Research Interests

Research Interests

During my graduate studies, I worked with my advisor, Dr. Krystal Taylor, to answer questions at the intersection of harmonic analysis, number theory, and geometric measure theory. Our primary project was counting lattice points on surfaces (with and without vanishing curvature) utilizing techniques in harmonic analysis.

Our paper, Lattice Points Close to the Heisenberg Spheres, was published in La Matematica in March 2023, and can also be found on arXiv. My dissertation, Lattice Point Counting through Fractal Geometry and Stationary Phase for Surfaces with Vanishing Curvature, is available on OhioLink and ProQuest.

I have recently started reading more on lattice-based cryptography as a post-quantum alternative to RSA and other systems. I am interested in pivoting my research into the cryptology or quantum sphere as a natural extension of my mathematics background and earlier cryptographic research.

Current Research

I am currently working on a research project studying the practical effect of the circuit design on the implementation of asymmetric phase-covariant cloning applied to the BB84 Protocol for quantum key distribution. This is an extension of my QuForce Innovation Fellows project (working with Brian Pigott and Hardik Routray) to determine the theoretical optimal strategy for asymmetric cloning on a quantum channel (minimizing disturbance while maximizing information gain). The experimental aspect of our research is performed on IonQ’s 11-qubit quantum computer (utilizing the Qiskit SDK) and on IBM’s publicly available quantum computers. We are currently compiling our results into a paper, following my presentation of our work at APS March Meeting 2023.