Murad Alim 教授学术报告
Title: Non-perturbative quantum geometry, resurgence and BPS structures
Speaker: Prof. Murad Alim
Affiliation: University of Hamburg（汉堡大学）
Time:16:00-17:00, Tuesday, 22nd November, 2022 (UTC+8, Beijing Time)
Inviter: Jie Gu（顾杰）
Venue: Zoom Meeting (ID: 385 442 0225; Passcode: yauc)
Abstract
BPS invariants of certain physical theories correspond to Donaldson-Thomas (DT) invariants of an associated Calabi-Yau geometry. BPS structures refer to the data of the DT invariants together with their wall-crossing structure. On the same Calabi-Yau geometry another set of invariants are the Gromov-Witten (GW) invariants. These are organized in the GW potential, which is an asymptotic series in a formal parameter and can be obtained from topological string theory. A further asymptotic series in two parameters is obtained from refined topological string theory which contains the Nekrasov-Shatashvili (NS) limit when one of the two parameters is sent to zero. I will discuss in the case of the resolved conifold how all these asymptotic series lead to difference equations which admit analytic solutions in the expansion parameters. A detailed study of Borel resummation allows one to identify these solutions as Borel sums in a distinguished region in parameter space. The Stokes jumps between different Borel sums encode the BPS invariants of the underlying geometry and are captured in turn by another set of difference equations. I will further show how the Borel analysis of the NS limit connects to the exact WKB study of quantum curves. This is based on various joint works with Lotte Hollands, Arpan Saha, Iván Tulli and Jörg Teschner.
Speaker
Professor Murad Alim is an interim professor (Vertretungsprofessor) as well as an Emmy Noether research group leader at the Department of Mathematics of the University of Hamburg. He is a mathematical physicist and geometer working on the geometry of quantum field and string theories. More specifically he is interested in differential, complex and algebraic geometry as well as representation theory with connections to mathematical physics.
More information could be found on his personal page link: https://www.math.uni-hamburg.de/home/alim/index.html
The seminar will be broadcasted online by Zoom.
Interested people are free to join, without registration in advance.
The Zoom info is
URL：https://us02web.zoom.us/j/3854420225?pwd=SXY4eWJKOTBFZWJDaE16aXpTamY1QT09
Meeting ID: 385 442 0225
Passcode: yauc