Dipartimento di Matematica, Aula Riunioni
In this talk we will define a pseudo-Kähler structure on the deformation space of properly convex projective structures over the 2-dimensional torus. The symplectic form and the pseudo-Riemannian metric are both compatible with the complex structure inherited from the identification of this space with the total space of the holomorphic vector bundle of cubic differentials over Teichmuller space. I will also explain briefly what we expect in higher genus and the strategy to solve the problem. This is the first part of an ongoing PhD research project under the supervision of Dr. A. Tamburelli.