EVENT DETAILS AND ABSTRACT

Title: The symplectic topology of Stein manifolds
Speaker: Mohammed Abouzaid
Speaker Info: MIT/Clay
Brief Description:
Special Note:
Abstract:

Those complex manifolds which admit a proper embedding in affine space are called Stein. In the early 90's, Eliashberg classified the smooth manifolds of real dimension greater than 4 which admit a Stein structure, leaving open the question of whether a manifold can admit two Stein structures which are not deformation equivalent. By making full use of the modern machinery of symplectic topology (i.e. Floer theory and the Fukaya category), the last five years, starting with work of Seidel and Smith, has seen much progress on this front. I will particularly focus on the case of Stein structures on manifolds diffeomorphic to euclidean space, and explain some ideas behind the proof that, in real dimensions greater than 10, the set of equivalence classes of such Stein structures (under deformation) maps surjectively to the set of sequences of prime numbers. In particular, it is uncountable.