Research

As I mention on the home page, my main mathematical interests are in Ergodic Theory and (Analytic) Number Theory. Broadly speaking, I am intrigued by connections that exist between these fields. My research projects to date have come from across these fields and others, including Differential Topology, Convex Analysis, and more.

Publications/Preprints

  1. Weakly Mixing Systems with Dense Prime Orbits (Colloquium Mathematicum 169 (2022), 11-23; arXiv:2010.09812)

  2. Extremizers of the J functional with respect to the d_1 metric; joint with Sam Bachhuber, Benjamin Christophel, and Tamás Darvas (to appear in Analysis Mathematica)

In preparation

None (...for now)

Talks and Presentations

  1. Free Groups - Dr. Lewis Bowen's summer 2022 reading group on Probability and Geometry on Groups, June 2022

  2. Topological Entropy - Dr. Lewis Bowen's summer 2022 reading group on Entropy, June 2022

  3. An Introduction to Ergodic Theory and Prime Orbits - UT Sophex, February 2022 (slides)

  4. An Introduction to Prime Number Theory - UT Sophex, December 2021 (slides)

  5. Frobenius' Theorem on Integrable Distributions - UMD Math 742: Geometric Analysis, December 2020 (slides)

  6. Clifford Algebras and Spinor Groups - UMD Math 744: Lie Groups, December 2020 (slides)

  7. Embedded Cobordisms - UVa Topology REU, July 2020 (slides)

  8. Exponential Mixing for Skew Products - UMD Independent Reading Course, May 2020 (slides)

  9. Weakly Mixing Systems with Dense Prime Orbits - Penn State Dynamics Workshop, September 2019 (slides)

  10. A Topological Proof of the Fundamental Theorem of Algebra - UMD DRP Presentation, December 2018

  11. A Proof of the Prime Number Theorem - UMD Math 299N: Topics in Number Theory, December 2017

  12. A Proof of the Prime Number Theorem - MBHS Complex Analysis, May 2017

  13. The Historical Development of Non-Euclidean Geometries - MBHS Logic Math, October 2016