A Mathematical Medley

Verlinde algebras are a special class of commutative Frobenius algebras, i.e. finite-dimensional associative unital algebras equipped with a trace functional. They have important applications in complex algebraic geometry and quantum topology. For instance, they control the number of generalised theta functions associated with compact Riemann surfaces. This talk concerns a one-parameter deformation of Verlinde algebras. I will elucidate the geometric origin of this deformation and discuss an algebraic presentation of the deformed algebras. This is joint work with M. Raziebrahimsaraei and A. Fok.