Analysis and potential theory on manifolds. Heat diffusion equation and heat kernel. Dirichlet forms and potentials theory on Lie groups and locally compact groups.
Gaussian convolution semigroups.
Finite Markov chains. Quantitative analysis of ergodic Markov chains. To appear On the stability of the behavior of random walks on groups, Journal of Geometric Analysis, with C. Pittet. Proceeding of an 1998 Edinburgh ICM conference, J-P. Anker, Ed, with A. Bendikov. On and off heat kernel behaviors on certain infinite dimesnional Dirichlet spaces, American Journal of Mathematics, with A. Bendikov.