BIMSA >
BIMSA-Tsinghua量子对称讨论班
A proof of Witten's asymptotic expansion conjecture for WRT invariants of Seifert fibered homology spheres via resurgence
A proof of Witten's asymptotic expansion conjecture for WRT invariants of Seifert fibered homology spheres via resurgence
演讲者
时间
2025年12月03日 10:30 至 12:30
地点
A3-3-301
线上
Zoom 242 742 6089
(BIMSA)
摘要
This report is structured into two main parts.
The first part will present conclusions from our recent research（arXiv：2510.10678）, focusing on the proof of the Witten $SU(2)$ conjecture for Seifert fibered integral homology spheres. The primary methodology involves a resurgent analysis of a suitable complexification of the Witten-Reshetikhin-Turaev (WRT) invariant – namely, the Gukov-Pei-Putrov-Vafa（GPPV） invariant. This analysis extends to characterizing the flat connections corresponding to the Stokes terms, distinguishing between $SU(2)$ and $SL(2,R)$ connections. We will also mention related findings: that the radial limit of the GPPV invariant recovers the WRT invariant, the property of quantum modularity possessed by the GPPV invariant, and its relation to the Habiro element.
The second part will provide a brief introduction to the theory of resurgence. This will be followed by a more detailed discussion of the technical aspects underlying the results presented in the first part, offering necessary background and elaboration.
The first part will present conclusions from our recent research（arXiv：2510.10678）, focusing on the proof of the Witten $SU(2)$ conjecture for Seifert fibered integral homology spheres. The primary methodology involves a resurgent analysis of a suitable complexification of the Witten-Reshetikhin-Turaev (WRT) invariant – namely, the Gukov-Pei-Putrov-Vafa（GPPV） invariant. This analysis extends to characterizing the flat connections corresponding to the Stokes terms, distinguishing between $SU(2)$ and $SL(2,R)$ connections. We will also mention related findings: that the radial limit of the GPPV invariant recovers the WRT invariant, the property of quantum modularity possessed by the GPPV invariant, and its relation to the Habiro element.
The second part will provide a brief introduction to the theory of resurgence. This will be followed by a more detailed discussion of the technical aspects underlying the results presented in the first part, offering necessary background and elaboration.
演讲者介绍
During the course of his doctoral studies, Yong LI primarily focused on resurgence theory and its applications. His recent work involves exploring the application of resurgence theory to various subjects, including modular forms, topological invariants of 3-manifolds, quantum mechanics, etc.