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

# Publications.

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

**Abstract:** We characterize all infinite-dimensional graded virtual modules for Thompsonâ€™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 orderDate/Time/Title TBA

*What is...? Seminar*

Online Seminar.

Date/Time/Title TBA

*Specialty Seminar in Partition Theory, q-Series, and Related Topics**.*

Online Seminar.

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

Virtual "Pre-Seminar" talk aimed at grad students, March 9th, 2021. (Link, Slides)

**Elliptic Curves and Moonshine; ***UW Algebra and Algebraic Geometry Seminar*

Online Seminar, March 9th, 2021. (Link, Slides.)

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

Online Seminar, February 19th, 2021. (Link.)

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

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

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

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

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

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

### (Contributed)

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

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

**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.)

**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.

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

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

**Elliptic Curves and Moonshine;***Madison Moduli Weekend.*

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

**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.)