I am interested in the analysis and development of numerical algorithms for machine learning. This covers algorithms to enable, accelerate, and optimize simulation and analysis of complex dynamical systems, as well as nonlinear manifold learning techniques, including data-driven approximations of Koopman and Laplace operators.

If you do not know about manifolds or manifold learning, you can read my informal introduction.

If you want to start learning programming, you can look at this list of resources to learn programming.

In addition to mathematical research, my collaborators and I work on applications such as gene pathway identification and system reconstruction from single-cell trajectories in Biology, tumor growth approximations in Medicine, and polymer/protein folding simulations in Chemical Engineering.

Take a look at the software tab for implementations I worked on.