Akshay Venkatesh, IAS

Period mappings and Diophantine equations

I will  give some friendly examples introducing the period mapping. This is an analytic mapping which controls many aspects of how algebraic varieties change in families.

After that I will explain joint work with Brian Lawrence which shows that one can exploit transcendence properties of the period mapping  to prove results about Diophantine equations.  For example we  give another proof of the Mordell conjecture (originally proved by Faltings): there are only finitely many rational points on an algebraic curve over Q whose genus is at least 2.