Hong Kong Geometry Colloquium

November 25, 2006 (Saturday)

Room 517, Meng Wah Complex, HKU

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Professor Minhyong Kim

Purdue University, USA, and RIMS, Japan

Anabelian geometry, path spaces, and Diophantine geometry

Abstract

In the 80's Grothendieck formulated a mysterious circle of conjectures and fantasies that eventually coalesced into the area now known as `anabelian geometry.’ A central theme of the program revolved around the principle that certain schemes were as `topologically rigid’ as hyperbolic manifolds. It was believed that understanding this rigidity in sufficient depth would lead to concrete consequences for Diophantine geometry, such as the finiteness theorems of Faltings and Siegel. We will describe recent progress in this direction that was achieved using the language of `motivic path spaces.’