Math 226C: Symplectic
Location: MS 6201
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
(for MS 7901)
- Basic notions, Darboux's theorem, local normal
- Some constructions
- J-holomorphic curves
- Applications, e.g., symplectic capacities
- Floer homology and Fukaya categories
- Math 225A, B, C or equivalent (a
good knowledge of differentiable manifolds and
homology). Math 226A and B are
not prerequisites for Math 226C.
- Based on attendance. If you want
an A+, submit your stack of HW at the end of the
- D. McDuff and D. Salamon, Introduction to
symplectic topology, 2nd edition, Oxford
Mathematical Monographs. The Clarendon Press, Oxford
University Press, New York, 1998.
- 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.
- A. Cannas da Silva, Lectures
on symplectic geometry, Lecture Notes in
Mathematics 1764, Springer-Verlag, 2008.
- 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
Last modified: October 10, 2017