Categorifying Hecke Algebras at Prime Roots of Unity

Explore the groundbreaking developments in categorifying Hecke algebras at prime roots of unity in this 1-hour 9-minute lecture by Ben Elias at the Hausdorff Center for Mathematics. Delve into the paradigm shift initiated by Soergel's algebraic construction of the Hecke category three decades ago, which categorified the Hecke algebra at a generic parameter using grading shifts. Discover the ongoing challenge in categorification to extend this concept to Hecke algebras at roots of unity. Learn about the innovative approach utilizing p-DG categories to propose a conjectural categorification, as presented through joint work with Y. Qi. Gain insights into this key open problem in categorification and its potential implications for advanced mathematical research.