Brice Loustau (Rutgers University - Newark)
Title: Bi-Lagrangian structures and Teichm眉ller theory.
Abstract: A Bi-Lagrangian structure in a manifold is the data of a symplectic form and a pair of transverse Lagrangian foliations. Equivalently, it can be defined as a para-K盲hler structure, i.e. the para-complex equivalent of a K盲hler structure. After discussing interesting features of bi-Lagrangian structures in the real and complex settings, I will show that the complexification of any K盲hler manifold has a natural complex bi-Lagrangian structure. I will then specialize this discussion to moduli spaces of geometric structures on surfaces, which typically have a rich symplectic geometry. We will see that that some of the recognized geometric features of these moduli spaces are formal consequences of the general theory while revealing new other features, and derive a few well-known results of Teichm眉ller theory. Time permits, I will present the construction of an almost hyper-K盲hler structure in the complexification of any K盲hler manifold. This is joint work with Andy Sanders.
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