# Mathematics Faculty Research Areas

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## Additional Information

## Rida Benhaddou

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

## 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.