Renato's teaching and research page

Renato Feres
Department of Mathematics
Campus Box 1146, Cupples I, Room 17
Washington University
Saint Louis
Missouri, 63130 USA.
+1 (314) 935 - 6752 (office phone)


Current courses

Past courses


My main research interests lie in differential/Riemannian geometry, ergodic theory for Lie groups and their discrete subgroups, foliation theory and probability theory. For a copy of my recent preprints in pdf format, go to the list of publications . For more info see my CV.

Here are some of my expository works. For a comprehensive survey of ergodic theory for general Lie groups and their discrete subgroups, see chapter 9 of Handbook of Dynamical Systems, volume 1A (Eds.: B. Hasselblatt, A. Katok. Elsevier, 2002), written by A. Katok and myself. See also this volume edited by P. Foulon. The differentiable dynamics of semisimple Lie groups and lattices is the subject of Dynamical Systems and Semisimple Groups (Cambridge University Press, 1998). A more gentle introduction to the main result of this book is contained in my contribution to the proceedings volume (Eds.: M. Burger, A. Iozzi. Springer, 2002) of a program on Ergodic Theory, Geometric Rigidity and Number Theory, that took place at the Newton Institute for the Mathematical Sciences, in Cambridge, UK, 2000.

Some of the topics of my current interest are random dynamical systems, foundations of statistical mechanics, and harmonic functions and group actions. Here are a few lectures on these subjects: Harmonic functions over group actions , catalysis. A lecture given to incoming freshmen at Wash. U. interested in science and math: Billiards and statistical physics. An undergraduate mathclub lecture on concentration of measures: Geometry in (very) high dimensions. A presentation given at a BIRS meeting in Banff in 2014: Statistical mechanics of random billiard systems. A short talk in the May 2015 conference in honor of the memory of Professor Nikolai Chernov: Dynamics and differential geometry of non-standard billiard models. A presentation at AIM in June 2015: From billiards to thermodynamics. A presentation at University of Ghent, MaCKiE in July 2015: Explicit formulas for reaction probability in reaction-diffusion experiments.