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Monday, July 24, 2017 - 11:30 to 12:30
SMS Seminal Hall
Rahul Kumar Singh
HRI, Allahabad
Maximal surfaces, Born-Infeld solitons and Ramanujan's identities

Abstract: In the first part of the talk we discuss a different formulation for describing maximal surfaces in Lorentz-Minkowski space $ \mathbb{L}^3:=(\mathbb{R}^3, dx^2+dy^2-dz^2) $ using the identification of $ \mathbb{R}^3 $ with $ \mathbb{C}\times \mathbb{R} $. This description of maximal surfaces help us to give a different proof of the singular Bj\"orling problem for the case of closed real analytic null curve. As an application, we show the existence of maximal surfaces which contain a given closed real analytic spacelike curve and has a special singularity. In the next part we make an observation that the maximal surface equation and Born-Infeld equation (which arises in physics in the context of nonlinear electrodynamics) are related by a Wick rotation. We shall also show that a Born-Infeld soliton can be realised either as a spacelike minimal graph or timelike minimal graph over a timelike plane or a combination of both away from singular points. Finally in the last part of the talk we show the connection of maximal surfaces to analytic number theory through certain Ramanujan’s identities.

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