Math 226C:  Symplectic Geometry

MWF 2-2:50pm
Location: MS 6201

Syllabus

This is a first course in symplectic geometry.  Symplectic geometry is the study of manifolds equipped with a closed nondegenerate 2-form, called a symplectic form.  It occupies a central role in modern mathematics and is related to low-dimensional topology, representation theory, algebraic geometry, string theory, and dynamical systems.


Instructor: Ko Honda
Office: MS 7901 (but will move to MS 7919 at some point)
Office Hours: Mondays 1-2pm, Wednesdays 3-4pm
E-mail: honda at math dot ucla dot edu.
Telephone: 310-825-2143 (for MS 7901)
URL: http://www.math.ucla.edu/~honda

Topics
  1. Basic notions, Darboux's theorem, local normal forms
  2. Some constructions
  3. J-holomorphic curves
  4. Applications, e.g., symplectic capacities
  5. Floer homology and Fukaya categories

Prerequisites
  • Math 225A, B, C or equivalent (a good knowledge of differentiable manifolds and homology). Math 226A and B are not prerequisites for Math 226C.
Grading
  • Based on attendance.  If you want an A+, submit your stack of HW at the end of the quarter.
References
  1. D. McDuff and D. Salamon, Introduction to symplectic topology, 2nd edition, Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, 1998.
  2. R. Bryant, An introduction to Lie groups and symplectic geometry, lecture notes from the Regional Geometry Institute in Park City, Utah, June 24-July 20, 1991.
  3. A. Cannas da Silva, Lectures on symplectic geometry, Lecture Notes in Mathematics 1764, Springer-Verlag, 2008.
  4. D. McDuff and D. Salamon, J-holomorphic curves and symplectic topology, 2nd edition, American Mathematical Society Colloquium Publications, 52. American Mathematical Society, Providence, RI, 2012.
 
WARNING:  The course syllabus provides a general plan for the course; deviations may become necessary. 

Last modified: October 10, 2017