# Research

Research activities and interests in the department encompass many areas of mathematics; below is a listing of the strongly represented areas in the department. Clicking on a person's name leads to their home page; clicking on the research group's name leads to the group's website.

## Algebra

- Datskovsky, Boris: algebraic number theory, analytic number theory, modular forms.
- Dolgushev, Vasily: noncommutative geometry, homological algebra, category theory and mathematical physics.
- Letzter, Edward: noncommutative algebra.
- Lorenz, Martin: noncommutative ring theory, representation theory, invariant theory, algebraic K-theory.
- Walton, Chelsea: noncommutative algebra and noncommutative algebraic geometry.
- Wang, Xingting: noncommutative algebras, Poisson algebras, noncommutative projective algebraic geometry, cohomology theory, and noncommutative invariant theory.

## Analysis

- Berhanu, Shiferaw: complex analysis, partial differential equations.
- Gutierrez, Cristian: partial differential equations, harmonic analysis.
- Mendoza, Gerardo: global analysis, manifolds with singularities, partial differential equations, differential complexes.
- Mitrea, Irina, harmonic analysis, partial differential equations, and geometric measure theory.
- Pesenson, Isaac: harmonic analysis on manifolds and graphs.

## Applied Mathematics and Scientific Computing

- Cui, Shumo: higher-order numerical schemes for hyperbolic conservation laws, traffic modeling, well-balanced numerical schemes.
- Grabovsky, Yury: calculus of variations, continuum mechanics, homogenization, phase transitions.
- Joshi, Sunnie: continuum mechanics, modeling cardiovascular diseases and fluid-structure interaction in blood flow.
- Klapper, Isaac: fluid dynamics, microbial ecology, biofilms.
- Gillian Queisser: numerical methods and scientific computing, high-performance computing, applications in the life sciences with a particular focus on neuroscience.
- Seibold, Benjamin: computational partial differential equations, numerical analysis, traffic modeling.
- Szyld, Daniel: numerical analysis and scientific computing, numerical linear algebra.
- Zhou, Dong: high order numerical schemes for nonlinear Hamilton-Jacobi equations and fluid flow problems.

## Geometry & Topology

- Fu, Ser-Wei: hyperbolic geometry, geometric group theory, geometric structures, low-dimensional topology, dynamical systems, ergodic theory, billiards, and Teichmuller Theory.
- Futer, David: knot theory, hyperbolic geometry, low-dimensional topology.
- Rivin, Igor: geometry, dynamical systems, combinatorics, group theory, crystallography.
- Rushton, Brian:: finite subdivision rules, geometric group theory.
- Stover, Matthew:: low-dimensional geometry, hyperbolic geometry, number theory.

## Probability

- Rider, Brian: probability and random matrices
- Yang, Wei-Shih: probability, quantum computing, mathematical physics.