Conjugacy Classes and Grothendieck Rings of Premodular Categories

Explore a research seminar from the BIMSA-Tsinghua Quantum Symmetry series where Sebastian Burciu from the Institute of Mathematics "Simion Stoilow" presents groundbreaking findings on conjugacy classes in fusion categories. Delve into the extension of classical group conjugacy classes to fusion categories, as introduced by Shimizu, and examine new properties of conjugacy classes in pivotal fusion categories. Learn about a Burnside-type formula for structure constants involving conjugacy class sums, and discover how these constants, when multiplied by dim(C), yield non-negative integers in braided weakly integral fusion categories. Drawing from published research in the Bulletin of the London Mathematical Society and ongoing work, gain insights into tensor categories, quantum groups, Hopf algebras, and representation theory from an experienced mathematician with extensive academic background from Syracuse University and the Romanian Academy.