# Research Seminar: Cohomology of modular curves and local Langlands for GL2

The aim of the seminar is to learn something about the local Langlands correspondence for GL(2) over Q_p, and in particular about the connection to the cohomology of modular curves. (This case has been known for a long time, based on the work of Langlands, Deligne and Carayol (among others). See Carayol's paper cited in the program.) We will not prove the local Langlands correspondence even in this case (for a proof, see the book by Bushnell and Henniart), but will learn about several methods and results which are useful for generalizations (such as the work of Harris and Taylor) and variants, and open perspectives, for instance to the p-adic Langlands program.

**Program:** pdf.

**Organizers:** G. Böckle, U. Görtz, G. Wiese

**Dates:** Thu, 10-12, T03 R04 D10. We start on April
29.

## Talks

April 29 | Overview and motivation | Ulrich Görtz |

May 6 | Admissible representations | Johan Bosman |

May 20 | Galois representations | Yamidt Bermudez Tobon |

May 27 | The local Langlands correspondence | Philipp Hartwig |

June 10 | Geometry of modular curves I | Martin Kreidl |

June 17 | Geometry of modular curves II | Juan Marcos Cerviño |

June 24 | Eichler-Shimura theory | Nicolas Billerey |

July 1 | Decomposition of the representation sigma_p | TONG Jilong |

July 8 | Analysis of sigma_1 | PARK Donghoon |

July 15 | Deformations of formal groups and the fundamental local representation I | Christian Kappen |

July 22 | Deformations of formal groups and the fundamental local representation II |