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

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

  • Rings
  • Groups
  • Semigroups
  • Linear Algebra

Probability & Statistics
  • Percolation Theory
  • Large Deviations

Algebra and Logic
  • Ring Theory
  • Abelian Group Theory
  • Set Theory
  • Semigroup Theory
  • Problem Posing

Non-linear waves and Coherent
  • 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 & Statistics
  • Probability models in population biology and epidemiology
  • Interacting particle systems

Probability & 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