3:30 pm, Seminar Hall
Hypersymplectic manifolds and associated geometries
Varun Thakre
ICTS, Bengaluru.
14-08-19

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Abstract

In this talk, I will present my latest result, characterizing hypersymplectic manifolds with certain symmetries. Hypersymplectic manifolds are pseudo-Riemannian analogues of hyperKähler manifolds and appear naturally in the study of integrable systems, string theory - where they are also known by Kleinian geometry - and gauge theory.

The talk will focus on hypersymplectic manifolds admitting a certain action of the group SU(1,1). Under vanishing of an obstruction, I will show that such a manifold is topologically equivalent to a metric cone over some split 3-Sasakian manifold. As an example of the theory, I will show that the moduli space of solutions to the Nahm-Schmid equations can be written as the total space of a metric cone over a split 3-Sasakian manifold. The latter were shown to carry a hypersymplectic structure by N. Romaõ, R. Bielawski and M. Röser.