Seminar on the $$p$$-adic Langlands program

## Fall 2022

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.

### Time and place

Thursdays 3 - 4 PM, 528 Mathematics

### References

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

### Schedule

 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. PDF September 22 Avi Zeff Overview of Fargues-Scholze PDF 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] PDF October 27 Cancelled November 3 Avi Zeff Connections and known cases PDF November 10 - 24 Break for coordination + Thanksgiving December 1 David Marcil Global applications: cohomology of Shimura varieties