Combinatorics and Arithmetic for Physics : Special Days

Collection Combinatorics and Arithmetic for Physics : Special Days

Organizer(s) Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson
Date(s) 28/11/2022 - 29/11/2022
linked URL https://indico.math.cnrs.fr/event/8730/
00:00:00 / 00:00:00
11 20

Introduction to resurgence

By Maxim Kontsevich

Also appears in collection : Maxim Kontsevich

I will explain the phenomenon of resurgence in a (apparently) new ex- ample related to Stirling formula, and its generalization to quantum dilogarithm. Let us define rational Stirling numbers (St_k) = (1, 1/12, 1/288, . . . ) as coeffi- cients in the asymptotic expansion of the normalized factorial: $n ! \sim \sqrt{2\pi n} n^n e^{-n} (1 + \frac{1}{12n} + \frac{1}{288n²} - \frac{139}{51849n³} + \cdots)$ Then the asymptotic behavior of St_k for large even k is controlled by numbers St_k for small odd k, and vice versa. In the case of quantum dilogarithm one deforms Stirling numbers to Euler poly- Nomials.

Information about the video

  • Date of recording 29/11/2022
  • Date of publication 30/11/2022
  • Institution IHES
  • Language English
  • Audience Researchers
  • Format MP4

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