Fall 2015 MATH 242 001 LEC

Symplectic Geometry
001 LECTuTh 1230-2P 2 EVANSREZAKHANLOU, F54497
Units/CreditFinal Exam GroupEnrollment
4NONELimit:28 Enrolled:16 Waitlist:0 Avail Seats:12 [on 10/04/15]
Additional Information: 


Syllabus: Hamiltonian systems appear in conservative problems in mechanics as in celestial mechanics but also in the statistical mechanics governing the motion of atoms and molecules in matter. The discoveries of last century have opened up new perspectives for the old field of Hamiltonian systems and let to the formation of the new field of symplectic geometry. In the course, I will give a detailed acount of some basic methods and results in symplectic geometry and its application to physics and other fields of mathematics.
Here is an outline of the course:

1. Sympletic linear algebra. Quadratic Hamiltonians.
2. Symplectic and Contact manifolds, cotangent bundles. Darboux's theorem.
3. Variational problems and Minimax principle. Hofer-Zehnder Capacity and Hofer Geometry.
4. Weinstein's conjecture, Viterbo's theorem. Gromov-Eliashberg $C^0$-rigidity.
5. Holomorphic Curves and Gromov's Symplectic Width.








Office: 803 Evans

Office Hours: 2-3:30 pm

Required Text: None

Recommended Reading: F. Rezakhanlou: Lectures on Symplectic Geometry

Grading: based on homework assignments


Course Webpage: https://math.berkeley.edu/~rezakhan/math242_html/