# 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 /// |
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