Topics in Geometry and Dynamics
Math 275 - Tu Th 10-11:30 - Science Center room 216
Harvard University - Spring 2015
Curtis T McMullen
A survey of fundamental results and current research.
Topics may include:
- Dynamics on the circle and the torus
- Lie groups and ergodic theory
- Hyperbolic surfaces and SL2(R)
- Lattices and Mahler's compactness criterion
- Amenability and expanding graphs
- Kazhdan's property T and SL3(R)
- Hyperbolic 3-manifolds and Mostow rigidity
- Ratner's theorem
- Conjectures of Oppenheim and Littlewood
- Geodesic currents and Teichmueller theory
- Entropy and complex dynamics
- Random walks and non-commutative ergodic theory
- Martingales and Furstenberg's theorem
- Pseudo-Anosov maps, IETs and billiards
- Dynamics over moduli space
Intended for advanced graduate students.
Undergraduate enrollment requires permission of the instructor.
- M. B. Bekka and M. Mayer,
Ergodic theory and topological dynamics of group actions on homogeneous spaces,
Cambridge University Press, 2000.
- Bekka, de la Harpe and Valette,
Kazhdan's Property (T), 2007.
- Benedetti and Petronio,
Lectures on Hyperbolic Geometry,
E. Ghys, Dynamique des flots unipotents sur les espaces homogènes,
Sem. Bourbaki 1991/92; Asterisque 206.
- M. Gromov,
Volume and bounded cohomology
- R. Mañé,
Ergodic Theory and Differentiable Dynamics
- D. Witte Morris,
Ratner's Theorems on Unipotent Flows,
Chicago Lectures in Math. Series, 2005.
- J. Ratcliffe,
Foundations of Hyperbolic Manifolds,
2nd Edition. Springer, 2006.
- W. P. Thurston,
Three-dimensional Geometry and Topology,
Princeton University Press, 1997.
Enrolled students should attend the course regularly.
Assignments will be provided for students requiring a letter grade.
- Tu, 27 Jan. First class (actually Th due to snow)
- M-F, 16-20 Mar. Spring break
- Tu, 28 Apr. Last class
- Th-W, 30 Apr.-6 May. Reading period