Writing

Papers

My papers in reverse chronological order:

1. Quadratic points on double plans with Nathan Chen, Hector Pasten, Isabel Voight. arXiv preprint (2025).
2. Obstructions to unirationality for product-quotient surfaces over F̄_p. arXiv preprint (2025).
3. Appendix to ‘Complex Bott Periodicity in algebraic geometry’ by Hannah Larson, Ravi Vakil. Submitted 2025.
4. Nowhere vanishing 1-forms on 4-folds. Submitted April 2025.
5. A non-isotrivial smooth Fano fibration over P¹ not intended for publication.
6. Appendix to ‘K-stability of Thaddeus’ moduli of stable bundle pairs on genus two curves’ by Junyan Zhao. Submitted December 2024.
7. SL₂-character varieties of 2-generated groups and failure of weak integrality. with Francisco García-Cortés. Submitted October 2024.
8. Nowhere vanishing 1-forms on varieties admitting a good minimal model. Submitted October 2024.
9. Curves on complete intersections and measures of irrationality. with Nathan Chen, Junyan Zhao. Submitted June 2024.
10. The fibering genus of Fano hypersurfaces. with Nathan Chen, Lena Ji, David Stapleton. Submitted August 2023.
11. Nowhere vanishing holomorphic one-forms and fibrations over abelian varieties. with Nathan Chen, Feng Hao. Advances in Mathematics (to appear).
12. Heating of Milky Way disc stars by dark matter fluctuations in cold dark matter and fuzzy dark matter paradigms. with Philip Mocz, Jeremiah P Ostriker. Monthly Notices of the Royal Astronomical Society (2019).
13. Investigating skewness to understand gene expression heterogeneity in large patient cohorts. with Henry T. Williams, Jessica C. Mar. BMC Bioinformatics 20 (2019).

Theses

My undergraduate thesis on embedding curves in toric surfaces advised by Aise Johan de Jong.

Talks

Here are some of the talks I have given in various contexts.

Stanford Learning Seminars

1. Jet bundles in enumerative geometry
2. Artin’s Axioms and Infinitesimal Deformation Theory
3. Method of Deligne-Illusie
4. Bend and Break
5. Stack of L-parameters
6. Variations of Hodge Structures

Just for Fun

1. Ehrhart Polynomials

For Undergrads

Talks I have given at Columbia UMS and Stanford SUMO

1. Ax-Grothendieck Theorem
2. Godel’s Incompleteness Theorems
3. Galois Representations and Elliptic Curves
4. Diophantine Approximation
5. Kaluza-Klein Theory

Talks for Splash

I taught a six-week course on elliptic curves at HSSP:

• Notes from Lectures 1, 2, 3, 4
• Advanced notes
• Background material and diagnostic for the class.

Random talks I have given at various splashes (Columbia, MIT, Stanford)

1. The Baire Category Theorem
2. Measure Theory
3. Quaternions and the Hopf Fibration
4. p-adic numbers
5. General Relativity
6. Liouville Numbers

Class Notes and More

I usually live-TeX my notes from classes, seminars, and lectures. You can find them on github