Research

Photo taken in Atlanta, GA

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. For a quick introduction to moonshine, you can watch this 30-minute talk I gave on the topic.

Publications.

  1. Elliptic Curves and Thompson's Sporadic Simple group; arXiv version; published version.

Abstract: 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.

Citation: Journal of Number Theory, Volume 224, 2021, Pages 274-306, ISSN 0022-314X, https://doi.org/10.1016/j.jnt.2021.01.015.;

Talks.

(Invited)

*in reverse chronological order
  1. Weight 3/2 Moonshine for the Thompson group; Joint Mathematics Meetings; AMS Special Session on Modular Forms and Combinatorics.

Seattle, Washington; January 5th-8th, 2022.

  1. Moonshine and Elliptic Curves; Rutgers Lie Group/Quantum Mathematics Seminar.

Online Seminar; November 12th, 2021.

  1. Moonshine and Arithmetic; John Conway Spirited Seminar Series, Lahore University of Management Sciences.

Online Seminar; November 1st, 2021.

  1. What is... Moonshine? What is...? Seminar at the University of Queensland.

120-min; Online Seminar; October 11th, 2021.

  1. Weight 3/2 Moonshine for the Thompson group; Specialty Seminar in Partition Theory, q-Series, and Related Topics.

Online Seminar; September 30th, 2021.

  1. What is... Moonshine? UW Algebra and Algebraic Geometry Seminar

30-min; Virtual "Pre-Seminar" talk aimed at grad students; March 9th, 2021.

  1. Elliptic Curves and Moonshine; UW Algebra and Algebraic Geometry Seminar

Online Seminar; March 9th, 2021.

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

Online Seminar; February 19th, 2021.

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

Virtual Conference; January 8th, 2021.

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

Online Seminar; September 16th, 2020.

  1. Elliptic Curves and Moonshine; Vanderbilt University Number Theory Seminar.

Online Seminar; September 1st, 2020.

(Contributed)

*in reverse chronological order
  1. Elliptic Curves and Moonshine; The Autumn Meeting of the Swedish Math Society.

Online Meeting/Uppsala, Sweden; Nov 19th, 2021

  1. Moonshine and Elliptic Curves; Women in automorphic forms at Universität Bielefeld.

Online Conference; September 20th, 2021.

  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; Women at the Intersection of Mathematics and Theoretical Physics.

Online Conference; February 22nd, 2021 (``Gong show'' style mini-presentation.)

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

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

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

Online Conference; September 19-20th, 2020.

  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.)