Proposed schedule of the lectures (all 1000--1200 hrs with a break in between for about quarter of an hour):
Short Abstract: Recently, Geordie Williamson and I proved Soergel's conjecture, which is the generalization to arbitrary Coxeter systems of the Kazhdan-Lusztig conjecture, thus realizing a long-standing program of Soergel. Our proof was an algebraic adaptation of de Cataldo and Migliorini's Hodge-theoretic proof of the Decomposition Theorem in geometry. Our goal in this lecture series is to provide a thorough introduction to Hecke algebras, Soergel bimodules, and the Hodge-theoretic techniques which went into the proof of the Soergel conjecture. We will also introduce the diagrammatic tools which are used to study Soergel bimodules.
Here is a more detailed abstract.
Two relevant papers:
Speaker's hand written notes (pdf files): lecture 1, lecture 2, lecture 3 (first part), lecture 3 (second part), lecture 4 (catch up), lecture 4, lecture 5, lecture 6 (also rouqier complexes), lecture 7.
Exercise sets (pdf files): the important ones are starred: lecture 1, lecture 2, lecture 3, lecture 4, lecture 5, lecture 6.
Videos of all the talks, including colloquia listed below, can be found here.
Organizers: Upendra Kulkarni upendra-at-cmi-dot-ac-dot-in and K N Raghavan knr-at-imsc-dot-res-dot-in