Preprints

• An effective Siegel theorem for positive integral points on acyclic cluster varieties.
  (formerly "Diophantine enumeration of Dynkin friezes")
• The Harris–Venkatesh conjecture for derived Hecke operators II: a unified Stark conjecture.
• The Harris–Venkatesh conjecture for derived Hecke operators I: imaginary dihedral forms.
  2023 ICCM Best Doctoral Thesis Award, Gold Prize (for theses by mathematicians of Chinese descent)

Articles (arXiv)

Research

• The Harris–Venkatesh conjecture for derived Hecke operators III: local constants.
  Annales Mathématiques Blaise Pascal, to appear.
• Mod ℓ gamma factors and a converse theorem for finite general linear groups,
  with J. Bakeberg, M. Gerbelli-Gauthier, H. Goodson, A. Iyengar, and G. Moss.
  Documenta Mathematica, to appear.
• Modular Gelfand pairs and multiplicity-free representations.
  International Mathematics Research Notices, 2024(7): 5490–5523, 2024.
  Erratum with P. Allen and P. Wake.
• A Galois–dynamics correspondence for unicritical polynomials.
  Arnold Mathematical Journal, 7(3): 467–481, 2021.
• Section rings of ℚ-divisors on minimal rational surfaces, with A. Landesman and R. Ruhm.
  Mathematical Research Letters, 25(4): 1329–1357, 2018.
• Spin canonical rings of log stacky curves, with A. Landesman and R. Ruhm.
  Annales de l'Institut Fourier, 66(6): 2339–2383, 2016.

Proceedings & surveys

• Towards the p-adic derived Hecke algebra for weight one forms.
  RIMS Kôkyûroku, to appear.
• The abcd conjecture, uniform boundedness, and dynamical systems.
  Publications Mathématiques de Besançon, 2024(1): 119–134, 2024.
• Grupos ortogonales sobre cuerpos de característica positiva.
  Revista de Matemática: Teoría y Aplicaciones, 29(2): 159–176, 2022.

Other

• Flushing: the melting pot's melting pot,
  with D. Le and photography by C. Trinh.
  In Made Here: Recipes & Reflections From NYC's Asian Communities, pp.125–127.
  New York: Send Chinatown Love, 2023. ISBN 9798218247164.

Books

• Made Here: Recipes & Reflections From NYC's Asian Communities (co-editor and research).
  New York: Send Chinatown Love, 2023. 352pp. ISBN 9798218247164.
  2024 James Beard Foundation Book Award Nominee

Theses

• The Harris–Venkatesh conjecture for derived Hecke operators.
  Ph.D. thesis, Columbia University, 2023. 155 pp.
  Split between two preprints above: The Harris–Venkatesh conjecture for derived Hecke operators I and III.
• The Grunwald–Wang theorem and isomorphic radical extensions.
  Honors thesis, Stanford University, 2017. 24 pp.

Notes

• Problem list from "The Mordell conjecture 100 years later"
  A problem list from a conference at MIT, 2024.
• Problem list from "Analytic, arithmetic, and geometric aspects of automorphic forms"
  A problem list from a workshop at AIM, 2024.
• Errata to Automorphic Forms and Representations by Daniel Bump
  An expansion of Daniel Bump's list, updated 2024.
• Bernstein center and Scholze's base change
  A talk in the Seminar on the Proof of Local Langlands at Columbia, 2019.
• L-factors and ε-factors
  A talk in the Seminar on the Proof of Local Langlands at Columbia, 2018.
• Weil–Deligne representations I
  A talk in the Local Langlands Seminar at Columbia, 2018.
• The Baker–Campbell–Hausdorff formula
  A presentation in the Lie Groups & Representations course taught by Eric Urban at Columbia, 2017.
• Poincaré duality
  An exposition for a reading course with Bruno Klingler at the Université Paris–Diderot, 2016.

Computer science & software

• Humanity's last exam,
  with L. Phan, A. Gatti, Z. Han, N. Li et al.
• Fully homomorphic encryption using multivariate polynomials,
  with M. Tamayo-Rios, J.-C. Faugère, L. Perret, and P. H. How.
  IACR Cryptology ePrint Archive, 458, 2017.
• Lynda.com / LinkedIn Learning
  Ratings & recommendations algorithms for educational videos, 2016.
• Kryptnostic
  Work on open-source fully homomorphic encryption algorithms & searchable encryption algorithms, 2015.
• Evil Hangman
  A Java hangman game that cheats against you as you play, 2015.