The faculty of the Mathematics Department conducts research in a broad variety of areas. Below are the research groups in our faculty, along with members of the groups and areas they work in.
The field of algebra, at its most basic level, examines the relationships between sets and the properties of those sets under different operations. Considered one of the fundamental areas of mathematics, the fundamentals of the discipline touch almost every part of modern mathematics. Historic work in algebra gave us the general solution to quadratic equations and the resulting discovery of the complex numbers. Current work often applies algebraic ideas to the mathematical fields of geometry and topology to expose similarities in structure between seemingly unrelated objects.
- Paul Allen: group theory, ring theory
- Jon Corson: geometric ring theory
- Martyn Dixon: infinite group theory
- Martin Evans: infinite group theory
The field of analysis, at its most fundamental level, explores the notion of limits, and forms the basis of many of our modern mathematics tools, including calculus. Although the field was formally developed during the Scientific Revolution, ancient Greek philosophers (among others) grappled with the fundamental ideas of limits in their discussion of ideas such as Zeno’s Paradox of Achilles and the tortoise. Modern analysis is often applied to develop functions and methods of modeling complex systems.
- David Cruz-Uribe: harmonic analysis, PDEs
- Tim Ferguson: complex analysis, operator theory, harmonic analysis
- Kabe Moen: harmonic analysis, PDEs
- Yuanzhen Shao: PDEs, geometric analysis
The field of geometry is one of the oldest in mathematics, with roots in ancient Egypt and Greece. The more modern development of topology evolved out of the study of geometry and now both fields have distinct areas of work, but also share a common orientation towards mathematics. Concerned with the properties of and relationship between objects in space, early work in these fields sought to describe the physical world. Modern work often explores how properties change as the space the objects exist within varies.
- Jon Corson: low dimensional topology
- Lawrence Roberts: low dimensional topology, homology theory, knot theory
- Vo Liem: geometric topology
- Bulent Tosun: low dimensional topology, contact and symplectic geometry
- Bruce Trace: geometric topology
The field of mathematics education examines how students learn and understand mathematics, as well as what and how mathematics gets taught. Although mathematics education has existed for as long as people have studied mathematics, the field took off with the launch of the Soviet satellite Sputnik in the 1950s and the resulting focus in the United States on the mathematics learning of K-14 students. The focus of the field constantly evolves to reflect curriculum and policy shifts in mathematics education that result from changing public priorities.
- Jim Gleason: Mathematical knowledge for teaching, educational measurement
- Martha Makowski: Math education, developmental math, STEM access, quantitative and mixed methods
Applied and Computational Mathematics
The field of applied mathematics broadly encompasses areas of mathematical research that find new ways to model or process real world data. Arguably, all mathematics has roots in these fields, although modern mathematics separates applied and computational areas of study from fields that have fewer direct real world applications. With the rise of big data, applied and computational mathematics sit at the cutting edge of computing, science, and technology.
Ordinary or Partial Differential Equations
- Shibin Dai: nonlinear PDEs, applied analysis, numerical analysis
- Layachi Hadji: fluid dynamics, materials science
- David Halpern: fluid dynamics, mathematics in the life sciences, scientific computing
- Mojdeh Rasoulzadeh: homogenization method, flow and transport in heterogeneous porous media
- Roger Sidje: numerical methods for ODEs, numerical linear algebra, computational biology
- Chuntian Wang: PDEs, stochastic PDEs, statistical-stochastic modeling with applications
- Shan Zhao: numerical methods for PDEs, scientific computing, mathematical biology
- Wei Zhu: image processing, numerical methods for PDEs
Optimization and Statistics
- Brendan Ames: optimization, machine learning
- Stavros Belbas: optimal control, game theory
- Yuhui Chen: big data analysis, Bayesian nonparametric modeling, survival models, statistical computing
- Dang Nguyen: applied probability, stochastic processes, optimal control, dynamical systems, mathematical biology
- Min Sun: global optimization and game theory with applications, modeling, simulation