Title: Symplectic forms and almost-complex structures in 4 dimensions
Speaker: Valentino Tosatti
Speaker Info: Columbia University
Consider a closed 4-manifold with a given almost-complex structure. A natural question to ask is: under what conditions can we find a symplectic form compatible with the almost-complex structure?Date: Wednesday, January 26, 2011
A necessary condition is that there exists a symplectic form "taming" it (in the sense of Gromov), and a conjecture of Donaldson says that this should be also sufficient.
I will discuss a possible approach to this conjecture that involves a generalization of the classical Calabi-Yau theory on Kahler manifolds, and report on some recent work on this (joint with B. Weinkove and partly with S.-T. Yau).