# Development of Galois-Teichmüller Theory and Anabelian Geometry

 October 26 Tuesday, 10:00--11:00 L. Schneps (CNRS) Survey of the theory of multiple zeta values The theory of multiple zeta values consists in the algebraic and geometric study of the values at positive integers $\zeta(k_1,\ldots,k_r)$ of many-variabled $\zeta$-functions. These numbers satisfy a double family of fundamental algebraic relations called "double shuffle relations". In this lecture, we will pose some of the main questions facing the theory at present, and give some of the major results. Then we will cover the astonishing connections between the double shuffle algebra and many other parts of mathematics: moduli spaces of curves and mixed Tate motives, modular forms and the Eichler-Shimura correspondence, and Grothendieck-Teichmüller theory.