IISER Pune
INDIAN INSTITUTE OF SCIENCE EDUCATION AND RESEARCH (IISER) PUNE
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An Autonomous Institution, Ministry of Human Resource Development, Govt. of India
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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).
 

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