# Research Interests

##
Research

## 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

## Peter Braza, Ph.D.

**General Area of Expertise: **Applied Mathematics

**Specific Research Topics: **

- Population dynamics
- Physical applied mathematics

## 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

## Justin Cole, Ph.D.

**General Area of Expertise: **Applied Mathematics & Nonlinear Waves

**Specific Research Topics: **

- Modeling of wave phenomena in dispersive media
- Solitons
- Asymptotic and perturbative approximations
- Inverse scattering transform
- Numerical solution of ordinary and partial differential equations

## 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 & 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 & 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

## Mark Tomforde, Ph.D.

**Specific Research Topics: **

- C*-algebras and K-theory
- Graph C*-algebras and Leavitt path algebras
- Rings, modules, and Morita equivalence
- Interactions of algebra and analysis

## 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