My primary research interests are the following ones:

1. Probability: My research investigates the intersection of Markov chains and graph theory, with a particular emphasis on random walks on graphs. I analyze essential aspects of these random walks, including mixing times, hitting times, eigenvalues, and cutoff phenomena. These techniques are employed to gain insights into the behavior of random walks and to study various models actively explored in computer science.

2. Dimensionality Reduction: Part of my research studies is based on Johnson-Lindenstrauss Lemma and its extensions, including terminal embeddings, which offer improved stability properties over classical methods. I am also interested in analyzing the efficiency of algorithms for constructing embeddings and exploring fast-structured matrices.

3. Lipschitz Functions and Lipschitz-Free Spaces: Finally, I investigate Lipschitz functions, particularly those that attain their Lipschitz constant, and their relation to Lipschitz-free spaces. These spaces, which act as natural preduals to the space of Lipschitz maps, are crucial for non-linear analysis and have applications in computer science and optimal transportation.

For more information on my work and publications, please explore the sections on Research Publications.