Math

I am a mathematics PhD student working with Amie Wilkinson at the University of Chicago. My interests are in dynamical systems and analysis.

I currently work in smooth ergodic theory, on the dimension theory of random diffeomorphisms. The basic question there is how the dimension of invariant and stationary measures is determined by Lyapunov exponents and entropy.

I have also worked on harmonic analysis, descriptive set theory, and function spaces arising in PDE, including a scale of anisotropic Sobolev spaces adapted to traveling wave problems.

Papers/Preprints

Exact dimensionality of stationary measures for nonuniformly conformally contracting random diffeomorphisms

Preprint · arXiv:2609.10538

On a scale of anisotropic Sobolev spaces

with Ian Tice · Communications on Pure and Applied Analysis

Other

Point-to-Set Principle for Measures

These are some notes I wrote for my presentation for the graduate Topics in Logic course at UChicago on complexity theory and the point-to-set principle (there are definitely some minor math/formatting errors). They included a known but unpublished result in the point-to-set principle for metric entropy.

On a Class of Anisotropic Sobolev Spaces, and an Extension of an Elementary Integral

This was my master’s thesis for the CMU math honors program. They include my published work on anisotropic Sobolev spaces, along with exposition of an extension of Dieudonne’s Cauchy integral, or regulated integral. I extended this integral to work in very general settings and integrate functions taking values in locally convex spaces.

Automatic Continuity of Group Homomorphisms

These are some notes I wrote for the Dynamics of Polish Groups class I took at Carnegie Mellon on automatic continuity of group homomorphisms

Topology Supplement

These are some notes I wrote for my recitations for the Math Studies Analysis classes at Carnegie Mellon to supplement the standard course notes

Singular Integrals

Spring 2023 Advanced Real Analysis notes

Convolutions and Approximate Identities

Math Studies Analysis II seminar notes

Complemented Subspaces

Math Studies Analysis II seminar notes