Topics in Geometry and Dynamics
Math 275  Tu Th 1011:30  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 SL_{2}(R)
 Lattices and Mahler's compactness criterion
 Amenability and expanding graphs
 Kazhdan's property T and SL_{3}(R)
 Hyperbolic 3manifolds and Mostow rigidity
 Ratner's theorem
 Conjectures of Oppenheim and Littlewood
 Geodesic currents and Teichmueller theory
 Entropy and complex dynamics
 Random walks and noncommutative ergodic theory
 Martingales and Furstenberg's theorem
 PseudoAnosov maps, IETs and billiards
 Dynamics over moduli space
Course Notes
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,
SpringerVerlag, 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,
Threedimensional 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)
 MF, 1620 Mar. Spring break
 Tu, 28 Apr. Last class
 ThW, 30 Apr.6 May. Reading period
