Galois theory for periods

Speaker:

Clement Dupont

Affiliation:

U Pierre et Marie Curie Paris 6/MPIM

Date:

Wed, 25/02/2015 - 14:15 - 15:15

Location:

MPIM Lecture Hall [2]

Parent event:

Number theory lunch seminar [3]

Periods are the complex numbers which may be defined by integrals of algebraic functions (with rational coefficients) over domains defined by algebraic inequalities (with rational coefficients). They include all algebraic numbers. The philosophy of motives predicts that classical Galois theory for algebraic numbers is a special case of a Galois theory for periods.

In this talk we will give the main ideas of this theory and discuss the important example of multiple zeta values, due to Goncharov and Brown. This example will illustrate the general leitmotiv that the Galois theory of mixed Tate periods is expressed by combinatorial formulas. We will further illustrate this by introducing the family of dissection polylogarithms and computing their Galois theory.