Thursday February 15, 2018 1:00 PM Math Tower 5127
 Brice Loustau, Rutgers University
BiLagrangian structures and Teichmüller theoryA BiLagrangian structure in a smooth manifold consists of a symplectic form and a pair of transverse Lagrangian foliations. Equivalently, it can be defined as a paraKähler structure, that is the paracomplex equivalent of a Kähler structure. BiLagrangian manifolds have interesting features that I will discuss in both the real and complex settings. I will proceed to show that the complexification of a realanalytic Kähler manifold has a natural complex biLagrangianstructure, and showcase its properties. I will then specialize this discussion to moduli spaces of geometric structures on surfaces, which have a rich symplectic geometry. I will show that some of the recognized geometric features of these moduli spaces are formal consequences of the general theory, while revealing other new geometric features; as well as deriving several wellknown results of Teichmüller theory by pure differential geometric machinery. Time permits, I will also mention the construction of an almost hyperHermitian structure in the complexification of any realanalytic Kähler manifold, and compare it to the FeixKaledin hyperKähler structure.
