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.
Lecturer
Date
24th March ~ 16th June, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday,Thursday | 09:50 - 11:25 | Shuangqing-A731 | Zoom 16 | 468 248 1222 | BIMSA |
Reference
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]
Video Public
Yes
Notes Public
Yes
Lecturer Intro
Bowen Zhao got her PhD from Yale University in December 2020. After a postdoc at BIMSA, she joined as Assistant Professor in 2025. She is interested in General relativity and Mathematical Physics and particularly problems about Black Hole.