**Gregor Masbaum**

CNRS, Paris, France

February 2, 2017

** An application of TQFT to modular representation theory**:
Let G=Sp(2n,k) be a symplectic group defined over an algebraically closed field k of characteristic p > 0. Simple G-modules in the natural characteristic can be classified up to isomorphism by highest weights, but their dimensions are largely unknown in general. In this talk, we will present a new family of highest weights for G whose dimensions we can compute explicitly. The corresponding G-modules appear as a byproduct of Integral Topological Quantum Field Theory, and their dimensions are given by formulae similar to the Verlinde formula from Conformal Field Theory.