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Mathematics Faculty Research Areas

Rida Benhaddou

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

William Clark

Applied Mathematics
Nonlinear Dynamics
Geometric Mechanics
Numerical Analysis

Alexei Davydov

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

E. Todd Eisworth

General Topology, Set Theory

Adam Fuller

Operator Algebras
Multivariate Operator Theory

Archil Gulisashvili

Financial Mathematics: General stochastic asset price models; classical stochastic volatility models (Hull-White, Stein-Stein, Heston); Gaussian Volterra type stochastic volatility models; fractional and rough models; scaling properties of stochastic volatility models; models with jumps; option pricing theory; asymptotic behavior of stock price distribution densities, option pricing functions, and the implied volatility; moment explosions, geometrical methods in financial mathematics; Heston geometry, large and moderate deviation principles; the G\"{a}rtner-Ellis theorem.
Stochastic Processes: Non-homogeneous Markov processes, time-reversal and duality theory for Markov processes, applications of Markov processes to parabolic initial and final value problems.
Semigroup Theory and Propagator Theory: Schroedinger semigroups and Feynman-Kac propagators; non-autonomous Kato classes of functions and measures; smoothing properties of Schroedinger semigroups.

Allyson H. Hallman-Thrasher

Wei Lin

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

Sergio Lopez-Permouth

Noncommutative rings and their modules, algebraic coding theory.

Vardges Melkonian

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

Martin J. Mohlenkamp

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

Tatiana Savin

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

Vladimir Uspenskiy

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

Vladimir Vinogradov

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

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

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.