Speaker: Francis Brown (Univ. of Oxford)

Title: Galois theory for multiple zeta values and other transcendental numbers

Abstract: Based on the example of multiple zeta values, which have a very intricate algebraic structure first investigated by Euler, I will explain how to set up a surprisingly rich `Galois theory' of multiple zeta values which builds on ideas of Grothendieck. It takes the form of a group of symmetries which acts on multiple zeta values, preserving all the known algebraic relations. In fact, this phenomenon holds for very general classes of transcendental numbers and gives a completely new way to think about different parts of mathematics and physics. Examples include: elliptic integrals, beta and hypergeometric functions, and Feynman integrals in quantum field theory.