Typical Courses Taught by Robert Bryant
 MATH 123S, GEOMETRY

 MATH 267, DIFFERENTIAL GEOMETRY

 MATH 268, Topics in DIFFERENTIAL GEOMETRY: Symplectic Geometry

 The first third of the course is devoted to
'classical' symplectic geometry: Lagrangians,
Legendre transformations, Hamiltonians, symplectic
manifolds and the DarbouxWeinstein theorem,
symmetries and conservation laws and the Arnold
Liouville theorem, momentum mappings,
reduction, and convexity.
The second third of the course is devoted to
developing elliptic methods: pseudoholomorphic
curves, Gromov compactness and moduli,
applications to packing and (non)squeezing
theorems, etc.
The final third covers related topics and recent
developments, such as relations with toric
varieties, representation theory, or other topics
that depend on the interests of the class.