**Gregor Masbaum**

CNRS, IMJ, Paris, France

January 22, 2015

**Modular TQFT-representations of mapping class groups**:
There are by now several mathematical constructions of
Topological Quantum Field Theories (TQFT) as defined by Atiyah and
Segal. These TQFTs give rise to finite-dimensional complex unitary
representations of mapping class groups of surfaces. I will explain
that in some cases, one can also get modular representations (i.e.,
representations in finite characteristic), using some integrality
properties of the TQFT. As an application, I will discuss joint work
with Reid where we use these representations to answer a question
of Hamenstaedt about finite index subgroups of the mapping class
group. I will also present Verlinde-like dimension formulas for the
irreducible factors of these representations in the case of equal
characteristic.