I will discuss recent progress, with Jeff Achter and Charles Vial, extending this theory to the case of perfect fields, as well as some applications to a question of Barry Mazur on weight one Galois representations arising from geometry.

 WednesdayNovember 01, 20174:00 PM - 5:30 PM Math Tower P-131 Inna Zakharevich, Cornell Constructing derived motivic measuresMotivic measures can be thought of as homomorphisms out of the Grothendieck ring of varieties. Two well-known such measures are the Larsen--Lunts measure (over $\mathbf{C}$) and the Hasse--Weil zeta function (over a finite field). In this talk we will show how to lift the Hasse--Weil zeta function to a map of $K$-theory spectra which restricts to the usual zeta function on $K_0$. As an application we will show that the Grothendieck spectrum contains nontrivial elements in the higher homotopy groups.

 WednesdayNovember 08, 20174:00 PM - 5:30 PM Math Tower P-131 Fedor Bogomolov, NYU $PGL(2)$-invariants of collections of torsion points of elliptic curvesThe main object of the talk is a (complex) elliptic curve $E$ with a standard degree $2$ projection $π$ on $P^1$. Assuming that we fix one of the ramification points as a zero we obtain a subset $PE_{tors}$ of the images of torsion points on $E$ inside $P^1$. This sets are different and we have shown jointly with Yuri Tschinkel that these sets are very different for different elliptic curves - they have finite intersection for any two nonisomorphic elliptic curves. However some subsets of the above $PE_{tors}$ are $PGL(2)$ equivalent. This holds for the images of points of order $3$ and order $4$. In this talk I am going to discuss general problem of the behavior of $PGL(2)$-invariants of the $k$-tuples of the images of torsion points of different order. For every subset of different $k$ points in $P^1$ we can define it's image in the moduli $M_{0,k}$ of $k$-tuples of points which is essentially a quotient of projective space $S^kP^1= P^k$ by the action of $PGL(2)$. Thus $M_{0,k}$ is a rational variety of dimension $k-3$. If we consider the images of points of finite order in different elliptic curves under natural projections then we obtain an( infinite) system of modular type curves with maps into $M_{0,k}$. I will formulate three conjectures (semi theorems) about properties of such maps which provide a possiblity of realistic universal estimate for intersections between subset of $PE^i_{tors},i=1,2$ for different elliptic curves $E^i$. These conjectures are formulated in our joint article with Yuri Tschinkel and Hang Fu. Note that there are pairs of curves $E^i$ with big intersection $≥ 22$ of $PE^i_{tors},i=1,2$ as it was shown in our joint article.

 WednesdayNovember 15, 20174:00 PM - 5:30 PM Math Tower P-131 Nicolas Addington, U. Oregon Special cubic fourfolds and apolarityIn the moduli space of cubic fourfolds, Hassett's Noether-Lefschetz divisors, which parametrize cubics containing special surfaces, are geometrically rich and heavily studied. Recently, Ranestad and Voisin considered some divisors parametrizing cubics "apolar" to special surfaces, and showed that one of them is _not_ a Noether-Lefschetz divisor. I will explain why this is surprising, and present a new, more direct proof that three of their divisors are not Noether-Lefschetz, using point-counting methods over finite fields. Joint with Asher Auel.

 WednesdayNovember 29, 20174:00 PM - 5:30 PM Math Tower P-131 Christian Schnell, Stony Brook University Extension theorems for differential forms on singular spacesThe talk is about the following problem: Suppose we have an algebraic (or holomorphic) differential form, defined on the smooth locus of an algebraic variety (or analytic space). Under what conditions does it extend to an algebraic (or holomorphic) differential form on a resolution of singularities of X?

 WednesdayDecember 06, 20174:00 PM - 5:30 PM Math Tower P-131 Davesh Maulik, MIT Gopakumar-Vafa invariantsIn this talk I want to explain a conjectural picture (joint with Toda) relating curve-counting invariants on Calabi-Yau threefolds with certain perverse sheaves on the Chow variety. If time permits, I'll try to discuss some more recent work connecting it with conjectural formula on the cohomology of moduli spaces of Higgs bundles.

 Show events for: All Events AGNES Algebraic geometry seminar Algebraic models in geometry seminar Am.Math.Soc. (AMS) Chapter Seminar Analysis Seminar Analysis 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 Postdoc Geometry/Dynamics Seminar Postdoc 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