Towards mirror symmetry of 3d N=2 Coulomb branches associated to gl(m|n)

Geometric Representation Theory Seminar

Organizers：

Lin Chen, Will Donovan, Penghui Li,

Peng Shan, Changjian Su, Wenbin Yan

Speaker：

Yixuan Li (Mathematical Sciences Institute of Australian National University)

Time：

Thur., 4:00-5:00 pm, Jan. 9, 2025

Venue:

B627, Shuangqing Complex Building A

Title:

Towards mirror symmetry of 3d N=2 Coulomb branches associated to gl(m|n)

Abstract

This talk is based on joint work in progress with Mina Aganagic, Spencer Tamagni and Peng Zhou. In this talk we discuss a proposal for Coulomb branches associated to quiver gauge theories where the quiver comes from the Dynkin diagram of gl(m|n). Coherent sheaves on these Coulomb branches are presented as matrix factorization categories. We'll also propose its conjectural mirror, which contains the Fukaya category of symmetric product of punctured spheres as examples. The main result is a variant of this mirror symmetry where we consider the Fukaya category of symmetric product of a hyperelliptic curve folded by the hyperelliptic involution. This work is a follow-up of the ICM talk of Mina Aganagic and arXiv:2406.04258, where the parallel case of gl(n) is discussed.