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

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

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

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

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

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

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

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

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

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

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