Welcome to our Faculty Research webpage! The list below provides a brief overview of the research interests of each faculty member in our department. The navigation link to the left also provides a list of recent work published by our students. Students interested in research are encouraged to discuss opportunities with their instructors!
Fields of interest: Differential geometry, partial differential equations.
Click here for a list of publications (Google Scholar)
Fields of interest: Real C*-algebras and K-theory
Fields of interest: Harmonic analysis and partial differential equations
Dr. Ding’s research fields are harmonic analysis and partial differential equations. Recently, he works on A-harmonic equations and Dirac-harmonic equations for differential forms and the theory of related operators, including the Dirac operator, Green’s operator, potential operator and homotopy operator on differential forms.
Fields of interest: Differential geometry
Fields of interest: Knot theory
Dr. Henrich's research is primarily in knot theory. She studies pseudoknots and virtual knots, among other generalizations of classical knots. She is also interested in questions related to unknots and unknotting operations as well as games involving knots. More detailed information about her research can be found on her webpage.
Fields of interest: Mathematical logic
Fields of interest: Algebraic and geometric combinatorics. Combinatorics of simplicial and cubical decompositions of polytopes and manifolds. Connections between combinatorics, commutative algebra, and algebraic topology.
Fields of interest: Algebraic combinatorics.
Dr. MacLean's main research interest is the study of distance-regular graphs. He often uses algebraic techniques to study these combinatorial objects.
Fields of interest: Graph Theory, Matroid Theory
Fields of interest: Number theory
Fields of interest: Algebraic geometry
Fields of interest: Math education and low-dimensional topology
Fields of interest: Partial differential equations
Dr. Carter's studies nonlinear partial differential equations (PDEs), with an emphasis on PDEs that model surface water waves. His work currently focuses on effects such as dispersion, viscosity, surface tension and vorticity. Many of these effects require the use of nonlocal PDEs such as the Whitham, fractional KdV and Dysthe equations. His research interests include stability analysis, fast numerical methods for nonlinear evolution equations and mathematical physics.
Within the broad field of mathematical biology, Dr. Cole’s research interests lie in modeling cellular level biophysical phenomena. Her dissertation focused on mathematical models for molecular motors. The mathematical methods used in this field are drawn from a broad range of areas, including partial differential equations, stochastic processes, and dynamical systems.
Fields of interest: Computational neuroscience
Dr. Fischer's research is in computational neuroscience with a focus on sound localization. He uses statistical analyses of neural data to determine how sound is processed in the brain. He is also interested in how principles of Bayesian statistical inference describe brain function.
Fields of interest: Nonlinear waves
My current research interests lie in the broad spectrum of integrable systems, and in particular, nonlinear waves. I am currently focusing on various aspects of solutions to Euler's equations for surface gravity-capillary waves using a nonlocal formulation of the water-wave problem due to Ablowitz, Fokas, and Musslimani.
Fields of interest: Statistical Forecasting, Environmental Modeling, Renewable Energy, Math Pedagogy
Dr. Sylvester's research interests focus on applications of partial differential equations to physical problems. This field draws heavily on ideas from analysis, differential equations, and linear algebra.