**Seminar on the \(p\)-adic Langlands program**

The goal of this seminar is to explore the categorical \(p\)-adic Langlands program, i.e. a series of conjectures giving a partial analogue of the work of Fargues-Scholze when \(\ell = p\). Along the way, we will discuss the "classical" Langlands program and the Taylor-Wiles method.

Thursdays 3 - 4 PM, 528 Mathematics

[1] Matthew Emerton, Toby Gee, Eugen Hellmann. "An Introduction to the Categorical p-Adic Langlands Program." *IHES Summer School on the Langlands Program* (2022).

Date |
Speaker |
Topic |
References |
Notes |

September 8 | Avi Zeff | Introduction, organization and overview | [1] | |

September 15 | Kevin Chang |
Overview of the Langlands program Overview of the Langlands program
I'll describe some of the main conjectures in the Langlands program and survey some known cases. |
||

September 22 | Avi Zeff | Overview of Fargues-Scholze | ||

September 29 | Haodong Yao | Taylor-Wiles patching | ||

October 6 | Haodong Yao | Taylor-Wiles patching, continued: connections to \(p\)-adic Langlands | ||

October 13 | David Marcil | \((\phi, \Gamma)\)-modules and the Emerton-Gee stack | ||

October 20 | Avi Zeff | Formulation of the \(p\)-adic Langlands conjectures | [1, §6.1] | |

October 27 | Cancelled | |||

November 3 | Avi Zeff | Connections and known cases | ||

November 10 - 24 | Break for coordination + Thanksgiving | |||

December 1 | David Marcil | Global applications: cohomology of Shimura varieties | ||