My main research interests lie in the following two areas of probability theory:

* Random processes in random media, in particular,random systems, the behaviour of which cannot be described using an averaging principle. Such systems occur in some simple and important situations and a prime example isthe intermittency effect, appearing in the parabolic Anderson problem.

* Diffusions on Riemannian manifolds.What happens if a Brownian or quantum particle in Euclidean space is forced to stay close to a manifold embedded in the space? Will it move as a free particle on the manifold or will its behaviour be influenced by the surrounding space?