Math 226B:  Symplectic Geometry

MWF 11-11:50am
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 7919
Office Hours:  Mondays at 10am or by appointment
E-mail: honda at math dot ucla dot edu.
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

Prerequisites
  • Math 225A, B, C or equivalent (a good knowledge of differentiable manifolds and homology). Math 226A is not a prerequisite for Math 226B.
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, 3rd edition, Oxford University Press, 2017.
  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: September 26, 2024