Colloquium abstracts

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.