# Research Seminar Algebraic Geometry

## Diophantine problems and the $p$-adic period morphism (after Lawrence and Venkatesh)

We will study the new proof of the Mordell conjecture (Faltings’s theorem) recently given by B. Lawrence and A. Venkatesh. This combines methods of number theory, algebraic geometry, complex geometry, and differential geometry/topology. For further details, see the seminar program.

Date: Thursday, 2-4 pm, WSC-N-U-3.05. First meeting: Oct. 18.

Program: pdf

## Talks

 Oct. 18 Introduction U. Görtz Oct. 25 The Gauss-Manin connection and the complex period morphism F. Gora Nov. 8 The $p$-adic period morphism and comparison with the complex situation L. Gehrmann Nov. 15 Galois representations R. Witthaus Nov. 22 The $S$-unit equation R. Venerucci Nov. 29 The proof of Mordell’s conjecture: Outline of the strategy and first steps M. Tamiozzo Dec. 6 Rational points on the base of an abelian-by-finite family M. Würthen Dec. 13 Construction of the Kodaira-Parshin family H. Zhao Dec. 20 The Kodaira-Parshin family has full monodromy I L.-C. Lefèvre Jan. 10 The Kodaira-Parshin family has full monodromy II J. Heinloth Jan. 17 at 10:15 The Theorem of Bakker and Tsimerman A. Marrama Jan. 17 Some conjectures on automorphic forms and the cohomology of spaces beyond Shimura varieties P. Scholze (Bonn) Jan. 24 Higher dimensional cases — /// cancelled /// –