Summer Graduate School

This summer school provides the mathematical background to recognize Koszul duality in representation theory. The school is especially oriented toward applications in the local Langlands program, with an emphasis on real groups. As Koszul duality patterns have been initially observed in the context of Hecke algebras, our school will also introduce the students to Hecke algebras and their categorifications.

School Structure

There will be two courses, each of which will have multiple lectures, background sessions and problem sessions. There will also be ice-breaking activities, a hike and some evening sessions.

Bibliography

Prerequisites

A background in algebraic groups, representation theory and/or algebraic geometry (first graduate courses level) will be assumed.  No previous knowledge of Hecke algebras or Number Theory is expected.  In particular, the school is open to newcomers in the Langlands Program.  Students are expected to be familiar with most of the material in the classical introductory book of Humphreys “Introduction to Lie algebras and representation theory”, and to have read the first three chapters of Pramod Achar’s “Perverse sheaves and applications to representation theory” (errata).  The expectations make the school particularly suitable for PhD students in their second or later years of PhD.  Aspects form both of these textbooks will be reviewed in background sessions but at an accelerated pace. We should also mention that students may find additional resources on Pramod Achar’s webpage, in particular course notes, which might be slightly more introductory than his book.

We also recommend reading:

• Local Langlands correspondence: the Archimedean case, by Knapp
• The local Langlands correspondence: the non-Archimedean case, by Kudla
• The local Langlands conjecture, by Vogan

Application Procedure

For eligibility and how to apply, see the Summer Graduate Schools homepage.