I will review the application of Hamiltonian flows in imaginary time to problems in geometric quantization. I will describe applications to symplectic toric manifolds and, time permitting, will also describe how this framework provides a geometric interpretation of the Peter-Weyl theorem....

Cartan geometries are structures on manifolds which are infinitesimally modelled on homogeneous spaces. For example, Riemannian structures are infinitesimally modelled by the euclidean space. The classical theory deals with "transitive" Cartan geometries, where the infinitesimal model is the...

TBA...