Geometry and Topology Seminar

We will review the relevant moduli spaces of flat connections which forms the corner stone in the construction of quantum Chern-Simons theory from a gauge theory point of view. We will further review the construction of the Hitchin connection in the bundles over Teichmüller space, which are obtained by applying geometric quantization to these moduli spaces. Following this, we will discuss the asymptotics of the Hitchin connection near certain points on the Thurston boundary of Teichmüller space. This will allow us to define both, the unitary structure preserved by the Hitchin connection, the handlebody boundary state vector and curve operators. We will then discuss their relations to Toeplitz operators and obtain asymptotics results about these TQFT. If time allows, we will also discuss quantum Chern-Simons theory with complex gauge group.