Papers
Note: papers are listed in reverse chronological order of arXiv posting.
2026
-
Forcible groups and Frattini covers (with
Sean Eberhard,
Robert M. Guralnick, and
Gareth Tracey).
Submitted. [PDF] -
On nearly consecutive sequences without long arithmetic progressions (with
Jacob Fox).
Submitted. [PDF] -
More sum-product type counterexamples: products with shifts and AA+A (with
Oliver Roche-Newton and
Audie Warren).
Submitted. [PDF] -
Dirac subgraphs of powers of cycles are Hamiltonian (with
Richard Lang,
Alp Müyesser, and
Mathias Schacht).
Submitted. [PDF] -
The sum-product conjecture is false for real numbers (with
Thomas F. Bloom,
Will Sawin, and
Dmitrii Zhelezov).
Submitted. [PDF]
2025
-
Abelian structure in approximate groups and Alon's conjecture on Ramsey Cayley graphs.
Submitted. [PDF] -
Words with Repeated Letters in a Grid (with Zachary Halberstam).
Submitted. [PDF] -
Statistics of Erdős-Rényi random numerical semigroups (with
Noah Kravitz and
Santiago Morales).
Eur. J. Comb., 2026. [PDF] -
Rainbow Trees in Hypercubes (with
Nicholas Crawford,
Maya Sankar, and
Sam Spiro).
Submitted. [PDF] -
Expansion in Distance Matrices (with
John Byrne, Jacob Johnston, and
Michael Tait).
Submitted. [PDF]
2024
-
More unit distances in arbitrary norms (with
Josef Greilhuber and
Jonathan Tidor).
Bull. Lond. Math. Soc., 2025. [PDF] -
Lower bounds for sphere packing in arbitrary norms.
Submitted. [PDF]
2023
-
Equiangular lines and large multiplicity of fixed second eigenvalue.
Submitted. [PDF]
2021
-
Graphs with high second eigenvalue multiplicity (with
Milan Haiman,
Shengtong Zhang, and
Yufei Zhao).
Bull. Lond. Math. Soc., 2022. [PDF] -
On a Mertens-type conjecture for number fields (with
Daniel Hu, Ikuya Kaneko, and Spencer Martin).
Math. Proc. Camb. Phil. Soc., 2024. [PDF] -
Order of Zeros of Dedekind Zeta Functions (with
Daniel Hu, Ikuya Kaneko, and Spencer Martin).
Proc. Amer. Math. Soc., 2022. [PDF]
AI Papers
This section contains papers of mine, of various types, which (in my judgment) consist primarily of mathematics which was done by generative AI instead of by human authors.2026
-
A new lower bound for two-color van der Waerden numbers (with
Marcelo Campos and
Jacob Fox).
Submitted. [PDF] - Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the Erdős Problems (Tony Feng, Trieu Trinh, Garrett Bingham, Jiwon Kang, Shengtong Zhang, Sang-hyun Kim, Kevin Barreto, Carl Schildkraut, Junehyuk Jung, Jaehyeon Seo, Carlo Pagano, Yuri Chervonyi, Dawsen Hwang, Kaiying Hou, Sergei Gukov, Cheng-Chiang Tsai, Hyunwoo Choi, Youngbeom Jin, Wei-Yuan Li, Hao-An Wu, Ruey-An Shiu, Yu-Sheng Shih, Quoc V. Le, Thang Luong). [PDF]