Given a family of complex algebraic varieties parameterized by a base variety B there is an associated period mapping, which (at least locally) goes from B to a certain flag variety. However, although both the source and target are algebraic varieties,

this period map is of a transcendental nature.

I will explain joint work with Brian Lawrence which shows how the transcendence of the period mapping

can be exploited to 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.

While this proof is closely related to Faltings' original proof, it also

gives some (modest) new higher-dimensional results. These use essentially a very strong transcendence statement for period maps that was recently established by Bakker and Tsimerman. I will describe some of the ideas involved.

this period map is of a transcendental nature.

I will explain joint work with Brian Lawrence which shows how the transcendence of the period mapping

can be exploited to 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.

While this proof is closely related to Faltings' original proof, it also

gives some (modest) new higher-dimensional results. These use essentially a very strong transcendence statement for period maps that was recently established by Bakker and Tsimerman. I will describe some of the ideas involved.

## Date:

Thu, 25/01/2018 - 14:15 to 15:45

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem