Exploration into divergent series, resurgence and non-pertrubative analysis
This course explores the mathematical structures underlying recent developments in the AdS/CFT factorization puzzle, particularly Hong Liu's proposal to decompose CFT partition functions into "smooth" and "erratic" parts via a filter. The erratic component, conjectured to behave like a Gaussian random variable, encodes wormhole contributions to the gravitational path integral.
The mathematical core of the course centers on transseries and resurgence theory, which provide the natural language for describing such non-perturbative phenomena. We will develop the theory of asymptotic series, Borel summation, Stokes phenomena, and Écalle's alien calculus, with emphasis on how divergent series encode complete non-perturbative information through singularities in the Borel plane.
The mathematical core of the course centers on transseries and resurgence theory, which provide the natural language for describing such non-perturbative phenomena. We will develop the theory of asymptotic series, Borel summation, Stokes phenomena, and Écalle's alien calculus, with emphasis on how divergent series encode complete non-perturbative information through singularities in the Borel plane.
讲师
日期
2026年03月24日 至 06月16日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二,周四 | 09:50 - 11:25 | Shuangqing-A731 | Zoom 16 | 468 248 1222 | BIMSA |
参考资料
1. Ovidiu Costin, Asymptotics and Borel Summability (CRC Press, 2009)
2. Inês Aniceto, Gökçe Başar, and Ricardo Schiappa, "A primer on resurgent transseries and their asymptotics," Physics Reports 809 (2019) 1-135 [arXiv:1802.10441]
2. Inês Aniceto, Gökçe Başar, and Ricardo Schiappa, "A primer on resurgent transseries and their asymptotics," Physics Reports 809 (2019) 1-135 [arXiv:1802.10441]
视频公开
公开
笔记公开
公开
讲师介绍
赵博文博士于2020年12月获得耶鲁大学博士学位，随后加入北京雁栖湖应用数学研究院（BIMSA）在丘成桐教授指导下从事博士后研究，并于2025年起任助理教授。她的研究方向聚焦于广义相对论与数学物理领域，致力于探索时空几何、引力理论及相关数学结构的深层联系。