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 et Vincel Hoang Ngoc Minh
Date(s) 11/30/21 - 12/2/21
linked URL https://indico.math.cnrs.fr/event/7040/
00:00:00 / 00:00:00
12 20

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

By Sergey Yurkevich

In a recent paper Don Zagier mentions a mysterious integer sequence $(a_{n})_{n\geq0}$ 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 $(a_{n})_{n\geq0}$ 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.

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