# Diophantine problems and the $p$-adic Torelli map

 Joint IAS/Princeton University Number Theory Seminar Topic: Diophantine problems and the $p$-adic Torelli map Speaker: Brian Lawrence Affiliation: Stanford University Date: Thursday, February 9 Time/Room: 4:30pm - 5:30pm/Fine 214, Princeton University

We explore the comparison isomorphism of $p$-adic Hodge theory in the case of elliptic curves, and discuss some ideas which may be used to prove the S-unit theorem and the finiteness of rational points on higher-genus curves (Faltings' theorem).