## Broué’s Abelian Defect Group Conjecture I

Jay Taylor

University of Southern California; Member, School of Mathematics

September 9, 2020

This talk will form part of a series of three talks focusing on Broué’s Abelian Defect Group Conjecture, which concerns the modular representation theory of finite groups. We will pay particular attention here to the ‘geometric’ form of the conjecture which concerns finite reductive groups such as GLn(q) and SLn(q). Broué’s conjecture gives a strong structural reason for many numerical coincidences one sees amongst characters and is part of a general ‘local/global phenomena’ that is abundant in the theory.