Research

My research lies at the intersection of dynamical systems and spectral theory. I am particularly interested in gap labeling and the spectral properties of dynamically defined operators.

Preprints

Dynamical Lifshitz Tails
with Grigorii Monakov (2026)
arXiv

On the Kotani–Last Conjecture for the Dirac Operator
with Nyah Davis, Long Li, and Hangqi Liang (2025)
arXiv

Publications

Gap labels and asymptotic gap opening for full shifts
with David Damanik and Jake Fillman
Journal of Spectral Theory 15 (2025), no. 3, 1383–1407.
arXiv · Journal

A scattering transform for graphs based on heat semigroups, with an application for the detection of anomalies in positive time series with underlying periodicities
with Bernhard G. Bodmann
Sampling Theory, Signal Processing, and Data Analysis 22, article 17 (2024).
arXiv · Journal

The Schwartzman Group of an Affine Transformation
with David Damanik and Jake Fillman
Journal of Spectral Theory 13 (2023), no. 4, 1281–1296.
arXiv · Journal

PhD thesis

Mind the Gap: Schwartzman Groups of Dynamically Defined Operators and Related Problems
Rice University, 2025
Thesis

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