Topics in Geometry and Dynamics
Math 275 - Tu Th 10-11:30 - Science Center room 216
Harvard University - Spring 2015
Instructor:
Curtis T McMullen
Description:
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
Course Notes
- C. McMullen, Notes on Teichmüller Theory and Complex Dynamics
- C. McMullen, Notes on Ergodic Theory
Suggested Texts
- 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, Springer-Verlag, 1992.
- 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.
Prerequisites.
Intended for advanced graduate students.
Undergraduate enrollment requires permission of the instructor.
Grades.
Enrolled students should attend the course regularly.
Assignments will be provided for students requiring a letter grade.
Calendar 2015.
- 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