ABSTRACT: Bethe/gauge correspondence relates quantum integrable systems to supersymmetric gauge theories. One of the mathematical consequences of this relation is the identification of the quantum cohomology ring of certain varieties with Bethe subalgebras of quantum algebras. In this talk the two dimensional gauge theories corresponding to the Yangians of super-algebras of A type will be described. In a parallel development … Read More

ABSTRACT: The Severi degrees of P1XP1 can be computed in terms of an explicit operator on the Fock space F[P1]. We will discuss this approach and will also describe several further applications. We will discuss using Fock spaces to compute relative Gromov-Witten theory of other surfaces, such as Hirzebruch surfaces and EXP1. We will also discuss operators which calculate descendants. … Read More

ABSTRACT: The local Gromov-Witten theory of curves studied by Bryan and Pandharipande revealed strong structural results for the local GW invariants, which were later used by Ionel and Parker in the proof of the Gopakumar-Vafa conjecture. In this talk I will report on a joint work in progress with Eleny Ionel on the extension of these results to the real … Read More

ABSTRACT: I’ll show that the partially spherical cyclotomic rational Cherednik algebra (obtained from the full rational Cherednik algebra by averaging out the cyclotomic part of the underlying reflection group) has four other descriptions: (1) as a subalgebra of the degenerate DAHA of type A given by generators; (2) as an algebra given by generators and relations; (3) as an algebra … Read More

ABSTRACT: We will review the Geometric Langlands Conjecture, a non-abelian generalization of the theory of curves and their Jacobians. We will compare it to its arithmetic variants and discuss its overlap with homological mirror symmetry. We will then outline our program for proving GLC using non Abelian Hodge theory and Hitchin’s system. Finally, we will describe some recent results on … Read More

ABSTRACT: Coulomb branch of a 3d gauge theory is defined (after Braverman-Finkelberg-N) as the spectrum of a certain commutative ring, defined as a convolution algebra of a certain infinite dimensional variety. A variant of its definition gives a (partial) resolution, when we have the so-called flavor symmetry in the theory. We identify the resolution with smooth Cherkis bow variety for … Read More

ABSTRACT: I will explain how the problem of expressing K-theoretic Gromov-Witten invariants in terms of cohomological ones leads to an elegant quantum-mechanical formula.

ABSTRACT: I will explain how to use Gromov-Witten theory to classify all rational curves with primitive curve class on the Fano variety of lines in a very general cubic fourfold. Joint work with Junliang Shen and Qizheng Yin.