The 3rd MSJ-SI

The Mathematical Society of Japan, Seasonal Institute

Development of Galois-Teichmüller Theory
and Anabelian Geometry

October 25 Monday, 16:00--16:50
M. Asada, H. Nakamura, N. Takao, H. Tsunogai;
Easy walking in GT theory and anabelian geometry, I
In this talk we shall introduce some basic notions to understand profinite aspects of the title of this conference for a wider public of mathematicians including graduate students. We introduce the fundamental exact sequence associated with arithmetic fundamental groups, and discuss typical basic examples: hyperbolic curves, their configuration spaces, and moduli spaces. After Belyi's Theorem, Grothendieck raised a series of questions that encourages closely looking at the extention structures of arithmetic fundamental groups, equivalently, understanding outer Galois representations (or more generally, universal monodromy representation arising from the moduli space of curves). We discuss generalization of Belyi's injectivity theorem. If time allows, the definition of Grothendieck-Teichmüller group and its characterization as the automorphism group of certain towers will be discussed.