2026-06-02 08:45-09:45 Omar Kidwai
智华楼209室
Title: Spectral networks from cubic differentials
Abstract: Spectral networks, introduced by Gaiotto-Moore-Neitzke following Berk-Nevins-Roberts and the Japanese school of WKB analysis, are certain graph-like objects on a Riemann surface obtained from the trajectory structure of differentials on the surface. They play a central role in a range of fundamental problems in diverse subjects from asymptotic analysis to supersymmetric quantum field theory. We will focus on the special case of spectral networks arising from (meromorphic) cubic differentials. We explain some general structural results and show how to use them to analyze spectral networks in the special case that the differential is polynomial, and describe the corresponding variation of BPS structures describing the BPS spectrum of the relevant QFT. Based on joint work with G. Tahar.
2026-06-02 11:00-12:00 Dylan Allegretti
智华楼209室
Title: Categorification of skein algebras
Abstract: The skein algebra of a surface is a noncommutative algebra that quantizes the SL(2,C)-character variety of the surface. It has been intensively studied in quantum topology for more than thirty years. In an influential paper from 2014, D. Thurston suggested that the skein algebra should have a natural categorification where the product in the algebra arises from a monoidal structure on a category. In this talk, I will describe such a categorification of the skein algebra of a genus zero surface with boundary. I will first review the construction of the variety of triples, a remarkable geometric object introduced by Braverman, Finkelberg, and Nakajima in their study of Coulomb branches of 3d N=4 gauge theories. I will then explain how the skein algebra arises as the Grothendieck ring of the bounded derived category of equivariant coherent sheaves on the variety of triples equipped with a natural monoidal structure. This talk is based on work with Hyun Kyu Kim and Peng Shan.
