# Partial Differential Equations

**Douglas Arnold**

McKnight Presidential Professor

arnold@umn.edu

Numerical analysis, differential equations,

mechanics, computational relativity.

**Jeffrey Calder ***Assistant Professor*

jwcalder@umn.edu *partial differential equations, numerical analysis, applied **probability, machine learning, image processing and computer vision*

**Maria-Carme Calderer***Professor*

mcc@math.umn.edu*applied mathematics, continuum mechanics, soft condensed matter physics and materials science, with emphasis on liquid crystals, ferroic materials, partial differential equations and calculus of variations*

**Paul Carter ***Assistant Professor*

pcarter@umn.edu *dynamical systems, nonlinear waves, partial differential equations, singular perturbations, applied mathematics, pattern formation*

**Max Engelstein***Assistant Professormengelst@umn.edu
harmonic analysis, geometric measure theory, calculus of variations*

**Hao Jia***Assistant Professor*

jiaxxo34@math.umn.edu*partial differential equations, regularity, stability, large data asymptotics *

**Markus Keel***Professor*

keel@math.umn.edu*partial differential equations; real, harmonic, and functional analysis*

**Nicolai Krylov***Samuel G. Ordway Professor*

krylov@math.umn.edu*partial differential equations, probability*

**Ru-Yu Lai***Assistant Professor*

rylai@math.umn.edu*inverse problems and partial differential equations*

**Mitchell Luskin***Professor*

luskin@math.umn.edu*numerical analysis, scientific computing,
applied mathematics, computational physics*

**Svitlana Mayboroda***Professor*

svitlana@umn.edu*analysis and
partial differential equations*

**Peter Olver***Professor*

olver@umn.edu*Lie groups, differential equations,
computer vision, applied mathematics,
differential geometry, mathematical physics*

**Peter Polacik***Professor*

polacik@math.umn.edu*partial differential equations, dynamical systems*

**Mikhail Safonov***Professor*

safonov@math.umn.edu*partial differential equations, probability*

**Arnd Scheel***Professor*

scheel@math.umn.edu*dynamical systems, partial differential equations, applied math*

**Daniel Spirn***Professor*

spirn@math.umn.edu*partial differential equations, applied mathematics*

**Vladimir Sverak***McKnight University Professor*

sverak@math.umn.edu*partial differential equations*

**Jiaping Wang***Professor*

jiaping@math.umn.edu*differential geometry and partial differential equations*

## More About Faculty Research Areas

- Algebra
- Algebraic Geometry
- Algebraic Topology
- Analysis
- Applied Mathematics
- Combinatorics
- Complex Analysis
- Data Science
- Differential Geometry
- Dynamical Systems and Differential Equations
- Inverse Problems and Imaging
- Lie Theory
- Materials Science
- Mathematical Biology
- Mathematical Fluid Mechanics
- Mathematical Logic
- Mathematical Physics
- Mathematics Education
- Number Theory and Automorphic Forms
- Numerical Analysis
- Probability and Stochastic Processes
- The Faculty Research Overview