Seminario de Geometría “Maximal surfaces, Born-Infeld solitons and Ramanujan’s identities”

Event Details

Título: Maximal surfaces, Born-Infeld solitons and Ramanujan’s identities
Lugar: Seminario 1ª planta (IEMath-Gr)
Abstract: In this talk, we will explain how one can obtain the Weierstrass- Enneper representation for maximal graphs( assuming that the Gauss map is one-one) in hodographic coordinates by making an observation that the maximal surface equation and Born-Infeld equation are related upto a wick rotation. This observation also gives us a way to construct a one parameter family of complex Born-Infeld solitons( solutions of Born-Infeld equation) from a given one parameter family of maximal surfaces. We 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. Next we show the existence of a maximal surface containing a given spacelike closed curve and having a special singularity. Finally, we show the connection of maximal surfaces to analytic number theory through certain Ramanujan’s identities.