Lectures: Monday, 10:20 ~ 11:10 and Thursday 15:30 ~ 17:20 at Astro-Math 204
Office hours: Friday 16:00 ~ 17:00 or by appointment, at Astro-Math 458
Grading scheme:
Homework 30%
You have three jokers: the lowest three grades will be discarded.
Midterm 30%
Final report 40%
References:
[CdS1] Ana Cannas da Silva, Lectures on symplectic geometry. MR
(I reserved this book in the library. The updated version can be downloaded from the author's website.)
[M&S] Dusa McDuff and Dietmar Salamon, Introduction to symplectic topology. MR
(I reserved this book in the library. The errata can be found on the author's website.)
[CdS2] Ana Cannas da Silva, Symplectic toric manifolds. MR
(This is a lecture note in a book of collected lectures. It can be found on the author's website.)
[G&S] Victor Guillemin and Shlomo Sternberg, Symplectic techniques in physics. MR
[G] Hansjörg Geiges, An introduction to contact topology. MR
(I reserved this book in the library. This book is not the main reference of this course. The errata can be found on the author's website.)
Lecture summaries and references
(9/9) origin of symplectic geometry, from Lagrangian mechanics to Hamiltonian mechanics. Reference: [M&S, p.12~15] and prelude.
(9/12) symplectic linear algebra, symplectic group, Lagrangian subspaces. Reference: [CdS1, §1], [M&S, p.19~21 and p.50~51], see also note0912.
(9/16) symplectic manifold; tautological 1-form and canonical symplectic form on the cotangent bundle. Reference: [CdS1, §2].
(9/23) Lagrangian submanifold in cotangent bundle. Reference: [CdS1, §3].
(9/26) construct symplectomorphism between cotangent bundles by generating functions. billiards. critical points of generating function and fixed points of symplectomorphism. Reference: [CdS1, §4, §5].
(9/30) the Poincaré--Birkhoff theorem. Reference: [M&S, §8.2], see also note0930.
(10/17) Lie algebra of the group of symplectomorphisms, Hamiltonian and symplectic vector fields, fixed points of Hamiltonian flows, Poisson bracket, integrable systems. Reference: [CdS1, §9.3, §18].