


Extended Graduate Orientation  Summer 2017.
Introduction to Lebesgue Integration  Spring 2017.
Stochastic Processes  Spring 2017.
Summer orientation minicourse  Contemporary Probability  Summer 2016.
Stochastic processes  Spring 2016.
Selfadjoint operators in Hilbert spaces  Spring 2016.
Lie Groups, Lie Algebras, and Representations  Fall 2015.
Summer orientation minicourse  pAdic Anaylsis  Summer 2015.
Math 407  An Introduction to Differential Geometry  Spring 2015.
Math 495  Stochastic Processes  Spring 2015.
Math 553  Stochastic Dynamical Systems  Fall 2014.
Math 523  Quantum Mechanics for Mathematics Students  Spring 2014.
Math 493  Probability  Fall 2013.
Summer orientation minicourse  pAdic Anaylsis  Summer 2013.
Math 3200  Statistics and Data Analysis  Spring 2013.
Math 547  Symplectic Geometry and Mechanics  Spring 2013.
Math 350  Introduction to Monte Carlo Methods  Fall 2012.
Math 449  Numerical Applied Mathematics  Fall 2012.
Graduate Orientation Course  pAdic Analysis  Summer 2012.
Math 233  Calculus III (sections 1 and 2)  Fall 2011.
Graduate Orientation Course  An invitation to modern dynamics  Summer 2011.
Math 5043  Algebraic topology  Spring 2011.
Math 5041  Geometry I  Fall 2010.
Math 543  Geometry of Physics  Fall 2010.
Math 350  Simulation analysis of random processes  Spring 2010.
Math 553  Brownian motion on Riemannian manifolds  Spring 2010.
Graduate Orientation Course  pAdic Analysis  Summer 2009.
Math 5052  Measure Theory and Functional Analysis II  Spring 2009.
Math 5051  Measure Theory and Functional Analysis I  Fall 2008.
Math 545  Topics in Riemannian Geometry  Geometry of Physics Fall 2008.
Math 132  Calculus II  Sections 1, 2  Spring 2008.
Math 450  Topics in Applied Mathematics  Computational random processes Spring 2007.
Math 523  Introduction to Ergodic Theory Fall 2006.
Math 449  Numerical Applied Mathematics Fall 2006.
Math 5032  Algebra II Spring 2006.
Math 5031  Algebra I Fall 2005.
Math 535  Topics in Combinatorics (Spectral Graph Theory) Fall 2005.
Math 309  Matrix Algebra Spring 2005.
Math 495  Stochastic Processes Spring 2005.
Math 545  Topics in Riemannian Geometry (Discrete Subgroups of Lie Groups) Fall 2004.
Math 308  Mathematics for the Physical Sciences Spring 2004.
Math 485  Groups, Representations, and Physics Spring 2004.
Math 350  Topics in Applied Math. (Mathematics of ReactionDiffusion Systems) Fall 2003.
Math 308  Mathematics for the Physical Sciences Spring 2003.
Math 418  Introduction to Topology and Modern Analysis Spring 2003.
Math 417  Introduction to Topology and Modern Analysis Fall 2002.
Math 441  Geometry I Fall 2002.
Math 100  Foundations for Calculus Spring 2002.
Math 545  Geometry and Probability (Stochastic calculus on Riemannian manifolds.) Fall 2001.
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 nonstandard 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 reactiondiffusion experiments.