# Research

Research in the Department of Mathematics and Statistics at Auburn University is undertaken by fifty internationally-recognized faculty members. Fields of study covered include various topics in pure and applied mathematics as well as statistics. Some professors pursue interdisciplinary mathematics as well.

## List of Research Fields

- Actuarial Mathematics
- Algebra
- representation theory of groups and Lie algebras
- algebraic geometry
- commutative and homological algebra
- invariant theory

- Analysis
- real and complex analysis
- harmonic analysis
- approximation theory
- wavelets

- Applied Mathematics
- Discipline-Based Education Research
- Discrete Mathematics
- graph theory
- design theory
- coding theory

- Differential Equations
- ODEs
- nonlinear oscillators
- neural networks
- stochastic equations
- equations in Banach spaces

- PDEs
- elliptic and parabolic equations
- reaction-diffusion systems
- applications in climate modeling, biology, and fluid dynamics

- ODEs
- Dynamical Systems
- monotone and skew-product flows
- complex dynamics
- symbolic and lattice dynamics

- Geometry
- Linear Algebra
- Numerical Analysis
- numerical and computational linear algebra
- numerical and computational PDEs
- finite-element and finite-difference methods
- applications in fluid dynamics, elasticity, chemistry, geology, and biology

- Statistics
- Stochastic Analysis
- Topology
- continuum theory
- set-theoretic topology
- algebraic topology