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


[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   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