Mathematics as Life: Irene Gamba and the Kinetic Lens

Dr. Irene M. Gamba, director of the ICES Applied Math Group, is a world leader in kinetic theory, the mathematics that describes how particles of matter interact under different conditions.

Irene M. Gamba, director of the ICES Applied Math Group, is a world leader in kinetic theory, the mathematics that describes how particles of matter interact under different conditions.

At the heart of her research is the analysis and numerical methods for the Boltzmann equation—a mathematical model for statistically predicting the behavior of particles en masse, and how that behavior influences a variety of properties— such as concentrations, bulk velocities, temperature, and pressures or stresses. Historically, kinetic models were viewed as the probabilistic evolution of random motion of interacting particles, such as molecules in a gas or fluid, and used to examine observable properties of interest such as viscosity or heat, with values expressed in terms of probabilistic expectations. But Gamba takes a broad view of what that interaction can be—from the more traditional molecular dynamics, to the up-and-coming approaches of modeling more sociological behavior, like people moving through a crowd or wealth transfer.

“Kinetic theory and statistical transport falls somewhere between quantum mechanics, or large dynamical systems, and continuum mechanics, as in classical advection diffusion in fluid models ” Gamba said. “Some of the most successful examples are in aerodynamics at dilute gas regimes or electron transport in semiconductor devices…there is also deep applications of mathematics to finance, biology, and social dynamics—from fish to insects to people.”

Gamba is currently a principal investigator of a National Science Foundation grant dedicated to spreading awareness of kinetic theory to researchers outside of the mathematical community, such as those in the natural and social sciences. The initiative is part of a large effort to build up the KI-NET research network, a research group centered around three kinetics research hubs: ICES, the Center for Scientific Computation & Math Modeling in the University of Maryland, and the Department of Mathematics at the University of Wisconsin-Madison.

Gamba is a good ambassador for the field. She has spent nearly the last 30 years advancing the study of kinetic theory, and has been elected a fellow of the American Mathematical Society as well as the Society for Industrial and Applied Mathematics. She serves on the editorial boards of several applied mathematics journals. In addition to her expertise in kinetics, Gamba is adept at seeing connections between her own field of study and others, said Nataša Pavlović, a professor in the UT Department of Mathematics specializing in partial differential equations arising from quantum systems. It’s a skill that helped foster research collaborations between her and Gamba, Pavlović said, as well as diversify the type of research happening at the UT mathematics department.

“The group that we have here is very broad, spanning many research directions in modern analysis and applied mathematics. We attract great graduate students, postdocs and faculty, and Irene and Luis [Caffarelli] are responsible in a lot of ways for that,” Pavlović said. “I enjoy talking mathematics with Irene, and I appreciate the fact that it’s not bounded by subarea. There are no boundaries of what we can dream and what we can try.”

Gamba’s own introduction to kinetics was much less intentional than the connections she is fostering now. She said learning kinetic theory was a necessity. As a Ph.D. student at the University of Chicago in the late 1980s, she started out studying the mathematics and numerical and computational methods modeling the properties of semiconductors used in transistors. But as transistors got smaller, the models she was originally using to investigate such properties were no longer applicable. She had to start thinking about the behavior of electrons flowing through the transistor to accurately capture the mathematics governing the properties of semiconductors by then at submicron length scales.

“I worried a lot at first,” Gamba said. “Modeling now had to be done on the statistical mechanics level. And it was a completely new perspective.”

Gamba honed her acumen in kinetic theory during a postdoctoral position at Purdue University and shortly after at New York University’s Courant Institute for Mathematical Sciences under the sponsorship of an NSF postdoctoral Fellowship. Her advisor at NYU was Cathleen Morawetz, the first woman to ever be elected to the Applied Mathematics section of the National Academy of Sciences. Gamba continued to study mathematics related to semiconductors, while also collaborating the Morawetz on her research on the mathematics describing transonic airflow on aircraft wings and stationary plasma potential flow approximations.

By the time Gamba was a few years into her own academic career as an assistant and then associate professor at New York University’s Courant Institute for Mathematical Sciences, she said she was “entranced” by the mathematics governing kinetic theory and statistical flows. When she joined UT in 1997 as a full professor, her experience using kinetic theory to investigate the mathematical and computational underpinnings of physical phenomena lined up with the mission of the Texas Institute for Computational and Applied Mathematics, or TICAM, the precursor to ICES, founded in 1993.

Gamba said that applied mathematics programs were just being established at the university when she was hired. Within ten years of her joining UT, the university’s applied mathematics program would be ranked among the top ten programs in the U.S.—an achievement that Gamba credits in large part to ICES Director Tinsley Oden.

“The vision of Dr. Oden paved the way and allowed everyone to get into a single unit to search, and improve, and move forward applied mathematics and prediction by computational modeling across engineering and sciences,” Gamba said.

Gamba said she considers applied mathematics a language of its own, and readily draws on mathematical concepts to describe the world. For example: she cautions against making haphazard decisions. Random choices, like randomly moving particles without an overarching direction, don’t lead to progress.

However, her view of mathematics was much narrower when growing up in Argentina. She enjoyed math (“I really liked it! I could do it fast and well,” Gamba said) but she thought that the only way to have a mathematics career was as a teacher. While enrolled in a teacher certification program after graduating high school, she was mentored by instructors who exposed her to mathematics as an area of active study. It was the moment that laid the groundwork for the rest of her career.

“In less than a year, I knew there was math beyond what I learned in high school,” Gamba said. “It was discovering a whole new world.”

From Morawetz to ICES’ Mary Wheeler, Gamba said that a host of female role models in mathematics inspired her as she developed her mathematics career. Gamba said her very first supporter was her mother.

“She was a teacher and a champion of having women valued for what they do—not what people were expecting them to do,” Gamba said.

While Gamba recognizes the importance of having women in mathematics, she points out that her most meaningful mathematics discussions transcend any sense of gender.

“Math and science are orthogonal to gender, to race, to religion,” Gamba said. “When talking with scientists, it’s only the math and its scientific contents that comes up.”

The KI-NET fall conference, held in September at ICES, exemplified that point. The meeting was dedicated to sharing the latest research on kinetic theory, with invited speakers coming from across the world. This year, the meeting honored Gamba’s contributions to mathematics, with the conference website describing the event as a scientific forum as well as a “celebration of Irene M. Gamba’s impact in modeling, analysis and numerical simulations of kinetic equations.”

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Posted: Oct. 30, 2017