The faculty in the Department of Mathematics conduct research in a broad variety of areas. Learn more about research groups in the department and which areas the faculty members work in below.

Read about research news and faculty accomplishments.

## Faculty Research Areas

### Algebra

- Ulysses Alvarez: algebra, combinatorics, topology
- Jon Corson: geometric group theory
- Kyungyung Lee: algebra, combinatorics, geometry, topology, mathematical physics
- Thomas Polstra: commutative algebra, algebraic geometry

Learn more about this specialty on the algebra research group page.

### Analysis

- Simon Bortz: harmonic analysis, geometric measure theory, partial differential equations
- David Cruz-Uribe: harmonic analysis, partial differential equations
- Tim Ferguson: complex analysis, operator theory, harmonic analysis
- Kabe Moen: harmonic analysis, partial differential equations
- Abba Ramadan: calculus of variations, analysis of nonlinear partial differential equations and their applications in physics, materials science, and fluid mechanics.
- Yuanzhen Shao: partial differential equations, geometric analysis
- Robert Smits: real and stochastic analysis, learning from data, applied probability, eigenvalue problems for partial differential equations

Learn more about this specialty on the analysis research group page.

### Data Science and Optimization

- Yuhui Chen: big data analysis, Bayesian nonparametric modeling, survival models, statistical computing,
- Min Sun: global optimization and game theory with applications, modeling, simulation
- Chuntian Wang: supervision-aware dimensionality-reduction models for classification, dynamic topic modeling with tensor decomposition, concept discovery approaches in medical image
- Yiran Wang: scientific computing, numerical analysis, machine learning
- Wei Zhu: data analysis, image processing, numerical methods for partial differential equations

Learn more about this specialty on the data science and optimization research group page.

### Geometry and Topology

- Ulysses Alvarez: algebra, combinatorics, topology
- Jon Corson: low dimensional topology
- Kyungyung Lee: algebraic geometry, cluster algebras, mathematical physics, Jones polynomials.
- Lawrence Roberts: low dimensional topology, homology theory, knot theory
- Bulent Tosun: low dimensional topology, contact and symplectic geometry

Learn more about this specialty on the geometry and topology research group page.

### Math Biology

- David Halpern: biofluid mechanics, pulmonary airway mechanics
- Hai-Dang Nguyen: stochastic processes, optimal control in population dynamics and infectious diseases
- Yuanzhen Shao: mathematical modeling of biomolecular problems
- Chuntina Wang: crime modeling, human-behavioral modeling, epidemic modeling with social behavior, Poisson processes, Markov pure jump processes, chemo-taxis equations
- Shan Zhao: mathematical methods for molecular bioscience and biophysics

Learn more about this specialty on the math biology research group page.

### Math Education

- Jim Gleason: mathematical knowledge for teaching, educational measurement
- Martha Makowski: math education, developmental math, STEM access, quantitative and mixed methods

Learn more about this specialty on the math education research group page.

### Numerical Analysis and Scientific Computing

- Roger Sidje: numerical methods for ordinary differential equations, numerical linear algebra, computational biology
- Zheng Sun: numerical methods for partial differential equations, computational physics, discontinuous Galerkin methods
- Shan Zhao: numerical methods for partial differential equations, interface problems
- Wei Zhu: image processing, numerical methods for partial differential equations

Learn more about this specialty on the numerical analysis and scientific computing research group page.

### Partial Differential Equation Modeling and Analysis

- Shibin Dai: calculus of variations, free boundary problems, and their applications in physical, biological, and materials science
- Tiziana Giorgi: nonlinear partial differential equations, soft matter systems, superconductivity
- David Halpern: interfacial fluid mechanics, surfactant spreading on viscous fluids, scientific computing
- Abba Ramadan: calculus of variations, analysis of nonlinear partial differential equations and their applications in physics, materials science, and fluid mechanics.
- Mojdeh Rasoulzadeh: homogenization method, flow, and transport in heterogeneous porous media
- Yuanzhen Shao: geometric flows, nonlocal diffusion, fluid dynamics, mathematical biology
- Chuntian Wang: advection-reaction-diffusion equations, mean-field population models, and partial differential equation modeling with applications in human behavior and epidemics dynamics
- Wei Zhu: image processing, numerical methods for partial differential equations

Learn more about this specialty on the partial differential equation modeling and analysis research group page.

### Probability & Statistics

- Yuhui Chen: big data analysis, Bayesian nonparametric modeling, survival models, statistical computing
- Hai-Dang Nguyen: stochastic processes, optimal control, dynamical systems, stochastic approximation
- Robert Smits: stochastic processes, stochastic differential equations, game theory
- Chuntian Wang: stochastic partial differential equations, statistical-stochastic modeling with applications

Learn more about this specialty on the probability & statistics research group page.