**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?"

# Publications.

**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**Weight 3/2 Moonshine for the Thompson group****;***Joint Mathematics Meetings**;*

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

**Moonshine****;***John Conway Spirited Seminar Series*, Lahore University of Management Sciences.

Online Seminar; November 1st, 2021.

**What is... Moonshine?***What is...? Seminar*

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

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

Online Seminar; September 30th, 2021.

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

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

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

Online Seminar; March 9th, 2021.

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

Online Seminar; February 19th, 2021.

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

Virtual Conference; January 8th, 2021.

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

Online Seminar; September 16th, 2020.

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

Online Seminar; September 1st, 2020.

### (Contributed)

*in reverse chronological order**Moonshine a****n****d Ell****iptic Curves****;***Women in automorphic forms*

Online Conference; September 20th, 2021.

**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.)

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

Online Conference; September 19-20th, 2020.

**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.)