GAAG seminar - Euler’s constant and exponential motives

The theory of exponential motives provides us with tools to predict all algebraic relations among exponential periods (i.e. integrals of exponentials of algebraic functions in several variables), in the same way that the theory of classical motives does for periods (i.e. integrals of algebraic functions). In the category of exponential motives over Q there is a new extension of Q(-1) by Q(0) which does not come from classical motives. Its exponential period matrix features Euler's constant, which one is tempted to think of as the regularised value of Riemann's zeta function at 1. I will discuss several results and open questions revolving around this extension, for example the role it plays as a "monodromy factor" for differential equations of E-functions. No previous knowledge of either motives or E-functions will be assumed. The talk is based on joint work with Peter Jossen.