معرفی
Patricia Alonso Ruiz is an Associate Professor in the Department of Mathematics at Texas A&M University (on leave AY24/25). She specializes in analyzing random phenomena in fractal-like environments, focusing on connections between analysis, probability, and geometry. Her research involves Dirichlet forms, heat kernels, and stochastic processes on fractals such as the Sierpinski gasket and diamond fractals.
Her academic journey includes leadership in the TAMU Fractals Research Team, supported by an NSF grant. She has organized conferences like the BIRS Workshop on New Trends in Stochastic Analysis and the Cornell Conference on Analysis, Probability, and Mathematical Physics on Fractals. Her outreach efforts include the Kenya Workshop and educational programs like the Summer Educational Enrichment in Math.
Key research areas include spectral theory of fractals, BV functions on metric measure spaces, and functional inequalities in fractal settings. Collaborations with researchers like Fabrice Baudoin and Alexander Teplyaev have yielded impactful work on heat kernel analysis and Besov spaces. She mentors undergraduate teams exploring spectral features of fractals, fostering the next generation of mathematicians.
Publications span topics from nonlocal energies to Orlicz-Sobolev embeddings, reflecting her interdisciplinary approach bridging pure and applied mathematics. Her work highlights the interplay between fractal geometry and stochastic analysis, advancing understanding of complex systems in porous and non-smooth environments.
