Dissertation Research
My dissertation applies Hamilton-Jacobi theory to two classes of optimal control problems. Each problem has discontinuous dynamics and lagrangian,
meaning that the standard result that the associated value function solves the appropriate classical Hamilton-Jacobi equation does not hold.
New techniques must be developed to handle the discontinuous and non-lipschitz dynamics.
Interdisciplinary Work
Stemming from my work at an
IMA workshop,
I also study denoising spectra obtained from polystyrenes in a mass spectrometer. Such spectra have large amounts of nonstationary noise.
At this workshop we began creating an algorithm to model the chemical background noise and then use this to denoise spectra obtained with an analyte.
I am working on making this algorithm unbiased, using segmentation algorithms to improve the denoising process.
