Mathematics Faculty Research Areas

Rida Benhaddou

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• Nonparametric statistics, inverse problems in statistics, empirical Bayes estimation.

William Clark

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• Applied Mathematics
• Nonlinear Dynamics
• Geometric Mechanics
• Numerical Analysis

Alexei Davydov

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• Algebra: representation theory, Hopf algebras, quantum groups;
• Category theory: monoidal categories;
• Mathematical Physics: conformal field theories

E. Todd Eisworth

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• General Topology, Set Theory

Adam Fuller

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• Operator Algebras
• Multivariate Operator Theory

Allyson H. Hallman-Thrasher

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Dan Guralnik

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• Hybrid dynamical systems
• Mobile agent networks
• Assured AI
• Geometric group theory
• Clustering
• Related fields

Wei Lin

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• Regression analysis, nonparametric statistics, dimension reduction and multivariate analysis.

Sergio Lopez-Permouth

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• Noncommutative rings and their modules, algebraic coding theory.

Vardges Melkonian

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• Combinatorial Optimization, Network Design Problems, Approximation Algorithms, and Applications of Operations Research.

Martin J. Mohlenkamp

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• Applied Mathematics
• Scientific Computing
• Optimization
• Numerical Analysis
• Numerical Methods in High Dimensions
• Machine Learning
• Data Science

Tatiana Savin

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• Applied analysis, analytic continuation of solutions to elliptic differential equations
• Partial differential equations, mathematical modeling in materials science.

Vladimir Uspenskiy

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• Functional analysis, and other related areas.
• General Topology, Topological Algebra
• Topological Dynamics. Topological groups and enveloping semigroups.

Vladimir Vinogradov

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• Stochastic Analysis, Stochastic Models of Financial and Actuarial Mathematics, Extreme Value Theory, Distribution Theory, Levy and Related Stochastic Processes, Markov and Branching Processes, Fluctuation Theory, Generalized Linear Models, Saddlepoint Approximations; Estimation, Particle Systems, Models of Population Genetics, Large Deviations, Asymptotic Expansions, Strong Limit Theorems, Weak Convergence, Special Functions

Qiliang Wu

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• Dynamical systems: nonlinear dynamics; traveling waves; pattern formation; infinite dimensional dynamical systems.
• Amphiphilic morphology. Turing patterns. Ecology.
• Qualitative analysis of partial differential equations, with an emphasis on the existence, stability and bifurcation analysis of various pattern forming systems arising from physics, chemistry and biology.

Todd Young

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• Bifurcation theory and some ergodic theory in Smooth Dynamical Systems.
• Bifurcation theory of Random Dynamical Systems.
• Cell cycle dynamics, particularly in Yeast. New methods for binary classification problems in biomedical informatics.
• Qualitative theory of Ordinary Differential Equations and Random Differential Equations,
• Bifurcations theory of ODE and RDE systems.