Speaker: Dr Rukmini Dey, ICTS, TIFR, Bengaluru | Shiv Nadar University
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Speaker: Dr Rukmini Dey, ICTS, TIFR, Bengaluru

15 Nov 2018

Prof. Dey is giving two lectures during her visit to SNU:

Nov 15, B219, 12:00:

TitleWhat are minimal surfaces?”

Abstract: We will review some basics of surface theory in Euclidean space.  Minimal surfaces in 3-d Euclidean space are defined to be zero mean curvature surfaces. The general solutions are given by the Weierstrass-Enneper representations of these surfaces. We will derive the Weierstrass-Enneper representation of a minimal surface. Next, we will talk about some identities we obtain from
certain  Euler- Ramanujan identities in connection with some of these surfaces.  We will also talk about interpolation of two real analytic curves by a minimal surface. If time permits, we will introduce maximal surfaces in Lorentzian space and talk about analogous results. 

Part of this talk is joint work with Dr Pradip Kumar, Dr Rahul Kumar Singh.

Nov 16, B219, 12:00:

TitleGeometric Quantization of various moduli spaces”

Abstract: 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.