Mathematics Department
Phanuel Mariano, associate professor of Mathematics

Phanuel Mariano

Job Title
Assistant Professor of Mathematics
Bailey Hall 108A

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 the setting of curved spaces with degeneracies. The operators I study are hypoelliptic and their natural setting are spaces called sub-Riemannian manifolds. A probabilistic tool used in my research involves the coupling of diffusion processes. Coupling is a way of constructing Markov processes with prescribed laws on the same space. 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.

Academic credentials

B.A., Western Connecticut State University; M.S., University of Connecticut; Ph.D., University of Connecticut