# PhD Seminar WS 2324

Welcome to the webpage of the Essen PhD Seminar for the Wintersemester 2023/24!

The seminar will take place every **Wednesday** starting from October 11th in the lecture room **WSC S-U-4.01**. The talks will start at **4**** pm** and last about 90 minutes.

You can find the latest version of the program here.

You can find an english translation of Deligne's paper *"Formes modulaires et representations l-adiques" *here. I do not know who translated it, it seems to me that there are not big mistakes, but there could very well be typos. In any case it may be useful if you don't know french.

**Topics for next semester:**

Date |
Title |
Speaker |
Notes |

11/10/23 | 1. Introduction | Giulio | |

18/10/23 | 2. Étale morphisms | Luca | Talk 2 |

25/10/23 | 3. Étale sheaves | Marc | Talk 3 |

8/11/23 | 4. Étale cohomology | Federica | Talk 4 |

15/11/23 | 5. The cohomology of curves and purity | Lukas | Talk 5 |

22/11/23 | 6. Proper base change and applications | Pietro | Talk 6 |

29/11/23 | 7. Smooth base change, Künneth formula and cycle map | Thiago | Talk 7 |

06/12/23 | 8. Poincaré duality and the Lefschetz fixed point formula | Lukas | Talk 8 |

20/12/23 | 9. Proof of the Weil conjectures (I) | Guillermo | Talk 9 |

10/01/24 | 10. The main lemma | Niklas | |

17/01/24 | 11. Proof of the Weil conjectures (II) | Riccardo | |

24/01/24 | 12. The Ramanujan conjecture (I) | Hind | |

31/01/24 | 13. The Ramanujan conjecture (II) | Paolo |