Seminars and Colloquia
Mathematics
Geometric Quantization: Various Moduli Spaces and the Toda system
Fri, Apr 27, 2018,
04:30 PM to 05:30 PM
at Madhava Hall
Prof. Rukmini Dey
ICTS Bangalore
We shall briefly introduce the Kostant - Souriau method of quantization of a symplectic manifold, which is known as geometric quantization.
We briefly describe our coadjoint orbit quantization of the finite Toda system (joint work with Dr. Saibal Ganguli). Next we introduce Quillen's
determinant line bundle. Then we will describe the quantization of various moduli spaces arising from physics using the Quillen construction. Examples
include the Hitchin system and the vortex moduli space. We will also talk about a general theorem which essentially says that the quantum bundle
(or a tensor power of the same) of a compact integral K\\"{a}hler manifold (or integral symplectic manifold) can be realised as a Quillen determinant
bundle (joint work with Professor Mathai Varghese).
