Research

My research involves moonshine and related aspects of number theory. I'm particularly interested in the question: "Can moonshine help solve problems in number theory?"

Slides for a 5-min lightning talk on my work can be found here.

Preprints.

  1. Elliptic Curves and Thompson's Sporadic Simple group; arXiv. (submitted)

We characterize all infinite-dimensional graded virtual modules for Thompson’s sporadic simple group, whose graded traces are certain weight 3/2 weakly holomorphic modular forms satisfying special properties. We then use these modules to detect the non-triviality of Mordell--Weil, Selmer and Tate--Shafarevich groups of quadratic twists of certain elliptic curves.

Talks.

(Invited)

*in reverse chronological order
  1. Elliptic Curves and Moonshine; Vanderbilt University Number Theory Seminar.

Online Seminar, September 1st, 2020. (Zoom information, Recording, Slides.)

  1. Elliptic Curves and Moonshine; Number Theory Seminar, University of Georgia.

Online Seminar, September 16th, 2020. (Zoom information, Slides.)

  1. Elliptic Curves and Moonshine; Joint Mathematics Meetings; AMS Special Session on Algebraic and Arithmetic Geometry.

Virtual Conference; January 8th, 2021. (Link).

(Contributed)

*in reverse chronological order
  1. Elliptic Curves and Thompson's Sporadic Group; New Developments in Number Theory.

Virtual Contributed talk series; March 2nd, 2021. (Organized by POINT.)

  1. Elliptic Curves and Thompson's group; Modularity in Quantum Systems.

Online Conference; December 15th, 2020 (``Gong show'' style mini-presentation.)

Recording (jump to 13:00); Slides.

  1. Elliptic Curves and Thompson's group; PAlmetto Joint Arithmetic, Modularity, and Analysis Series (PAJAMAS).

Online Conference; September 19-20th, 2020. (Recording, Slides.)

  1. Elliptic Curves and Moonshine; Madison Moduli Weekend.

Online Conference; September 26-27th, 2020. (5-minute "Lightning talk." Slides)

  1. Measuring the Role of Curiosity in Student Engagement and Performance; The Advanced Graduate Teaching Fellowship Symposium.

Virtual Symposium; May 5th, 2020. (A Teaching-as-Research Project; Slides.)