The Department of Mathematics emphasizes good teaching and takes great pride in the research and teaching accomplishments of its faculty members. Members of the department faculty have received a variety of University Awards, including the Distinguished Teaching Award, the Distinguished Service Award for Administration, the Natural Science Teaching Award, the Honors Professorship, the Natural Sciences Research Award, and the Distinguished Service Award for Research. Faculty members in the Department have given invited lectures on 6 continents and in 68 countries. They have published more than 1000 research papers in technical journals.
Number Theory, Arithmetic Geometry, Mathematical Ecology and Evolution
Topology, geometry, and data analysis. More specific subfields of interest include applied topology, computational topology and geometry, combinatorial topology, metric geometry, machine learning, and sensor networks
Monte Carlo methods, interacting particles, sampling, statistical physics
Preparation and development of K-12 mathematics and statistics teachers
Numerical analysis, scientific computing, mathematical software
Distance Learning, Numerical Analysis/Simulation, Lasers and Photonic Crystals, Cell Dynamics
Combinatorics, coding theory, design theory, algorithms, mathematical software, parallel computing
My research centers on the nanoscale patterns that develop spontaneously when a solid surface is bombarded with a broad ion beam. These patterns include ordered arrays of nanodots and surface ripples with wavelengths as short as 10 nm. From a more mathematical standpoint, I study self-organization in systems driven far from equilibrium as well as solitons and shockwaves.
Algebraic Geometry, Moduli Spaces
Inverse Problems, Radar Imaging
Control and Optimization, Communication Networks, Wireless Systems
Partial differential equations, optimal control, inverse problems
Combinatorics, with applications to Algebraic Geometry and Representation Theory
Undergraduate Mathematics Education
(Computational) Group Theory, Group Actions, Combinatorics, Number Theory, Symbolic Computation. Co-Author of the system GAP
My research interests are in the field of algebraic number theory, and more specifically, arithmetic dynamics. The main focus of my research is studying how the absolute Galois group of a field acts on pre-images of a point under iterates of a rational function. This area has many nice applications to number theory and dynamics.
My research interests include pure & applied harmonic analysis, data analysis, frame theory (in particular algebraic, geometric, and combinatorial methods in frame theory), and signal and image processing.
Computational and Applied Mathematics, Optimization and Mathematical Modeling
Numerical Analysis, Scientific Computing
My research is on efficient algorithms for combinatorial problems. I am especially interested in recursive decompositions of arbitrary graphs and digraphs, algorithms for classes of graphs that are subclasses of the class of perfect graphs, and classes of graphs that have geometric representations.
Inverse problems, electrical impedance tomography, medical imaging, PDE's
Dynamical systems; pattern formation; fluid dynamics, hydrodynamic and hydromagnetic stability and bifurcation; numerical analysis; mathematical modeling
Statistical signal processing, coding theory, applied harmonic analysis, radar/sonar imaging
Partial Differential Equations, Waves in Random Media, Inverse Problems, Quantum Transport
Arithmetic Geometry, Number Theory, Galois theory
Statistical Signal Processing , Wireless Communication
Applied Maths, Dynamical Systems, Differential Geometry
Algebraic Geometry, Mathematical Physics
Differential and symplectic geometry, geometric probability, knot theory, and applications of these areas to polymer physics and signal processing
Teaching and learning of undergraduate mathematics with an embodied cognition lens
My research focuses on how the interplay between ecological and evolutionary mechanisms affects the dynamics and persistence of ecological systems. We particularly focus on disease ecology and trait-based approaches in ecology and use quantitative techniques to address questions in these areas.
Groups, algebras, and computation
Numerical Methods for PDEs, Mathematical Biology, Fluid Dynamics
Abstract algebra education research
Arithmetic Dynamics on Character Varieties, Data Learning using Varieties, Mathematics Education, Complex Hyperbolic Geometry
Dynamical Systems and Applications
Algebraic Topology, Algebraic Geometry, K-Theory
Kenneth Whitcomb / Emeritus