Punshon-Smith, Sam

Dr. Punshon-Smith received his Ph.D in Mathematics from University of Maryland in 2017. In 2018 he joined the Division of Applied Mathematics at Brown University for 3 years as an NSF Postdoctoral Fellow. In 2021 he joined the Institute for Advanced Study as a Member for the special year on "h-Principle and Flexibility in Geometry and PDEs". He joined Tulane in the Fall 2022 as a tenure track Assistant Professor in the Mathematics department.

Dr. Punshon-Smith's research lies in the intersection of dynamical systems, partial differential equations and stochastic analysis, with particular interest in problems from fluid mechanics, plasma physics and nonlinear waves related to turbulence. His research on universal laws in scalar turbulence (known as Batchelor's law) has been featured prominently in various mathematical news sites, most notably Quanta magazine ("Mathematicians Prove Universal Law of Turbulence") and SIAM news ("Uniform in Diffusivity Chaotic Mixing and the Batchelor Spectrum"). His current research involves both mathematical and computational elements, using both computational fluid mechanics and computational algebraic geometry to assist in rigorous mathematical proofs of theorems in fluid mechanics. Additionally, he is interested in the mathematical mechanisms behind the tendency for two-dimensional fluids to form large stable vortices (like hurricanes) from small scale fluctuations, a poorly understood phenomenon known as the "inverse cascade". In May 2022 he was awarded a 3 year NSF grant from the Division of Mathematical sciences titled "Instability, Chaos, and Mixing in Stochastic Fluid Mechanics and Related Models".