The Department has active research in the following main domains. Click links below or to the left to find out more about a given domain, including faculty members and students involved, publications, etc.

A. Clay studies geometric group theory and group actions on ordered sets.
J. Chipalkatti's interests are in algebraic geometry, as well as classical invariant theory.
S. Kirkland works in matrix theory and graph theory, with particular interest in the theory and applications of nonnegative matrices, combinatorial matrix theory, and spectral graph theory.
T. Kucera studies injective modules and related concepts in module theory and ring theory.
S. Sankaran's interests include number theory, modular and automorphic forms and arithmetic algebraic geometry.
Yang Zhang's interests are algebra, computer algebra and applications.

R. Clouatre works in operator theory and operator algebras.
C. Cowan works in the area of partial differential equations.
E. Schippers works in complex analysis, Teichmuller theory and two-dimensional conformal field theory.
Yong Zhang works in Banach algebras and Harmonic analysis.
N. Zorboska works in operator theory, complex analysis and spaces of analytic functions.

K. Kopotun works in approximation theory with particular interest in various topics in nonlinear approximation, constrained approximation, measures of smoothness, weighted approximation, adaptive algorithms, and other related areas.
A. Prymak works in approximation theory and geometric methods in analysis, with particular interest in shape-preserving approximation, measures of smoothness and approximation, and relations to other areas of analysis and mathematics.

R. Craigen studies orthogonal matrices and related objects in the field of Combinatorial Matrix Theory.
K. Gunderson works in random graph theory.
S. Kirkland works in matrix theory and graph theory, with particular interest in the theory and applications of nonnegative matrices, combinatorial matrix theory, and spectral graph theory.

T. Kucera studies problems in model theory, in particular applications of model-theoretic techniques to problems in module theory and ring theory.

A. Clay studies the relationship between geometry of 3-manifolds and the algebraic properties of their fundamental groups. D. Krepski's interests are in symplectic geometry and quantization, as well as the topology of smooth Deligne-Mumford stacks.

J. Arino focuses mainly on mathematical epidemiology, F. Magpantay works with differential equations and stochastic systems for modeling biological systems, while S. Portet's work deals with cellular structure.

S. Lui works in numerical analysis, in particular numerical PDEs and numerical linear algebra. F. Magpantay works on numerical aspects of delay differential equations. R. M. Slevinsky works in numerical methods for singular integral equations.