Daniil Rudenko: Polylogarithms, cluster algebras and Zagier conjecture

Описание: The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics.

Abstract:
Polylogarithms appeared already in the work of Leonhard Euler and have been actively studied since then. The importance of these functions and there role in mathematics was clarified greatly when polylogarithms were interpreted as periods of mixed Tate motives. After sketching this general picture, I will talk about the relation between polylogarithms and cluster varieties, which helps to find some functional equations, satisfied by classical polylogarithms. As an application, I will explain the role of this relation in the proof of Zagier conjecture in weight four. The talk is based on the joint work with Alexander Goncharov.