We study the local Langlands correspondence for GL_n over p-adic fields. This is a non-abelian generalization of local class field theory. It was first proved in the late 1990's by Harris and Taylor using the cohomology of certain unitary Shimura varieties. A few months later, a simpler proof was given by Henniart. In 2010, Scholze gave a new proof of the local Langlands correspondence which by-passes the numerical local Langlands correspondence of Henniart.
The aim of our seminar is to first understand the two sides compared by the local Langlands correspondence for GL_n, and then to study how Scholze's approach differs from the previous proof.
The program can be found here.