Department of Mathematics

Applied Mathematics and Numerical Analysis

The research interests of the Applied Mathematics and Numerical Analysis group encompass analysis, asymptotic methods, and development of state of the art numerical schemes applied to material science, optics, molecular biology, plasmas and kinetic problems, signal processing, large dimensional data sets, persistent homology, inverse problems, and optimization.

Areas of particular focus include
  • Mutli-physics and multi-scale modeling of stochastic systems arising in biochemical networks and nano-optics.
  • Development of models of solvation, minimal molecular surfaces, and ion channels
  • Analysis of vortices in superconductors
  • Applications of persistent homology to artist identification
  • Computational harmonic analysis with applications to phase retrieval and compressed sensing
  • Analysis of gene regulatory networks
  • Network formation in amphiphilic materials with applications to fuel cells, Lithium ion batteries, and polymer solar cells
  • Development and analysis of higher order numerical schemes, including discontinuous Galerkin methods, integral deferred correction, fully Lagrangian schemes with applications to Hamilton-Jacobi equations, kinetic systems, and plasmas
  • Fast numerical methods for high-frequency wave propagation, Hamilton-Jacobi equations, Gaussian beams, traveltime tomography, seismic imaging, medical imaging, and inverse gravimetry.
  • Regularization of inverse problems with applications to imaging
  • Applications of homotopy continuation methods to polynomial systems