Lectures by Benjamin Elias

20th January to 03rd February 2014 Institute of Mathematical Sciences (IMSc)

Proposed schedule of the lectures (all 1000--1200 hrs with a break in between for about quarter of an hour):

27 Jan (Mon), 29 Jan (Wed), 31 Jan (Fri), 03 Feb (Mon)

Venue: Chandrasekhar Hall, except on Friday 31 Jan, for which day it is Room 326, and on Monday 03 Feb, for which day it is Room 423

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.

Important note: Some of the material below is cannibalized from a similar lecture course at Aarhus given jointly by Ben Elias and Geordie Williamson. There are links on Geordie Williamson's home page to videos and notes of those lectures.

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.

Colloquium talks:

- Thursday 24th Jan, 1400--1500 hrs, IMSc room 123: Categorical actions of Coxeter groups and braid groups notes
- Thursday 30th Jan, 1400--1500 hrs, CMI: Perverse sheaves (for dummies!) notes
- Thursday 30th Jan, 1515--1645 hrs, CMI: Quantum Geometric Satake (without tears!) notes
- Friday 31st Jan, 1400--1500 hrs, IMSc room 326: The new homological algebra: p-complexes and categorification at roots of unity notes

Organizers: Upendra Kulkarni upendra-at-cmi-dot-ac-dot-in and K N Raghavan knr-at-imsc-dot-res-dot-in