Research

Papers (Reverse chronological)

16. "The eigenvalues of random graphs follow the Tracy-Widom distribution." with Lior Silberman.

• Status: In preparation.

15. "Lower Bounds for the Capacity of Hypergraphs."

• Status: In preparation.

14. "The Chromatic Number of R^n with Multiple Forbidden Distances"

• Status: To appear in Mathematika.

• arXiv/PDF: https://arxiv.org/abs/2205.12312

13. "Upper Bounds For Families Without Weak Delta-Systems."

• Status: To appear in Combinatorica.

• arXiv/PDF: https://arxiv.org/abs/2203.13370

12. "Paley Graphs and Sárközy's Theorem In Function Fields."

• Status: The Quarterly Journal of Mathematics, 2022, https://doi.org/10.1093/qmath/haac035 

• arXiv/PDF:  https://arxiv.org/abs/2203.01293

11. "Monochromatic equilateral triangles in the unit distance graph."

• Status: Bulletin of the London Mathematical Society 52, no. 4, 687–692, 2020, MR4171395,  https://doi.org/10.1112/blms.12359

• arXiv/PDF:  https://arxiv.org/abs/1909.09856

10. "Exponential bounds for the Erdős-Ginzburg-Ziv constant."

• • Status: Journal of  Combinatorial Theory Series A  174, 105185, 19 pp, 2020 (MR4078996)

  • arXiv/PDF: https://arxiv.org/abs/1701.04942

9. "The partition rank of a tensor and k-right corners in F_q^n." 

• Status: Journal of Combinatorial Theory Series A 174, 105190, 25 pp, 2020 (MR4078997)

• arXiv/PDF: https://arxiv.org/abs/1701.04475

8. On cap sets and the group-theoretic approach to matrix multiplication." with Jonah Blasiak, Tom Church, Henry Cohn, Joshua A. Grochow, William F. Sawin and Chris Umans.

• • Status: Discrete Analysis , 2017:3, 2017 (MR3631613)

  • arXiv/PDF: https://arxiv.org/abs/1605.06702

7. "Upper bounds for sunflower-free sets."  with William F. Sawin.

• • Status: Forum Mathematics Sigma, Vol. 5, e15, 2017 (MR3668469)

  • arXiv/PDF: http://arxiv.org/abs/1606.09575

6. "Primitive Points in Lattice Polygons." with Imre Barany, Greg Martin and Sinai Robins.

• • Status: Canadian Mathematical Bulletin 63, no. 4, 850–870, 2020, (MR4176774), https://doi.org/10.4153/S0008439520000090

  • arXiv/PDF: http://arxiv.org/abs/1509.02201

Undergraduate Research

5. "On Improving Roth's Theorem in the Primes."

• • Status: Mathematika, Vol 61, Issue 01, Pages 49-62, 2015, (MR3333960) 

  • arXiv/PDF: http://arxiv.org/abs/1302.2299

4. "The Tail Distribution of the Sum of Digits of Prime Numbers." (MR3408577)

• • Status: Uniform Distribution Theory, 10, no. 1, Pages 63-68, 2015

  • arXiv/PDF: http://arxiv.org/abs/1211.2455

3. "The Median Largest Prime Factor."

• • Status: Journal of Number Theory, Issue 141, Pages 109-118, 2014.

  • arXiv/PDF: http://arxiv.org/abs/1207.0232

2. "The Average Largest Prime Factor."

• • Status: Integers, 13A, 2013

  • arXiv/PDF: The Average Largest Prime Factor

1. "Integers with a Predetermined Prime Factorization."

• • Status: Waterloo Mathematics Review, Vol II Issue 1, 2012.

  • arXiv/PDF: http://arxiv.org/abs/1203.2363

** "A density increment approach to Roth's Theorem in the Primes."

Status: An error was found by (thank you to Kevin Henriot for pointing this out) in manuscript I posted on the arXiv.

Expository

1. "Higher Fourier Analysis"

• • Status: CMS Notes from the Margin, Vol VI, 2013

  • arXiv/PDF: Higher Fourier Analysis.pdf