Mathematics

In a Kahler manifold there is a duality between the symplectic and the complex point of view. In the case where the manifold is toric this can help parametrize all the complex structures compatible with a fixed "canonical" symplectic form. After giving an overview of the properties of the moment polytope that describes a toric manifold I will explain how this duality is given by the Legendre transform. Finally we will see an application to eigenvalues of the Laplacian.