UO Algebra Seminar 2022-2023

Usual time: Tuesday 4pm-4:50pm

Usual localtion: University Hall 210

Schedule of Fall 22

Week 3, October 11, Song Yu (Columbia University)

Title: Open Crepant Transformation Conjecture for toric Calabi-Yau 3-orbifolds
Abstract: The Crepant Transformation Conjecture of Ruan proposes an identification of the quantum cohomologies and Gromov-Witten theories of K-equivalent manifolds or orbifolds. In this talk, I will discuss various formulations and known cases of the conjecture, and focus on its extension to open Gromov-Witten theory. I will further present an approach to the conjecture for toric Calabi-Yau 3-orbifolds based on techniques from mirror symmetry. The talk is based on joint work with Bohan Fang, Chiu-Chu Melissa Liu, and Zhengyu Zong.

Week 4, October 20 (Thursday) 10am-10:50am, at Tykeson Hall 260, Konstantin Aleshkin (Columbia University)

Title: Central charges in abelian GLSM
Abstract: GLSMs are enumerative theories associated to critical loci of functions in GIT quotients and generalize Gromov-Witten theory. A large part of structure of such a theory can be captured by certain generating series of genus 0 invariants called central charges which depend on a matrix factorization of the GLSM. These generating series remarkably have two integral representations: Euler type and Mellin-Barnes type. In this talk I will outline our construction of central charges and explain how the integral representations lead to mirror symmetry, Higgs-Coulomb correspondence and wall crossing phenomena for GLSM invariants.

Week 8, November 15, Siu-Cheong Lau (Boston University)

Schedule of Winter 23

Week 10, March 17, Friday 11am, Eric Larson (Brown University)

Schedule of Spring 23

Week 2, April 11, Anne Schilling (UC Davis)

Title: What about type B?
Abstract: We will discuss ten reasons of why the combinatorial theory of crystal bases is very helpful in representation theory, geometry, and beyond.

Week 4, April 25, David Nadler (UC Berkeley)

Title: Cocenter of affine Hecke category
Abstract: I will discuss recent work with Penghui Li and Zhiwei Yun identifying the cocenter of the affine Hecke category with “elliptic character sheaves”, ie automorphic sheaves for a genus one curve.

Week 6, May 9, 11am-noon, Location: Fenton Hall 117, Isabel Vogt (Brown University)

Title: Curve classes on conic bundles threefolds and applications to rationality
Abstract: In this talk I'll discuss joint work with Sarah Frei, Lena Ji, Soumya Sankar and Bianca Viray on the problem of determining when a geometrically rational variety is birational to projective space over its field of definition. Hassett--Tschinkel and Benoist--Wittenberg recently refined the classical intermediate Jacobian obstruction of Clemens--Griffiths by considering torsors under the intermediate Jacobian of a geometrically rational threefold. By work of Hassett--Tschinkel, Benoist--Wittenberg and Kuznetsov--Prokhorov, this obstruction is strong enough to characterize rationality of geometrically rational Fano threefolds of geometric Picard rank 1. Moving into higher Picard rank, we compute this obstruction for conic bundles over P^2. As a consequence of our work, when the ground field is the real numbers, we show that neither the topological obstruction nor the refined intermediate Jacobian obstruction is sufficient to determine rationality.