## Gene Abrams, Ph.D.

**General Area of Expertise: **Algebra

**Specific Research Topics: **

- Associative rings and modules
- Leavitt algebras and connections to C*-algebras
- Morita equivalences between module categories

## Oksana Bihun, Ph.D.

**General Area of Expertise: **Applied Mathematics & Analysis

**Specific Research Topics: **

- Mathematical physics
- Integrable dynamical systems
- N-body problems
- Orthogonal polynomials and special functions
- Spectral (numerical) methods for solving differential equations

## Robert Carlson, Ph.D.

**General Area of Expertise: **Analysis & Differential Equations

**Specific Research Topics: **

- Analysis on graphs
- Spectral theory for quantum graphs

## Radu Cascaval, Ph.D.

**General Area of Expertise: **Applied Analysis & Computational Mathematics

**Specific Research Topics: **

- Spectral theory of integrable systems
- Nonlinear PDEs and fluid mechanics
- Applications in optical communications, physiology & medicine

## Sarbarish Chakravarty, Ph.D.

**General Area of Expertise: **Differential Equations & Applied Math

## James Daly, Ph.D.

**General Area of Expertise: **Harmonic Analysis

**Specific Research Topics: **

- Singular integral operators
- Multiplier operators
- Fourier and Walsh series
- Dyadic analysis

## Zachary Mesyan, Ph.D.

**General Area of Expertise: **Algebra

**Specific Research Topics: **

- Rings
- Groups
- Semigroups
- Linear algebra

## Greg Morrow, Ph.D.

**General Area of Expertise: **Probability & Statistics

**Specific Research Topics: **

- Percolation theory
- Large deviations

## Greg Oman, Ph.D.

**General Area of Expertise: **Algebra and Logic

**Specific Research Topics: **

- Ring theory
- Abelian group theory
- Set theory
- Semigroup theory
- Problem posing

## Barbara Prinari, Ph.D.

**General Area of Expertise: **Non-Linear Waves and Coherent Structures

**Specific Research Topics: **

- Inverse scattering transform for continuous and discrete integrable systems
- Solvability for the nonlinear Schrödinger equation
- Solving the initial value problem for nonlinear 2+1 dimensional PDEs with potentials that do not decay at spatial infinity
- Multicomponent nonlinear Schrödinger systems with nonvanishing boundary conditions

## K.M. Rangaswamy, Ph.D.

**General Area of Expertise: **Algebra

**Specific Research Topics: **

- Abelian groups
- Associative rings and modules

## Rinaldo Schinazi, Ph.D.

**General Area of Expertise: **Probability & Statistics

**Specific Research Topics: **

- Probability models in population biology and epidemiology
- Interacting particle systems

## Yu Zhang, Ph.D.

**General Area of Expertise: **Probability & Statistics

**Specific Research Topics: **

- Mathematical physics and biological models, including percolation theory, first passage percolation, infinite particle systems and random graphs
- General probability theory, including the central limit theorem by martingale approaches