Abstract：

This talk will discuss series expansions of algebraic Mellin transforms, and the periods that appear as their coefficients. The basic example is Euler's beta function, whose series expansion features values of the Riemann zeta function at integers. I will explain how the motivic Galois group acts on series expansions of algebraic Mellin transforms, and give examples. As an application, we obtain a ''cosmic Galois theory'' (prophesized by Cartier) for Feynman integrals in dimensional regularization. This is joint work with Francis Brown, Javier Fresán, and Matija Tapušković.

About the Speaker:

I am a maître de conférences at the Université de Montpellier, France.

I am interested in the following subjects:

- motives, periods, regulators;

- amplitudes in quantum field theory and string theory;

- multiple zeta values and multiple polylogarithms;

- mixed Hodge theory;

- arrangements and matroids from the point of view of combinatorics, topology and geometry;

- combinatorial Hopf algebras;

- operads and operadic structures, especially in connection with algebraic geometry.