Columbia Mathematics Department Colloquium


The symplectic topology of Stein manifolds


Mohammed Abouzaid




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.


Wednesday, December 7th, 5:00 - 6:00 p.m.
Mathematics 520
Tea will be served at 4:30 p.m.