Mathematics · Purdue University
First-year doctoral student in mathematics — interested in the regularity theory of nonlinear elliptic equations, with a continuing curiosity for planetary surfaces and the combinatorics of graphs.
I am a first-year Ph.D. student in the Department of Mathematics at Purdue University, having completed my B.S. in Mathematics with a minor in Physics at the University of Central Florida in the spring of 2025. My work sits at the intersection of analysis and geometry — at the moment, on questions of regularity: when, and how smoothly, do solutions of variational problems exist?
For my undergraduate honors thesis, supervised by Eduardo Teixeira, I wrote a self-contained exposition of Hilbert's 19th problem, developing De Giorgi's iteration scheme and the local Hölder continuity of weak solutions to elliptic equations in divergence form. That circle of ideas — the variational origin of an equation, the geometry of its level sets, the moduli by which it regularizes — is where I expect to spend the next several years.
Outside of analysis, I have been a long-running undergraduate research assistant in planetary science at UCF, studying the photometric properties of anorthositic exposures on the lunar surface, and I have worked on the combinatorial side of DNA self-assembly through the Summer@ICERM program at Brown. A few of those projects continue.
A self-contained development of the regularity theory of minimizers of elliptic functionals, culminating in local Hölder continuity for weak solutions to divergence-form equations.
Photometric analysis of mature and immature lunar craters using LRO Narrow Angle Camera imagery and Moon Mineralogy Mapper data. Pipeline development, digital terrain models, and Christiansen-feature maps.
Cataloguing optimal constructions for graphs of small order across scenarios one through three, and extending the analysis to stacked-prism, hexagonal-lattice, and web graphs.