Ph.D. (1977) University of Chicago
My area of interest is dynamical systems. I have done work on polygonal billiards and dynamics of flows on Teichmüller space; analysis of algorithms; and diffeomorphisms of surfaces. I am currently working on complex dynamics in two dimensions.
Ergodicity of billiard flows and quadratic differentials (with S. Kerckhoff and H. Masur), Annals of Mathematics 124 (1986), 293–311.
Polynomial diffeomorphisms of C2 VI: connectivity of J (with E. Bedford), Annals of Mathematics, 148 (1998), 695–735.
Polynomial diffeomorphisms of C2 VII: hyperbolicity and external rays (with E. Bedford), Ann. Scient. Ec. Norm. Sup. 4 (32) (1999), 455–497.
The dynamics of billiard flows in rational polygons; in Encyclopedia of Mathematical Sciences, vol. 100 (edited by Yu. Sinai), Springer-Verlag, 1999.
Billiards on rational-angled triangles (with R. Kenyon), Comment. Math. Helv. 75 (2000), 65–108.
Dynamics in Two Complex Dimensions; in Proceedings of the International Congress of Mathematicians, Beijing 2002, Vol. III: Invited Lectures, Higher Education Press, Beijing 2002, pp. 373–382.
Real polynomial diffeomorphisms with maximal entropy: tangencies (with E. Bedford), Annals of Mathematics 160 (2004), 1–26.