Lie Groups, Lie Algebras, and Representations - Fall 2015.
Summer orientation minicourse - p-Adic 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 - p-Adic 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 - p-Adic Analysis - Summer 2012.
Math 233 - Calculus III (sections 1 and 2) - Fall 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 - p-Adic 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 Reaction-Diffusion Systems) Fall 2003.
Math 308 - Mathematics for the Physical Sciences Spring 2003.
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 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.