The Asymptotic Expansion Conjecture on Seifert Fibered Homology Sphere via Resurgence Theory
发布时间:2024年04月22日
浏览次数:599
发布者: Ruixin Li
主讲人: Yong Li (Tsinghua University)
活动时间: 从 2024-04-23 14:00 到 15:00
场地: 北京国际数学研究中心,全斋全29教室
Abstract: We introduce the Gukov-Pei-Putrov-Vafa (GPPV) invariant (or Z-hat invariant) in Chern-Simons theory associated with a Seifert fibered integral homology sphere (SFIHS). The GPPV invariant is a partial theta series and a higher-depth quantum modular form. By philosophy of resurgence theory, Ecalle's alien derivations provide all components of $SL(2,\mathbb{C})$-irreps of the fundamental group of the SFIHS. As the complex variable goes to a rational number, the GPPV invariant becomes the Witten-Reshetikhin-Turaev (WRT) invariant. Simultaneously, only $SU(2)$ components remain in the transseries expansion. This yields a proof of the so-called asymptotic expansion conjecture of the WRT invariant of SFIHS.
The talk is based on a joint work with J. Andersen, L. Han,W. Mistegard, D. Sauzin, S. Sun.
The talk is based on a joint work with J. Andersen, L. Han,W. Mistegard, D. Sauzin, S. Sun.