Phanuel Mariano

Research interests

My research lies at the intersection of probability, geometry and analysis. In particular, I am interested in using probabilistic tools to solve problems in analysis in a geometric setting. One example of a probabilistic tool used in my research involves the coupling of stochastic processes. I have also been interested in applying probabilistic techniques in proving inequalities for the expected lifetime of diffusion processes and the first Dirichlet eigenvalue of a domain. One can think of the first Dirichlet eigenvalue as the fundamental frequency of a drum. These inequalities often show the beautiful connection between probability, analysis and physics.