# Diophantine Problems and $$p$$-adic Period Mappings (after Lawrence and Venkatesh) (Fall 2021)

The goal of this seminar is to go over the recent proof of Faltings's theorem by Lawrence and Venkatesh [LV]. The method of this proof, which heavily involves $$p$$-adic Hodge theory rather than heights and abelian varieties, may also be applied to higher dimensional varieties. We will follow the program outlined here.

• Organizers: Caleb Ji and Ivan Zelich
• When: Friday 1:30 pm - 3:00 pm
• Where: Room 528
• References:
[LV] Brian Lawrence and Akshay Venkatkesh Diophantine problems and $$p$$-adic period mappings https://arxiv.org/abs/1807.02721

#### Schedule

Sept 24
Caleb Ji
Faltings's theorem: comparison of approaches
I will give an overview of both Faltings's original proof of the Mordell conjecture and the Chabauty-Kim approach. Then I will outline the strategy of the proof given by Lawrence and Venkatesh.
Oct 1
Caleb Ji
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