Research

The Department has active research in the following main domains.

Algebra and algebraic geometry

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. Cooper’s expertise is commutative algebra. 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 works in arithmetic geometry, modular forms and number theory. Yang Zhang’s interests are algebra, computer algebra and applications.

Analysis

L. Butler’s research interests are Hamiltonian mechanics and integrable systems. R. Clouâtre works in operator theory and operator algebras. C. Cowan works in the area of partial differential equations. A. Prymak interests are in approximation theory and geometric methods in analysis, including relations to geometry of Banach spaces, harmonic analysis and Fourier analysis. 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.

Approximation theory

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. Prymakworks 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.

Combinatorics (finite and discrete mathematics)

R. Craigen studies orthogonal matrices and related objects in the field of Combinatorial Matrix Theory. K. Gunderson works in random graphs, percolation and extremal combinatorics. 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. A. Prymak is interested in questions related to strongly regular graphs and their Euclidean representations.

Foundations (logic and set theory)

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

Geometry and topology

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. A. Prymak studies low-dimensional and asymptotic convex geometry, in particular questions on Banach-Mazur distance.

Numerical and computational mathematics

S. Lui works in numerical analysis, in particular numerical PDEs and numerical linear algebra. A. Prymak works on questions related to discretization and foundations of certain numerical methods. R. M. Slevinsky works in numerical methods for singular integral equations.