|Speaker:||Joergen E. Andersen (Aarhus University)|
|Title:||Non-abelian theta functions and unitarity of the hitchin connection|
|Date:||Wed, Jul 24, 2013, 15:30 - 17:00|
Theta functions forms a basis for the Hilbert space one obtains by quantizing an abelain variety.
We will show the existence of non-abelian theta functions which forms a basis for the quantization of the moduli space of flat connections on a surface and which is parallel with respect to the Hitchin connection. This construction of this basis depends on the choice of a singular Lagrangian torus fibration of this moduli space. We will describe how they can be used to provide a unitary structure which is preserved by the Hitchin connection and which is invariant under the mapping class group action. This part uses our joint work with Kenji Ueno, which identifies the quantization of the above mentioned moduli space with the Reshetikhin-Turaev TQFT vector spaces.