Faculty in the Department of Mathematics are deeply committed to excellence in teaching and research. Many specialize in both current and emerging areas of pure and applied mathematics.
George Androulakis
(Ph.D., University of Texas, Austin, 1996),
Functional Analysis. Research interests include: Banach space theory, Operator theory, and applications of Functional Analysis to Mathematical Physics.
Colin Bennett
(Ph.D., University of Newcastle upon Tyne, 1971),
Analysis. Research interests include: harmonic analysis and the theory of interpolation of operators and concurrent computation.
Dmitriy Bilyk
(Ph.D., University of Missouri-Columbia, 2005),
Research interests include: Harmonic analysis, functional analysis, discrepancy theory.
Peter Binev
(Ph.D., Sofia University, 1985),
Scientific Computing, Approximation Theory, Numerical Analysis. Research interests include: nonlinear approximation, learning theory, high dimensional problems, numerical methods for PDEs, computer graphics, image and surface processing.
Matthew Boylan
(Ph.D., University of Wisconsin, 2002),
Number Theory. Research interests include: Number theory. In particular, elliptic modular forms and Maass forms and their applications to algebraic number theory, elliptic curves, L-functions, partitions, and other topics in number theory.
Joshua Cooper
(Ph.D., University of California, San Diego, 2003),
Combinatorics and Number Theory. Research interests include: extremality, regularity, and quasirandomness of graphs and permutations; combinatorial number theory; universal cycles; coding theory; combinatorial algorithms.
Eva Czabarka
(Ph.D., University of South Carolina, 1998),
Combinatorics and Biostatistics. Research interests include: extremal set theory, crossing numbers of graphs, statistics and the use of discrete mathematics in bioinformatics.
Stephen Dilworth
(Ph.D., University of Cambridge, 1985),
Functional Analysis. Research interests include: finite-dimensional and infinite-dimensional Banach space theory; classical Banach spaces; approximation in Banach spaces.
Daniel Dix
(Ph.D., University of Chicago, 1988),
Analysis. Research interests include: initial value problems for partial differential equations governing the evolution of nonlinear waves, asymptotic behavior of solutions, solutions with special symmetry, completely integrable equations, and solitons.
Michael Filaseta
(Ph.D., University of Illinois, 1984),
Number theory, including analytic, classical algebraic, combinatorial, computational, elementary, and transcedence topics. Research interests include lattice points close to (or on) a curve or surface, the distribution of special sequences of integers in short intervals, applications of Pade approximations to Number Theory, the irreducibility of polynomials over the rationals, and computations with sparse or lacunary polynomials.
Maria Girardi
(Ph.D., University of Illinois, 1990),
Functional Analysis. Research interests include: functional analysis, esp. classical and geometrical Banach space theory.
Jerrold Griggs
(Ph.D., Massachusetts Institute of Technology, 1977, Department Chair),
Combinatorics. Research interests include extremal set theory, extremal graph theory, graph coloring, and applications of discrete math to biology, number theory, analysis of algorithms, and communications.
Ralph Howard
(Ph.D., California Institute of Technology, 1982),
Differential and Integral Geometry with excursions into Analysis. Research interests include: global Lorentzian geometry, geometricinequalities, stochastic geometry and analysis related to differential equations arising in geometry.
Lili Ju
(Ph.D., Iowa State University, 2002),
Computational Mathematics. Research interests include: Scientific computation and numerical analysis. Exact boundary controllability problems for the wave equation. Parallel algorithms and high-performance computing. Human brain imaging.
Andrew Kustin
(Ph.D., University of Illinois, 1979),
Commutative Algebra and Algebraic Geometry. Research interests include: the study of Cohen-Macaulay and Gorenstein algebras, finite free resolutions, linkage, deformation theory, and differential graded commutative algebras.
Lincoln Lu
(Ph.D., University of California, San Diego, 2002),
Discrete Mathematics. Research interests include: large information networks, combinatorial probabilistic methods, extremal graph theory, algorithms, computational geometry, computational biology, and Internet computing.
George F. McNulty
(Ph.D., University of California, Berkeley, 1972),
Logic, Algebra, and Discrete Mathematics. The central themes of Dr. McNulty's research lie at the confluence of algebra , logic and computer science. They include finite axiomatizability of equational classes of algebras, structural properties of the lattices of equational theories, and algorithmic computability in algebraic, logical, and combinatorial settings.
Douglas Meade
(Ph.D., Carnegie Mellon University, 1989, Undergraduate Director),
Applied Mathematics. Current research interests include numerical methods for wave propagation on unbounded domains, non-overlapping domain decomposition methods, and computer algebra systems.
Matthew Miller
(Ph.D., University of Illinois, 1979, Graduate Director),
Commutative Algebra and Mathematical Biology. Research interests involve problems in commutative algebra mostly using homological techniques, and the relationships between betti numbers and Hilbert functions. Recent interests are in mathematical biology, especially modeling of animal behavior.
Peter Nyikos
(Ph.D., Carnegie Mellon University, 1971),
Topology. Research interests include: point-set topology, especially covering and base properties of regular spaces, and the structure theory of locally compact spaces; the application of special axioms from set theory to constructing examples and establishing consistency and independence results; and applications of point-set topology, especially to Boolean algebras and functional analysis.
Konstantin Oskolkov
(Ph.D., Steklov Institute, 1972),
Fourier Series, Approximation, Oscillatory Sums and Integrals, Schrödinger type equations, Wavelets and Bases.
Pencho Petrushev
(Ph.D., Sofia University, 1977),
Approximation Theory, Harmonic Analysis, Numerical Methods. Research interests include: nonlinear approximation by rational functions, splines, and wavelets, approximation by ridge functions and neural networks, image processing.
Anton Schep
(Ph.D., University of Leiden, 1977, Assistant Chair),
Functional Analysis, Operator Theory. Research interests include: the study of linear integral operators on Banach function spaces, positive operators and C0-semigroups of positive operators on Banach lattices, spectral properties, and compactness properties of special classes of operators.
Robert Sharpley
(Ph.D., University of Texas, Austin, 1972, IMI Director),
Classical Analysis and its applications. Research interests include Fourier analysis, approximation theory, multiresolution analysis, signal and image processing, numerical analysis, visualization, and autonomous navigation. Professor Sharpley has served as PI on research projects supported by NSF, DOD (ARO, AFOSR, ONR), NASA, and DOE as well as several large equipment and industrial technology transfer grants.
Manfred Stoll
(Ph.D., Pennsylvania State University, 1971),
Function Theory, Potential Theory, Several Complex Variables. Research interests include: the study of holomorphic, harmonic, and plurisubharmonic functions of one and several complex variables; Hp spaces, Bergmann spaces, and other spaces of harmonic and holomorphic functions of one and several complex variables; boundary behavior of Green potentials in domains in Rn and Cn.
László Székely
(Ph.D., Eötvös University, 1983),
Combinatorics and Graph Theory. Research interests include extremal combinatorics, discrete geometry, graphs drawn on surfaces, reconstruction of phylogenetic trees from genetic sequences.
Vladimir Temlyakov
(Ph.D., Steklov Institute, 1978),
Approximations of functions in one variable and multivariable cases (approximations by polynomials, n-widths, optimal cubature formulas). Integral operators (estimates of singular numbers, approximation numbers, bilinear approximation of kernels of these operators).
Frank Thorne
(Ph.D., University of Wisconsin, 2008),
Number Theory; distribution of primes and broadly related questions.
Ognian Trifonov
(Ph.D., Sofia University, 1989),
Analytic Number Theory and Approximation Theory with particularinterests in the use of finite differences to determine information about lattice points close to a curve or surface. Interests also include the application of these results to gap problems in Number Theory.
Adela Vraciu
(Ph.D., University of Michigan, 2000),
Commutative Algebra and Algebraic Geometry. Reseach interests include: tight closure theory, linkage, and homological properties of rings and modules.
Hong Wang
(Ph.D., University of Wyoming, 1992),
Numerical Analysis and Differential Equations. Research interests include: Numerical approximation to differential/integral equations, scientific computations.
Qi Wang
(Ph.D., Ohio State University, 1991),
Applied and Computational Mathematics, Computational Fluid Dynamics and Rheology of Complex Fluids, Continuum Mechanics and Kinetic Theory, Multiscale Modeling and computation of soft matter and complex fluids of anisotropic Microstructures, Multiscale modeling and computation of biofluids and biomaterials, Parallel and high performance Computing.
Brett Wick
(Ph.D., Brown University, 2005),
Complex Analysis and Harmonic Analysis. Research interests include: interactions and applications of complex and harmonic analysis to operator theory.
Xian Wu
(Ph.D., Harvard University, 1986),
Algebraic Geometry, Differential Geometry, Complex Manifolds.