Research

I am interested in a wide variety of problems in applied Mathematics, including scientific computing, numerical analysis, optimization, machine learning and image processing. Below is a list of my on-going projects

Adversarial Path planning

Computation of least visible path around unknown observer locations using fast marching methods and non-smooth optimization. Joint work with Professor Alex Vladimirsky.
  • Numerical Analysis
  • Optimization
  • Game Theory

Inverse Problem in Electromagnetic Wave Propagation

Making inference about the environment using radars by exploiting the low rank structure of the field. Joint work with Professor Christoper Earls and Professor David Bindel.
Presentation
  • Inverse Problem
  • Scientific Computing
  • Numerical Analysis

Continuous Conjugate Gradient

Generalizing the Krylov subspace method to continuous and differential operators. Joint work with Professor Alex Townsend.
  • Numerical Analysis
  • Optimization
  • Scientific Computing

Combining Image Processing using Non-smooth Optimization

Perfoming registration, fusion and superresolution of images all at once using state of the art non-smooth optimization methods.
  • Inverse Problem
  • Optimization
  • Image Processing