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.