I am working in Asymptotic Theory of finite dimensional normed
spaces and related topics in Convex Geometry and Probability.
Passing to the language of Convex Geometry, my research is devoted
to the study of asymptotic behavior of convex (and quasi-convex)
bodies in high dimensional spaces as well as random aspects of
that behavior. More precisely, we investigate various
parameters connected to convex bodies, their sections and projections,
assuming that the dimension is large enough (grows to infinity).
Probabilistic technique and tools play crucial role in Asymptotic Theory.
Part of my research is closely related to
the study of the smallest non-trivial eigenvalue of a random matrix,
i.e. the study of the norm of the inverse (from the image)
operator, corresponding to a random matrix. I am also interested
in describing the behavior of order statistics of a sequence
of random variables in terms of the sequence of their first moments.
Both these directions have many applications in different
areas of Pure and Applied Mathematics.