Combinatorics and Arithmetic for Physics: special days

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

1 déc. 2021, 14:50

50m

Centre de conférences Marilyn et James Simons (Le Bois-Marie)

Orateur

Sergey Yurkevich (University of Vienna & INRIA)

Description

In a recent paper Don Zagier mentions a mysterious integer sequence $(a_n{)}_{n\ge 0}$ 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 $(a_n{)}_{n\ge 0}$ 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.

Documents de présentation

cap2021-Yurkevich.pdf

Vidéo