Research

Papers

• Localization Of The 1D Non-Stationary Anderson Model (to come)

Projects

Master’s Thesis

Dynamical Systems and Matching Symmetry in β-Expansions

September 2021 - June 2022

Self-motivated study of topological and ergodic dynamical systems, advised by Dr. Erin Pearse. Consists of an exposition of known theory as well as an exploration of new directions by investigating the matching symmetry that arises in β-shifts and β-expansions.

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FROST Summer Research

Flat Portions on Numerical Ranges of Nilpotent Matrices

June 2021 - September 2021

In partnership with Kelsey Lowrey and Timothy Royston under the supervision of Dr. Linda Patton. Explored a conjecture about the maximum number of flat portions on the boundary of the numerical range of a general nilpotent n × n matrix using Mathematica and other tools. Using the associated Kippenhahn curve and its algebraic geometry, we made key observations about the behavior of singularities and their effects on the flat portions on the boundary of a numerical range.

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FROST Summer Research

Faithfulness of the Burau Representation for B4

June 2019 - December 2019

In partnership with Joel Pion and Cameron Fredrickson under the supervision of Dr. Anton Kaul. Studied braid groups and in particular the Burau representation of the B4 group. Applied the algebraic theory of buildings and modules to the question of faithfulness. Research extended into the school year due to promising preliminary results found.