Orateur
Prof.
Maxim KONTSEVICH
(IHES)
Description
I will explain the phenomenon of resurgence in a (apparently) new example related to Stirling formula, and its generalization to quantum dilogarithm.
Let us define rational Stirling numbers ($St_k$) = (1, 1/12, 1/288, . . .) as coefficients in the asymptotic expansion of the normalized factorial:
$n! ∼ $$\sqrt{2π nn^ne^{-n}}$ (1$+$ $\frac{1}{12n}$ $+$ $\frac{1}{288n^2}$ $+$ $\frac{1}{51849n^3}$ $+$.... 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 polynomials.
