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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.