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. 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.