Sebastian Burciu
Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania

In this talk we extend a classical vanishing result of Burnside from the character tables of finite groups to the character tables of commutative fusion rings, or more generally to certain classes of abelian real non-negative hypergroups. We also treat the dual vanishing result. As applications we prove new identities that hold in the Grothendieck ring of any weakly-integral fusion category satisfying the dual Burnside vanishing result. Based on a joint work with Sebastien Palcoux.