# Combinatorics and Arithmetic for Physics: special days

30 November 2021 to 2 December 2021
Le Bois-Marie
Europe/Paris timezone

## How to Conjecture and Prove that the Generating Function of the Yang- Zagier Numbers is Algebraic (in person)

1 Dec 2021, 14:50
50m
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

Sergey Yurkevich (University of Vienna & INRIA)

### Description

In a recent paper Don Zagier mentions a mysterious integer sequence $(a_{n})_{n≥0}$ which arises from a solution of a topological ODE discovered by Marco Bertola, Boris Dubrovin and Di Yang. In my talk I show how to conjecture, prove and even quantify that $(a_{n})_{n≥0}$ actually admits an algebraic generating function which is therefore a very particular period. The methods are based on experimental mathematics and algorithmic ideas in differential Galois theory, which I will show in the interactive part of the talk. The presentation is based on joint work with A. Bostan and J.-A. Weil.

### Presentation Materials

 cap2021-Yurkevich.pdf Vidéo