The 2019 IMA Prize in Mathematics and its Applications has been awarded to Jacob Bedrossian. Bedrossian is a professor of mathematics and a member of the Center for Scientific Computation and Mathematical Modeling at the University of Maryland, College Park. Established in 2014, the IMA Prize is awarded annually to a mathematical scientist who received his/her Ph.D. degree within 10 years of the nomination year. The award recognizes an individual who has made a transformative impact on the mathematical sciences and their applications. Bedrossian’s important contributions to the study of partial differential equations of fluid dynamics and in particular to the area of hydrodynamic stability, formed the basis for this year’s recognition.
Bedrossian’s research focuses on stability and coherent structures in fluid mechanics and plasma physics. "Stability" refers to understanding which configurations of a fluid might be robust to small disturbances and which configurations will break down easily. A simple analogy for this would be to compare the stability of a pencil lying on the table versus the instability of a pencil balanced on its point. On the other hand, “coherent structures” arise in fluids, like air and water, which tend to organize themselves into vortex structures. One can think of tornadoes or hurricanes, both of which approximately keep their form despite disturbances, and these structures even move around in a coherent manner. The subtle behaviors of fluid mechanics are important to the dynamics of many systems and have been studied since the late 1800s. Researchers want to understand what should really happen and why certain configurations are preferred over others, especially in a precise, quantitative sense. Bedrossian’s accomplishments include remarkable results on the stability of shear flows. Inspired by the Fields Medal work of Clement Mouhot and Cedric Villani on Landau damping of plasmas, the work of Bedrossian and his collaborators required developing wholly new analytical methods for the more complicated fluid setting.
Bedrossian’s interest in differential equations started as a freshman at Case Western Reserve University. “Professor Steve Izen, was energetic and inspiring. I was always interested in physics, and this course showed me that mathematics plays a leading role in a lot of our understanding of the physical world, especially when it comes to understanding how simple physical systems can have behavior so beautiful, subtle, and startlingly complex that it defies all description. I changed my major to mathematics not long after." His interest in studying fluid mechanics started in graduate school, during his work with his advisors Joseph Teran and Andrea Bertozzi. “Each had done exciting work on applied fluid mechanics from various different angles and I was sort of hooked from there.”
In addition to his advisors, Bedrossian learned a great deal from UCLA faculty, Inwon Kim and Monica Visan. “In my postdoc, I was greatly influenced by Nader Masmoudi and Vladimir Sverak. Of course there are many mathematicians whose works impacted me even before I met them in person, for example, Andrew Majda and Cedric Villani.”
Currently, Bedrossian’s major focus is on laying down mathematically rigorous foundations for the theories of turbulence in the physics literature. Turbulence refers to the chaotic creation of small features in a fluid, for example, the complexity and unpredictability in a cloud of smoke rising from a smokestack. The physical theories make predictions which seem correct, or at least not far off when compared to experiments. However, it is currently not understood how to deduce these 'laws' directly from the mathematical equations without adding in additional empirical assumptions, assumptions that one has no idea how to prove mathematically from the equations, but which seem to be approximately true in experiments. “It is of paramount theoretical interest to find some way to deduce these laws mathematically from the equations, offer more concrete understanding and maybe better quantitative predictions, because these ‘laws’ are quite fundamental to our practical understanding and modeling of problems that arise in countless engineering and geophysical applications, such as the design of land, air, and sea vehicles, climate and weather prediction, and the development of controlled fusion devices.” Recently, together with Alex Blumenthal and Sam Punshon-Smith, Bedrossian verified one of the simplest of such laws in a certain range of physical settings. The effort required to verify this simplified law was substantial, involving four separate papers that draw ideas from several fields of mathematics. Bedrossian says that this is only the beginning of what he hopes will be a much larger endeavor."
The prize consists of a certificate and a cash award of $3000. Funding for the IMA Prize in Mathematics and its Applications is made possible by generous donations of friends of the IMA.