My current research centers around box lattice models and structured prediction. I am broadly interested in program synthesis, deep learning, optimization techniques, and interpretability. I enjoy exploring the theoretical underpinnings of machine learning and identifying areas where my mathematical background can be leveraged to increase understanding or improve performance. I am also interested in game theory, parallel and distributed algorithms, programming languages and theory of computation.
My mathematics background is focused primarily in analysis, with an emphasis on partial differential equations. My coursework also included differential geometry and topology, probability, stochastic processes, and combinatorics.
In computer science, I focused on artificial intelligence, machine learning, and deep learning. I have also taken courses in programming languages, computational theory, and information theory, as well as independently studying game theory.
My PhD research concentrated in the area of partial differential equations, using techniques from harmonic analysis, calculus of variations, and Riemannian geometry. My thesis was comprised of two parts, the first of which proved bounds for the Sobolev norms of solutions to the Nonlinear Schrödinger equation in dimensions 2, 3, and 4. The second part proved a uniqueness theorem for solutions to a class of degenerate elliptic partial differential equations. The thesis is published online, you can access it from Scholarworks:
I received a BA in mathematics and economics from Central Connecticut State University, and decided to pursue a PhD in mathematics. While in the graduate program for math at UMass Amherst I took a course on artificial intelligence which sparked an interest in deep learning and machine learning in general. While continuing to finish my PhD in mathematics, I also completed the requirements for a MS in Computer Science with a particular emphasis on machine learning.