Dr. Alonso Ruiz is highly deserving of this award. She has developed a strong and innovative research program while successfully mentoring undergraduates in research, and she has further plans to make her research accessible to a wide range of students and teachers to ensure even greater impact.
Dr. Patricia Alonso Ruiz, an assistant professor in the Department of Mathematics at Texas A&M University, has been selected to receive a National Science Foundation Faculty Early Career Development (CAREER) Award, a prestigious honor intended to help kick-start the careers of rising faculty with the potential to become academic leaders in both research and education.
Alonso Ruiz’s proposal, “Heat Semigroups and Strichartz Estimates on Fractals,” has been funded through the Division of Mathematical Sciences and begins in September 2022 and continues through August 2027. Her project aims to study the Schrödinger equation in fractal settings to determine the answers to questions such as how electrons move within highly porous media.
In the process of developing the mathematical tools necessary to study the Schrödinger equation in fractal settings, Alonso Ruiz hopes to contribute new knowledge to the fields of analysis and probability using fractals that can be applied in other novel areas, such as the mathematical modeling of quantum particles traveling in a percolating system. She will develop new techniques at the crossroads of probability, potential theory, functional analysis and partial differential equations to construct suitable heat-semigroup based function spaces, to prove novel estimates for products of eigenfunctions, and to derive non-trivial dispersive (Strichartz) estimates of solutions to the linear Schrödinger equation on fractals. Her project will also analyze the effects of random initial data on the existence and regularity of solutions and explore possible notions of quantum probability and quantum dynamics on fractals.
To help integrate her research with educational efforts at both K-12 and university levels, Alonso Ruiz intends to create a new sustainable seminar course involving graduate students, undergraduate students, and pre-service and in-service teachers. They will develop innovative teaching materials using fractals as visually appealing models in the subjects of probability and analysis.
“Fractals are more than nice pictures with repeating patterns,” Alonso Ruiz said. “They serve as mathematical models for highly porous media, such as sponges and filters, or intricately branching structures like vessels and large networks.”
Alonso Ruiz joined the Texas A&M Mathematics faculty in 2019 after serving the previous three years as Evarist Giné Assistant Research Professor at the University of Connecticut. She earned her Ph.D. in mathematics at the University of Siegen in 2013 and spent three years as a scientific employee at Ulm University prior to joining the faculty at Connecticut. Her research focuses on random phenomena that happen in environments with fractal-like features. She is particularly interested in how the time evolution of these processes is connected to the geometry of the specific environments in which they take place. By investigating how probabilistic techniques and functional inequalities can be applied and extended in such environments, she hopes to gain a better understanding of the connections between the analytic, geometric and probabilistic aspects of stochastic processes — defined in probability theory as those involving randomness — in highly porous and non-smooth settings.
Alonso Ruiz is a member of the American Mathematical Society, the National Association of Mathematics, the Association of Women in Mathematics, the Women in Probability Group and the Association Fachgruppe Stochastik (DMV). At Texas A&M, she is active in department, college and university-level research, outreach and service programs, including the annual Mathematics and Statistics Fair and the Take A Scientist To Eat (TASTE) pilot program in fall 2021. In fall 2020, she founded the Texas A&M Fractal Research Team, an effort that is partially supported by another of her NSF grants.
“Dr. Alonso Ruiz is highly deserving of this award,” said Dr. Sarah J. Witherspoon, professor and head of Texas A&M Mathematics. “She has developed a strong and innovative research program while successfully mentoring undergraduates in research, and she has further plans to make her research accessible to a wide range of students and teachers to ensure even greater impact.”
Each year, the NSF presents an estimated 500 CAREER awards totaling around $250 million to early career faculty at U.S. institutions of higher learning, museums, observatories, research laboratories, professional societies, and similar organizations associated with research or educational activities.
Learn more about the NSF CAREER program or Alonso Ruiz and her research.
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