Faculty Research Interests

General Area of Expertise
More Specific Research Topics
  • Associative rings and modules
  • Leavitt algebras and connections to C*-algebras
  • Morita equivalences between module categories
Analysis & Differential Equations
  • Analysis on Graphs
  • Spectral theory for quantum graphs
Applied Analysis & Computational Mathematics
  • Spectral theory of integrable systems
  • Nonlinear PDEs and fluid mechanics
  • Applications in optical communications, physiology & medicine
Differential Equations
& Applied Math
Zak Mesyan Algebra
  • Rings
  • Groups
  • Semigroups
Probability and Statistics
  • Percolation Theory
  • Large Deviations
Algebra and Logic
  • Ring Theory
  • Abelian Group Theory
  • Set Theory
  • Semigroup Theory
  • Problem Posing
Non-linear waves and Coherent Structures
  • 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
  • Abelian Groups
  • Associative Rings and modules
Probability and Statistics
  • Probability models in population biology and epidemiology
  • Interacting particle systems
Probability and Statistics
  • 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