People

Faculty


Sergeui Denissov 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 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.


Xianghong Gong 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 d-bar equation on domains whose boundaries have minimum smoothness.  My recent research includes using d-bar solution operators to study the stability of deformations of complex structures on a domain.


Shaoming Guo 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 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 two-dimensional 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 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 Marshall 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 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
UC-Berkeley, 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 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 sub-Riemannian geometry, especially linear and multi-linear singular integrals, and partial differential equations.


Hung Tran 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.