People

My area of research is Analysis. I work mainly in two classical areas: Approximation theory and Scattering theory. Recently, I have been also working on some projects related to two-dimensional fluid motion. The Approximation theory is a classical area in Analysis with links to almost any other branch of Mathematics. I am mostly interested in the behavior of polynomials orthogonal on the unit…

I am interested in nonlinear PDE and free boundary problems. My recent research include study of shock reflection in gas dynamics, which involves study of free boundary problems for nonlinear degenerate-elliptic equations. I also work on semigestrophic system of PDE, which models atmospheric flows, and this work involves methods related to Monge-Kantorovich mass transport theory.

Andreas' research interests include singular integrals, pointwise convergence of Fourier series, Fourier and spectral multiplier transformations, function spaces, wave propagation, oscillatory and Fourier integral operators, maximal functions related to geometric questions, and other applications of harmonic analysis.

My research has focused on the nonlinear effects of inertia-gravity waves in atmosphere/ocean flows and the self-organization of waves and turbulence into large-scale coherent structures. Such structures are ubiquitous in nature, and include jets (the North American jet stream and the Gulf stream), vortices (low pressure areas, hurricanes, etc) and persistent layered flows (such as in the…

Saverio Spagnolie's main research focus is at the interface between fluid and solid structures in soft biological matter. He investigates problems in biological propulsion, cell mechanics, and collective behavior using a number of techniques, from the application of classical methods of applied mathematics to the development of novel numerical methods.

Broadly speaking, my research is in applied math and climate science, and it involves a wide range of areas: stochastic models, multiscale asymptotics, partial differential equations (PDEs),and numerical models. These areas of mathematics play a crucial role in the Tropics, where clouds and storms – i.e., atmospheric convection – are organized through complex interactions with atmospheric…

Betsy Stovall's main research focus is on harmonic analysis.

I am interested in singular integrals as they relate to linear partial differential equations. For instance, if P is a partial differential operator, there is sometimes an inverse operator T with PT=I, where I denotes the identity. Much of my research revolves around studying operators like T. More precisely, under what conditions on P can we obtain a good picture of what T looks like.

…

Jean-Luc Thiffeault's main research focus is on mixing in fluid dynamics. Mixing is relevant to many areas of science and engineering, including the pharmaceutical and food industries, oceanography, atmospheric sciences, and environmental engineering.

Currently, I am interested in studying well-posedness and fine properties of some nonlinear PDEs such as Hamilton-Jacobi equations, fully nonlinear elliptic equations, front propagation, mean curvature flows, etc. In particular, I focus on some asymptotic problems (homogenization, large time behavior), duality nature, dynamical properties of solutions (connection to weak Kolmogorov-Arnold-…

Fabian Waleffe's main research focus has been on `Exact Coherent States', how to calculate them and how they control turbulent flows.

Exact coherent states are particular steady, traveling wave or periodic solutions of the governing partial differential equations (Navier-Stokes, Boussinesq) in physically realistic wall-bounded domains. These solutions are generally unstable, strongly…

Professor Zlatoš works in the areas of applied analysis and partial differential equations (PDEs), where his interest is primarily in parabolic and elliptic PDEs and fluid dynamics. His recent work has been focused on reaction-diffusion and advection-diffusion equations. These model evolution of quantities such as densities of chemicals or animal species, or temperatures of combusting media,…