Theoretical Statistics and Mathematics Unit, ISI Delhi

November 14, 2018 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Rukmini Dey,
ICTS, Bangalore

Title:
Geometric Quantization of various moduli spaces

Abstract of Talk

We will give a brief introduction to geometric quantization and 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 intergral K\"{a}hler manifold can be realised as a Quillen determinant bundle.This is joint work with M Varghese. Recently we have been able to carry out geometric quantization for moduli spaces of 3-vortex equations on K\"{a}hler surfaces. This is joint work with S. Ganguli.

If time permits, we will talk about geometric quantization of the finite Toda system. This is joint work with S. Ganguli.