Wei Xiangsheng: Introduction to Anabelian Geometry

In this talk, I will give a short introduction to Anabelian Geometry posed by Grothendieck as a generalization of class field theory. The goal of Anabelian Geometry is to recover/reconstruct certain arithmetic variety from its algebraic fundamental group. I will explain basic motivation and some elementary example. In particular, I shall discuss the proof of Neukirch-Uchida theorem, which is the first example in Grothendiek’s program. If time permits, I also sketch some idea of the proof of Grothendiek Conjecture on the fundamental groups of algebraic curves (due to Mochizuki).