Fundamental Group -- the Intertwine of Arithmetic and Geometry

Date: 
Monday, 16 April, 2018 - 11:00 - 12:00
Venue: 
LSB 219
Seminar Type: 
Seminar
Speaker Name: 
Dr. Lei ZHANG
Affiliation: 
Freie Universität Berlin
Abstract: 

In this talk I am going to present the beautiful theory of fundamental groups in algebraic and arithmetic geometry. I will start by recalling the fundamental group of a topological space and the Galois group of a field. Then I will explain a striking analogy between these two groups which come from geometry and number theory respectively. Next, I will introduce the étale fundamental group in algebraic arithmetic geometry which is an analogy of the topological fundamental group and which is a generalization of the Galois group. Finally, I will explain Grothendieck's anabelian program which arises naturally from the study of fundamental groups, and then I will present a recent result of M. Romagny, F. Tonini, and me in this direction.