Workshop on WKB Analysis in Mathematical Physics
Time: 2023-07-21
Published By: Wenqiong Li
Speaker(s): Dylan Allegretti (Tsinghua University) & Jie Gu (Southeast University) & Omar Kidwai (University of Birmingham)
Time: 09:00-10:00 July 24, 2023
Venue: Room 29, Quan Zhai, BICMR
9:00-10:00
Speaker: Dylan Allegretti
Title: Meromorphic differentials and Teichmüller space
Abstract: In the late 1980s, Nigel Hitchin and Michael Wolf independently discovered a parametrization of the Teichmüller space of a compact surface by holomorphic quadratic differentials. In this talk, I will describe a generalization of their result where one replaces holomorphic differentials by meromorphic differentials. I will explain how this fits into an even more general story involving spaces of stability conditions and cluster varieties.
10:00-11:00
Speaker: Jie Gu
Title: Resurgent quantum periods and BPS invariants
Abstract: Quantum periods appear in many contexts, from quantum mechanics to local mirror symmetry. They can be determined in terms of topological string free energies and Wilson loops, in the Nekrasov–Shatashvili limit. We solve in closed form trans-series extensions of free energies and Wilson loops using holomorphic anomaly equations, and study their resurgent properties. Based on these results, we propose a unified picture of the resurgent structure of quantum periods. Their Stokes transformation follows the Delabaere–Dillinger-Pham formula, which suggests that Stokes constants of quantum periods are given by BPS invariants. We also show that the Stokes constants of NS free energies and conventional topological string free energies should be BPS invariants as well. We illustrate our general results with explicit calculations for quantum periods of local P2.
11:00-12:00
Speaker: Omar Kidwai
Title: Refined topological recursion: degree two and genus zero
Abstract: The Eynard-Orantin topological recursion (arising from the study of matrix models in quantum field theory) takes an algebraic curve with some additional data, and outputs an infinite collection of geometric objects (multidifferentials), often of enumerative interest. We review their formalism and explain how to modify it to obtain the "$\beta$-deformed'' or "refined" topological recursion when the initial data is sufficiently nice. We give the fundamental properties of the resulting multidifferentials in this case, and explain the similarities and crucial differences from the original (unrefined) setting. Based on joint work with K. Osuga.
