Seminar in Real and Complex Geometry

Tuesday, 22.07.2015, 16:00-17:00, Schreiber building, room 210

Mikhail Verbitsky, High School of Economics

Teichmuller space of symplectic structures


Let Symp be the (infinite-dimensional) space of all symplectic forms, and Teich:=Symp/Diff_0 its quotient by the group of isotopies (that is, by the connected component of the group of diffeomorphisms). It was proven by Moser that Teich, known as "Teichmuller space of symplectic structures", is a smooth manifold. Nevertheless, its structure is still very much mysterious. Denote by Teich_k a subset of Teich consisting of all symplectic structures which are Kahler for some complex structure. By Kodaira, under additional non-restrictive assumptions, the manifold Teich_k is open in Teich. I will describe the structure of Teich_k on a hyperkahler manifold, and explain how it can be used to solve problems of symplectic packing. These is a joint work with Ekaterina Amerik.