Equal sized hyperbolic fish from M. C. Escher
Math 537B Spring 2006
Room/Time: Tuesday, Thursday 12:30-1:45 in Math East 246
Instructor: David Glickenstein
Office: Mathematics 213
Office Phone: 621-2463
Presentations on May 4
Presentations will be given May 4 (Dead Day) in Math 320 1pm to 5pm (if it takes that long).
We will begin by finishing Lee's book, Chapters 7-11. After that, we will
explore one or more of the following topics: Geometrization of
three-manifolds, Laplacian comparison, Bishop comparison theorem, the
sphere theorem, Gromov's compactness theorem, Cheeger's finiteness theorem.
The books we are currently using are:
Other books of note:
These lecture notes are not particularly well edited and not for general
distribution, which is why the files are password protected.
Possible project topics
The following are possible project topics. Please talk with me about the
scope of the work. You are also welcome to suggest other topics.
- Simplectic geometry
- Spherical and hyperbolic trigonometry
- Hodge theorem
- Finsler geometry
- Nonlinear averaging and center of mass
- Moduli space of flat metrics
- Frobenius theorem
- Bochner technique
- Riemannian submersions
- Chern-Gauss-Bonnet theorem
- Morse Index Theorem