Prof Rukmini Dey
Prof Rukmini Dey is a faculty member at International Centre for Theoretical Sciences (ICTS), Bengaluru from 2015 onwards. Prior to joining at ICTS, she was a faculty member at Harish-Chandra Research Institute, Allahabad. She did her PhD in the year 1998 from S.U.N.Y. at Stony Brook. Her area of research is Mathematical Physics and Geometry.
She studies the minimal surfaces in R^3, constant mean curvature surfaces in R^3 and maximal surfaces in Lorentz-Minkowski 3-space. Her research interests include the geometric quantization of various moduli spaces of solutions of equations coming from physics and certain integrable systems.
Title of the talk: Some aspects of Maximal and Minimal surfaces
Abstract: Minimal surfaces in 3-d Euclidean space and maximal surfaces in 3-d Lorentz Minkowski space are defined to be zero mean curvature surfaces. The general solutions are given by the Weierstrass-Enneper representations of these surfaces. We will first re-derive the Weierstrass-Enneper representation of a minimal and maximal surface using hodographic coordinates which was introduced in the context of solitons by Barbishov and Chernikov. We will mention an interesting link between minimal surfaces and maximal surfaces and Born-Infeld solitons. Next we will talk about some identities we obtain from certain Euler- Ramanujan identities and their relation with some of these surfaces. This link was first studied by Kamien, U. Penn, in the context of liquid crystals. We will also talk about some number theoretic results in this context. Finally we talk about interpolation of two real analytic curves by minimal and maximal surfaces. Some of this work is done jointly with Dr. Pradip Kumar and Dr. Rahul Kumar Singh and Mr. Rishabh Sarma.