research email: paruiz(at)math.tamu.edu
teaching email: paruiz(at)tamu.edu
I am a tenure-track Assistant Professor in the Department of Mathematics at Texas A&M. My research revolves around Analysis and Probability; in particular I am interested in the interconnections between probabilistic, analytic and geometric aspects of stochastic processes on spaces with a rough structure. Most of the problems I work on are related to diffusion processes and heat kernels on metric measure spaces with fractal-like features.
Fractals can often be viewed as limits of finite graphs and this sometimes allows us to make explicit computations and create computer simulations. These help to visualize and provide an insight into more abstract results. These tasks are of significant relevance to more theoretic problems and their difficulty ranges from undergraduate to graduate levels. If you are interested in learning more about this area of research, feel free to browse through my work, the Undergraduate Fractals Research Team, or contact me :)