MAT 562: Symplectic Geometry and Topology

Stony Brook            Fall 2024

 

General Course Information, A Proof and a Modern ``Proof"

References

All readings listed in the table below are from McDuff&Salamon's Introduction to Symplectic Topology, except as noted. Audin refers to Torus Actions on Symplectic Manifolds, 2nd revised Ed.

Tentative Schedule

Date Topic Read Problem Set
08/26, Mno lectures Intro
Sections 1,2		 ps1
solutions
08/28, W
09/04, WExamples of symplectic manifolds Section 3.1
Notes Appendix B
Warner pp69,70
09/09, MHamiltonian flows
09/11, WMoser's principleSection 3.2 ps2
solutions
09/16, MSymplectic tubular neighborhood theorem Section 3.4
09/18, WLagrangian tubular neighborhood theorem
09/23, MAlmost complex structures Sections 4.1,4.2
Notes Section 2.1
09/25, WComplex structures and nondegenerate 2-forms
09/30, MPseudoholomorphic maps Section 4.5
Notes Section 2.2		 ps3
solutions
10/02, WKahler manifolds Sections 4.3,4.4
Notes Section 2.3
10/07, MTorus actionsSection 5.1 ps4
solutions
10/09, WMoment mapsSections 5.2,5.3
Warner 3.1-3.10,3.29-3.33,3.44-3.47
10/16, WConvexity Theorem Section 5.5
Atiyah's paper
Convexity notes
10/21, M
10/23, Wps5
solutions
10/28, M
10/30, W
11/04, MProperties of moment polytopes Atiyah's paper
Audin's Sections IV.4def
11/06, Wps6
11/11, M
11/13, WKahler case
11/18, M
11/20, WSymplectic quotientsSection 5.4
11/25, MDelzant theorem: surjectivity Eckhard's Section 7.5
Ana's Chapter 2
Alexandra's Chapter 2		 ps7
12/02, MHamiltonian symplectic cut
12/04, WDelzant theorem: injectivity
12/09, MSymplectic cut 
 
This page is maintained by Aleksey Zinger.
Last modified: December 2, 2024.