Writings and Publications

Publications

1. On Powerful Integers Expressible as Sums of Two Coprime Fourth Powers (with Noam D. Elkies). Res. Number Theory 9, 78 (2023) (proceedings of ANTS-XV 2022). doi: 10.1007/s40993-022-00415-9

Preprints

1. The Chow Ring Classes of \(\mathrm{PGL}_3\) Orbit Closures in \(\mathbb{G}(1, 5)\). 2022. [arXiv]

Research Articles in Preparation

1. Chow Classes of Varieties of Secant and Tangent Lines to a Projective Variety. Advisor: Hannah Larson. (Poster presented at SRI'25.)

Theses

1. Galois Cohomology (and the Isogeny Invariance of the Strong Birch and Swinerton-Dyer Conjecture for Abelian Varieties). Part III Essay, supervised by Jack Thorne. May 2025.
2. The Joys of the Atiyah-Singer Index Theorem. Undergraduate Senior Thesis, advised by Dan Freed and Joe Harris. March 2024. (Updated July 2025 to include minor corrections.)

Expository

1. Archimedean Local Fields
2. Some Remarks on Fundamental Groups and Cohomological Dimension
3. An Introduction to Clifford Algebras and Spin Groups
4. Elliptic K3 Surfaces
5. Hamiltonian Actions and Marsden-Weinstein-Meyer Reduction
6. Symplectic Geometry and Hamiltonian Mechanics (with Charley Hutchison)
7. Covariant Derivatives, Connections, and Curvature
8. The Character Table of the Nonabelian Group of Order \(pq\)
9. An Introduction to Modular Jacobians
10. Rectangular Circumhyperbolae

Lecture Notes

Graduate Level

1. Mathematical Ghostbusters: Despookifying Spectral Sequences (in progress)
2. Cohomology of Curves
3. Commutative Algebra (in progress)

Undegraduate and High School Level

1. Plane Algebraic Curves
2. A Second Course in Real Analysis (in progress)
3. Representation Theory Review Notes
4. Math 57: Introduction to Group Theory