My main current interest has to do with sequence comparison. These problems involve a lot of deep mathematics and have connections to various subfields such as algebraic combinatorics and random matrices. Among my ultimate goals is the development of quantitative and statistical techniques in sequence comparison to analyze various problems arising in computational genetics and computational linguistics.
Over the years, I have been interested in isoperimetric and functional inequalities to obtain probabilistic "large deviations" estimates for functions of multivariate vectors. This work was done in various frameworks, from metric spaces to graphs and Markov chains, leading to spectral gap and log-Sobolev estimates useful in Combinatorics, Statistical Physics and Theoretical Computer Science. More recently, my interests have been towards obtaining such results for the important class of infinitely divisible random vectors.
I am also interested in nonstationary stochastic processes (representation, prediction, filtering, wavelet transform,...) and some aspects of Lévy processes.
My research in Mathematical Finance has mainly to do with understanding how classical Brownian models can be extended to more realistic situations containing jumps.
My statistical interests are mainly in non-parametric estimation. Past projects involved the use of wavelet methods in Statistics while a more recent one deals with the estimation of Lévy measures motivated by Mathematical Finance. In that context, my work on concentration inequalities for infinitely divisible laws appear to be quite useful.
I have also interacted with various individuals on applied research projects, where stochastics tools were needed, in Aerospace Engineering, Biology, Chemistry and Electrical Engineering all of it at Georgia Tech.
Finally, I was on the editorial board of