Chris Bowman-Scargill – Torsion-explosion in Hecke categories 2

Abstract. A prime focus of twentieth century representation theory was the (doomed!) attempt to prove Lusztig’s conjecture. Loosely speaking, this conjecture stated that some of the most important problems in representation theory should admit combinatorial solutions by counting “p-Kazhdan–Lusztig polynomials” for p any reasonable prime number. Counterexamples to these expected bounds were found in 2011 by Geordie Williamson. This was done by re-imagining Lusztig’s conjecture in terms of calculating “p-torsion” within the “intersections forms” of the “anti-spherical Hecke category”. The purpose of this series of talks is to take an audience with zero background in Hecke categories through to the point where they completely understand every detail of the proof of this result, in the context of the Hecke category. This is done by taking an elementary, diagrammatic approach to the material. Remarks. Videos from the conference "Categorification in representation theory" organized by Asilata Bapat, Andrew Mathas, Daniel Tubbenhauer and Oded Yacobi. The slides can be found here: https://www.maths.usyd.edu.au/u/catre... For any other questions and remarks email me dtubbenhauer@gmail.com