Resurgence in Mathematics and Physics

11-14 June 2019
Le Bois-Marie
Europe/Paris timezone

Considerations about Resurgence Properties of Topological Recursion

12 Jun 2019, 14:00
1h
Centre de Conférences Marilyn et James Simons (Le Bois-Marie)

Centre de Conférences Marilyn et James Simons

Le Bois-Marie

35, route de Chartres 91440 Bures-sur-Yvette

Speaker

Bertrand Eynard (IPhT - CEA - CRM Montreal - IHES)

Description

To a spectral curve $S$ (e.g. a plane curve with some extra structure), topological recursion associates a sequence of invariants: some numbers $F_g(S)$ and some $n$-forms $W_{g,n}(S)$. First we show that $F_g(S)$ grow at most factorially at large $g$, $F_g = O((\beta g)! r^{-g})$ with $r>0$ and $\beta\leq 5$. This implies that there is a Borel transform of $\sum_g \hbar^{2g-2} F_g$ that is analytic in a disk of radius $r$. The question is whether this is a resurgent series or not? We give arguments for this, and conjecture what are the singularities of the Borel transform, and we show how it works on a number of examples.

Primary author

Bertrand Eynard (IPhT - CEA - CRM Montreal - IHES)

Presentation Materials

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