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. Mostly I work on diffusion processes and heat kernels on metric measure spaces with fractal-like features. I also study related equations of interest in mathematical physics.
- Ruiz, P. A., & Baudoin, F. (2021). Gagliardo-Nirenberg, Trudinger-Moser and Morrey inequalities on Dirichlet spaces. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 497(2), 124899-124899.
- Ruiz, P. A. (2021). Heat kernel analysis on diamond fractals. Stochastic Processes and their Applications. 131, 51-72.
- Ruiz, P. A., Baudoin, F., Chen, L. i., Rogers, L. G., Shanmugalingam, N., & Teplyaev, A. (2020). Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities. Journal of Functional Analysis. 278(11), 108459-108459.
- Alonso-Ruiz, P., Baudoin, F., Chen, L. i., Rogers, L., Shanmugalingam, N., & Teplyaev, A. (2020). Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates. Calculus of Variations and Partial Differential Equations. 59(3), 103.
- Alonso Ruiz, P., Chen, Y., Gu, H., S. Strichartz, R., & Zhou, Z. (2020). Analysis on hybrid fractals. Communications on Pure & Applied Analysis. 19(1), 47-84.
- NSF - DMS 855349 awarded by National Science Foundation - (Arlington, Virginia, United States) 2019 - 2021
- Feodor Lynen Fellowship awarded by Alexander von Humboldt Foundation - (Bonn, Germany) 2016 - 2018