Math 226B:  Symplectic Geometry

MWF 1-1:50pm
Location: MS 5127

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
Office Hours: Wed. 11-12, Fri. 10-12
E-mail: honda at math dot ucla dot edu.
Telephone: 310-825-2143
URL: http://www.math.ucla.edu/~honda

Topics

  1. Basic notions, Darboux's theorem, local normal forms
  2. Moment maps, symplectic quotients, toric manifolds
  3. Some constructions
  4. Symplectic fibrations
  5. Generating functions and the symplectomorphism group
  6. J-holomorphic curves
  7. Applications, e.g., symplectic capacities
  8. Floer homology and Fukaya categories

Prerequisites

  • Math 225B or equivalent (a good knowledge of differentiable manifolds and homology). Math 226A is not a prerequisite for Math 226B.
Grading
  • TBA
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: February 4, 2014.