Research in the Math Department

The department is home to world-class research mathematicians in specialties as diverse as mathematics itself. These research areas may be loosely grouped into:

Faculty, graduate students, and undergraduates meet weekly in seminars, detailed on the events page. The main seminars are:

Several members of the department are regular co-organizers of local recurring conference series:

In recognition of its research output, the Carnegie Classification of Institutions of Higher Education designates OU as an R1 university.



Algebra is the study of abstract objects that adhere to simple rules, such as number systems, polynomials, vector spaces, and symmetries. These patterns and results have been applied everywhere from Sudoku to string theory. The algebra group meets weekly at the Algebra and Representation Theory Seminar (ARTS) and is involved in the TORA conference series.

Representation Theory

Representation theory explores mathematical objects by studying the spaces they act upon. It leverages powerful tools from linear algebra, Lie theory, partial differential equations and category theory. It illuminates and generalizes Fourier analysis via harmonic analysis. It is connected to geometry via invariant theory. The subject lies at the heart of the Langlands program, a web of conjectures that guides much of modern number theory. It has many applications in physics and engineering — in particular, to quantum information theory. Members of the representation theory group at OU include:

Number Theory

As old as mathematics itself, number theory studies equations and surprising patterns of integers and prime numbers. Modern number theory integrates geometry, algebra and analysis through objects such as zeta functions, elliptic curves, modular forms and automorphic representations. Members of the number theory group at OU include:

Algebraic Geometry

At its most basic level, algebraic geometry is simply the study of systems of polynomial equations. But more broadly it is the art of using algebraic tools to study geometric objects and using geometric tools to study algebraic objects. As such, it has evolved in close relation to several other areas of mathematics, most notably number theory, representation theory, algebraic combinatorics, and complex geometry. Members of the algebraic geometry group at OU include:


Combinatorics is a catch-all term that encompasses the study of a wide array of discrete structures such as graphs, networks, and counting problems. Combinatorics is widely used in computer science, from algorithm design to error-correction. Members of the combinatorics group at OU include:

Related Faculty to Algebra

Algebra Post-Docs

Emeritus Faculty in Algebra


Analysis/Applied Math

Analysis is the study of the infinitesimal behavior of functions, such as limits, integration, and other tools from calculus. The ubiquity of differential equations in scientific models makes tools from analysis some of the most important in applications.


The analysis group meets weekly at the Analysis Seminar, and features working groups specializing in convexity theory, partial differential equations, and the theory of frames. Members of the analysis group at OU include:

Applied Math

The applied math group meets weekly at the Dynamical Systems Working Seminar and the Applied Math Seminar, and features specialties in dynamical systems and partial differential equations. Members of the applied math group at OU include:

Related Faculty to Analysis and Applied Math

Analysis and Applied Math Post-Docs

Emeritus Faculty in Analysis and Applied Math

Hyperbolic Tiling


Geometry is the study of distance, length, angles, geodesics etc., but in a modern context this includes the study of these attributes on manifolds (e.g., surfaces, 3-space) with positive or negative curvature and on more combinatorial objects. Topology, in part, is the study of continuous deformations and transformations and properties of spaces which are preserved by such deformations and transformations. The geometry/topology group meets weekly at the Geometry and Topology Seminar, and is involved in the organization of the Redbud Topology Conference and the Midwest Geometry Conference. Our Geometry/Topology group has a few main areas of focus: geometric group theory, low-dimensional/geometric topology, Riemannian geometry and algebraic topology.

Geometric Group Theory and Low-dimensional/Geometric Topology

Broadly speaking, geometric group theory is the study of groups, often infinite and discrete, from geometric properties of the group itself or of its action on geometric objects. Low-dimensional topology is the study of manifolds of 2, 3, or 4 dimensions. Some particular topics studied by our faculty are growth rate in groups, Dehn filling functions, stable commutator length, mapping class groups, and Teichmüller geometry.

Riemannian Geometry

Riemannian geometry is the study of manifolds and the geometry and curvature of their Riemannian metrics. Some particular topics studied by our faculty are isometry groups, hyperbolic geometry, manifolds with nonnegative curvature, nilpotent/solvable Lie groups, and Einstein and Ricci soliton metrics.

Algebraic Topology

Algebraic topology is the study of algebraic invariants of topological spaces and the study of algebraic objects from a topological perspective.

Topological Data Analysis

Topological Data Analysis (TDA) provides a mathematical framework for identifying and describing relevant features of complex and possibly high dimensional data. In many applications data is sampled from an unknown manifold. The methods of TDA allow us to study the shape of the manifold from its finite sample. The shape is described by topological invariants which can be computed using algebraic topology.

Related Faculty to Geometry/Topology

Geometry/Topology Post-Docs

Emeritus Faculty in Geometry/Topology


Research in Undergraduate Mathematics Education (RUME)

The RUME (Research in Undergraduate Mathematics Education) program at OU offers a PhD in mathematics with research emphasizing mathematics education. The RUME group meets weekly at the RUME seminar, and features research specializations in linear algebra instruction, conceptualization of proofs, and active-learning techniques.

Faculty affiliated with the RUME program include:

Related Faculty to RUME

Emeritus Faculty in RUME


Conference Series

Midwest Geometry Conference

The Midwest Geometry Conference is an annual meeting in topics related to differential geometry and geometric analysis. Members of the department have been frequently involved in its organization since its founding in 1991. See here for an overview of its history until 2015. Recent installments: 2016, 2017, 2019.

Redbud Topology Conference

The Redbud Topology conference series is a recurring regional conference in topology and related areas, hosted in rotation by the University of Arkansas, Oklahoma State University, and the University of Oklahoma.


TORA stands for "Texas-Oklahoma Representations and Automorphic forms", and is a conference series hosted in rotation by Oklahoma State University, the University of Oklahoma, and the University of North Texas.