• Class Meetings: TuTh 9:30-11a in 939 Evans
• Office Hours: M 2-3p & W 2-3p in 1062 Evans
Course Control Number: 18832
Course Mailing List: STopLearning@lists.berkeley.edu
Grading Scheme: 50% Homework, 50% Participation

• Introduction to Symplectic Topology (2nd Edition) by D. McDuff & D. Salamon
• Lectures On Symplectic Geometry by A. C. da Silva
• Mathematical Methods In Classical Mechanics (2nd Edition) by V. I. Arnold

This seminar will be a first course in symplectic geometry and topology. We will definitely cover Part I of McDuff-Salamon (Chapters 1-4). We will also hopefully cover portions of Part II (Chapters 5-7) and discuss additional topics. Here is an outline of the first 4 chapters.

• Ch. 1: Hamiltonian mechanics, Lagrangian mechanics, general overview
• Ch. 2: linear symplectic geometry, affine non-squeezing, symplectic vector bundles
• Ch. 3: symplectic manifolds, homotopy method, Darboux theorem, submanifolds, almost complex geometry
• Ch. 4: almost complex structures, Kahler manifolds

• See here for a complete schedule and the list of exercises.
• Solutions To Salamon-Mcduff: [pdf]. These are mostly complete through Chapter 5
• Notes For 10.4: [pdf]. These are some very brief notes on homology and cohomology theory to supplement the lecture on 10.4
• Note 1: Exercises are due the thursday of the week after they are assigned. For instance, the exercises of Tu 9.6 and Th 9.8 are due on Th 9.15.
• Note 2: Exercises surrounded by parentheses are optional.
• Tu 11.8: [Julian C., S-M p. 161-172, Ex. (5.19), (5.21)] moment maps, examples
• Th 11.10: [Kat C., S-M p. 173-179, Ex. (5.42), (5.43)] symplectic quotients
• Tu 11.15: [Julian C., S-M p. 179-191, Ex. (5.49)] Morse theory I: Morse functions, handle-body decompositions
• Th 11.17: [Julian C.] Morse theory II: Morse homology
• Tu 11.22: [Joseph F.] J-holomorphic curves I: definitions, gradient flow formulation
• Th 11.24: no meeting.
• Tu 11.29: [Julian C.] J-holomorphic curves II: essential results
• Th 12.01: [Julian C.] Survey of Floer Theory: Hamiltonian & Lagrangian Floer Theory