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Research in the Department of Mathematics & Statistics at Auburn University spans a wide range of theoretical, computational and applied areas. Faculty and graduate students investigate fundamental mathematical structures while also developing methods that address problems in science, engineering, industry and data analysis.
The department’s research strengths include pure mathematics, applied mathematics, statistics and interdisciplinary areas that connect mathematical theory with real-world applications.
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Algebra
Research in algebra explores the structure of algebraic systems and their connections to geometry, topology and mathematical physics. Faculty work in areas such as representation theory of groups and Lie algebras, abelian groups, homological algebra and invariant theory.
Analysis & Stochastic Analysis
Analysis focuses on the study of functions, limits and mathematical structures arising from calculus. Research in this area includes real and complex analysis, harmonic analysis, approximation theory and wavelets, with applications ranging from signal processing to mathematical modeling.
Applied Mathematics
Applied mathematics connects mathematical theory with practical problems arising in science, engineering and industry. Researchers develop mathematical models and analytical techniques to study complex systems and physical phenomena.
Differential Equations
Differential equations describe relationships between quantities and their rates of change. They are essential tools for modeling change in fields such as engineering, physics, economics and biology.
Discipline-Based Education Research (DBER)
Faculty also study the teaching and learning of mathematics and the broader role of mathematics within scientific disciplines. This work examines how mathematical concepts are taught, learned and applied across fields.
Discrete Mathematics
Discrete mathematics focuses on mathematical structures that are fundamentally finite or countable. Research areas include combinatorics, graph theory and other discrete structures that play important roles in computer science, optimization and network analysis.
Statistics & Data Science
Statistics focuses on the collection, analysis and interpretation of data. Research areas include statistical modeling, data analysis and methods that support applications in science, engineering, business and public policy.
Topology & Geometry
Topology explores the properties of space that remain unchanged through continuous deformation, such as stretching or bending, but not tearing or gluing. The field grew from geometry, set theory and analysis, with key concepts including connectedness, compactness, dimension and transformation.
At Auburn, topology research includes algebraic topology, continuum theory and set-theoretic topology.
Algebra
Analysis & Stochastic Analysis
Applied Mathematics
Differential Equations
Discipline-Based Education Research (DBER)
Discrete Mathematics
Numerical Analysis
Statistics & Data Science
Topology & Geometry
