A new approach to multiple elliptic polylogarithms

Abstract: Multiple polylogarithms may be viewed as the monodromy of a certain "universal" unipotent differential equation on the projective line minus three points. This observation lies at the heart of their relation to mixed Tate motives, a point of view which brings powerful new tools to bear on the study of these functions and its special values.

The goal of this talk is to describe an analogous picture for a once-punctured elliptic curve $E'$. In particular, we obtain a new description of the unipotent de Rham fundamental group of $E'$, generalizing and improving on previous works of Levin-Racinet, Brown-Levin, Enriquez-Etingof, and others. Joint work in progress with Tiago J. Fonseca (Oxford).

algebraic geometrynumber theory

Audience: researchers in the topic

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Rendez-vous on special values and periods

Series comments: The main objective of this conference is to gather together young researchers interested in special values of L-functions and periods. These objects are at the crossroads of many recent important developments in arithmetic geometry, such as Euler systems or the theory of motives. The different talks will portray the variety of viewpoints with which L-functions and periods are studied at present.

Registration is free and mandatory, to get access to the livestream and recording of the talks.

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