People
Faculty
Sergey Denisov Professor Moscow State University, 1999 denissov at math dot wisc dot edu Research Interests: Analysis, Mathematical Physics Research Description: I work on problems in approximation theory, complex and harmonic analysis, and spectral theory. I also study mathematical theory of fluids and wave propagation. 
Mikhail Feldman Professor UC Berkeley, 1994 feldman@math.wisc.edu Research Interests: Nonlinear PDEs Research Description: 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 degenerateelliptic equations. I also work on semigestrophic system of PDE, which models atmospheric flows, and this work involves methods related to MongeKantorovich mass transport theory. 
Xianghong Gong Professor gong {at} math {dot} wisc {dot} edu Research Description: My research is in several complex variables and dynamical systems. I have worked on normal forms of real submanifolds in C^n. I am interested in derivative estimates for solutions of the dbar equation on domains whose boundaries have minimum smoothness. My recent research includes using dbar solution operators to study the stability of deformations of complex structures on a domain. 
Shaoming Guo Assistant Professor University of Bonn 2015 shaomingguo {at} math {dot} wisc {dot} edu Research Interests: Harmonic Analysis Research Description: My research is in harmonic analysis and its connections to analytic number theory and geometric measure theory.

Mihaela Ifrim Associate Professor UC Davis 2012 ifrim {at} math {dot} wisc {dot} edu Research Interests: Nonlinear PDEs, Dispersive Equations, Fluid Dynamics Research Description: Mihaela's research is in partial differential equations, more precisely she is interested in nonlinear hyperbolic PDE’s with an emphasis on fluid dynamics. Over the years her mathematical interests have broadened, extending in many directions, from incompressible to compressible flows within fluid dynamics, but also from fluids to other nonlinear dispersive hyperbolic models. Her recent work has roughly been following two threads (i) the analysis of the twodimensional water wave equations, which govern the evolution of a free fluid surface, or of the interface between two fluids, and (ii) the analysis of free boundary problems for several compressible Euler type flows. In addition to these two main research directions, Mihaela's research interests have also extended to the field of nonlinear wave equations, which ties directly to very interesting projects related to in General Relativity.

Chanwoo Kim Associate Professor Brown University 2011 chanwoo.kim {at} math {dot} wisc {dot} edu Research Interests: Applied PDEs (kinetic theory, fluid dynamics) Research Description: I am interested in applied PDEs in the fields of kinetic theory and related areas. My recent research include study of hydrodynamic limit from the Boltzmann equation toward various fluid models. I also work on long time behavior of the Vlasov equation, which models plasma and galaxies. 
Simon Marhsall Associate Professor Princeton University, 2010 marshall {at} math {dot} wisc {dot} edu Research Interests: Automorphic forms, symmetric spaces Research Description: I study problems in the analytic theory of automorphic forms, and harmonic analysis on symmetric spaces. These include questions about counting the number of automorphic forms in families, and understanding the asymptotic behaviour of eigenfunctions with large eigenvalue. 
Andreas Seeger Professor Technische Hochschule Darmstadt, 1985 seeger at math dot wisc dot edu Research Interests: Harmonic Analysis Research Description: 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. 
Betsy Stovall Professor UCBerkeley, 2009 stovall at math dot wisc dot edu Research Interests: Harmonic Analysis Research Description: Betsy Stovall's main research focus is on harmonic analysis. 
Brian Street Professor Princeton University, 2007 street at math dot wisc dot edu Research Interests: Singular Integrals, Several Complex Variables, PDE Research Description: I work in problems related to subRiemannian geometry, especially linear and multilinear singular integrals, and partial differential equations. 
Hung Tran Professor UC Berkeley 2012 hung at math dot wisc dot edu Research Interests: Nonlinear PDE 
Postdocs
Jack Burkart Van Vleck Assistant Professor Stony Brook, 2021 burkart2 at math dot wisc dot edu Research Description: I am interested in topics surrounding complex analysis and fractal geometry, including complex dynamics and analysis on metric spaces in particular. Much of my work in complex analysis surrounds the study of examples to examine possible topology and geometry of multiply connected wandering Fatou components, and I am interested in discovering more general ways to categorize the phenomena that occur in these examples.

David Beltran Van Vleck Assistant Professor University of Birmingham, 2017 dbeltran at math dot wisc dot edu Research Description: My research focuses on Euclidean harmonic analysis and related areas. Particular examples are questions related to the Fourier restriction conjecture, decoupling inequalities, local smoothing estimates, averages along manifolds, maximal and variation norm Radon transforms, the Kakeya conjecture, extremisers for Strichartz estimates, regularity of maximal functions, pseudodifferential operators, weighted inequalities and sparse domination.
