Eilenberg Lectures: Symplectic topology of affine complex manifolds

Yasha Eliashberg: Symplectic topology of affine complex manifolds

Eilenberg Lectures, Fall 2007

Eilenberg Lectures, Fall 2007. These lectures will be held on Fridays from 3:30pm-5:30pm, in room 312. The lectures will start on Friday, September 7th.
Note: on Fri, Oct 12th, the lecture will take place in Math 203.

abstract. Affine, or Stein complex manifolds have a canonical built-in symplectic geometry which is crucial for understanding many complex analytic problems. A systematic study of this geometry and its applications will be one of the central themes of the course. In the second part of the course we will explore complex analytic tools, namely the theory of holomorphic curves, necessary for understanding of symplectic topology of Stein manifolds.

A more precise breakdown of topics is listed below.

Pseudoconvexity, plurisubharmonic functions and the built-in symplectic geometry.

Basic complex analysis on Stein manifolds.

Morse theory of plurisubharmonic functions.

Surgeries preserving pseudoconvexity.

Construction of Stein complex structures on smooth manifolds.

Plurisubharmonic h-cobordism problem.

From Stein to Weinstein and back.

The subcritical case.

Distinguishing Weinstein manifolds: computation of symplectic and contact homology.

Symplectic Field Theory of Weinstein manifolds.

For a reference, click here

	Pseudoconvexity, plurisubharmonic functions and the built-in symplectic geometry.
	Basic complex analysis on Stein manifolds.
	Morse theory of plurisubharmonic functions.
	Surgeries preserving pseudoconvexity.
	Construction of Stein complex structures on smooth manifolds.
	Plurisubharmonic h-cobordism problem.
	From Stein to Weinstein and back.
	The subcritical case.
	Distinguishing Weinstein manifolds: computation of symplectic and contact homology.
	Symplectic Field Theory of Weinstein manifolds.