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Math Graduate Students Place Top 10 in International Student Paper Competition

Math Graduate Students Place Top 10 in International Student Paper Competition
From left to right: Ioakeim Ampatzoglou, Nataša Pavlović, Matthew Rosenzweig

At a conference of the American Institute of Mathematical Sciences (AIMS) in Taipei, Taiwan in July, Matthew Rosenzweig was awarded second place and Ioakeim Ampatzoglou received an honorable mention in the Student Paper Competition, which named ten finalists. Both are graduate students of UT Austin mathematics professor Nataša Pavlović.

The AIMS Conference on Dynamical Systems, Differential Equations and Applications is a biennial series for mathematicians and scientists working in the fields of analysis and applied analysis. Physicists use many equations from the field of analysis to model the behavior of particles from atoms to stars, so they need those equations to be both mathematically sound and capture the behavior of real systems.

"What my research area is focused on is the application of rigorous analysis tools to explain and model physical phenomena," Ampatzoglou said. "This is a very long process in general in the history of math, and there is still plenty of work to be done; that's why I'm here."

Matthew Rosenzweig researches mathematical equations that describe physical phenomena like water waves. His second-place paper was on the Davey-Stewartson equation, an important tool in fluid dynamics.

Ampatzoglou is working with kinetic equations, which are used in physics to statistically describe the behavior of many-particle systems, including in hydrodynamics and semiconductors. In physics, gases are sometimes treated in a simplified way, ignoring the ways that molecules take up space and attract or repel each other. These are called ideal gases. In the paper he submitted to the competition, he mathematically derived an equation that could be applied to non-ideal gases. In the future, he hopes to combine it with the existing Boltzmann equation, which describes the flow of dilute ideal gases.

"We already have kinetic equations to study the structure of very dilute gases," Ampatzoglou said. "So what we are doing, and what was presented in the paper, is to derive a new equation, which doesn't exist in the literature so far, to describe denser gases. So the main motivation behind that is to actually solve a new problem, and to derive a new equation which hopefully will have applications in the future."

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Friday, 27 January 2023

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