Research

Papers (Reverse chronological)

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

  • Status: In preparation.

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

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

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

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

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

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

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

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.

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

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

Undergraduate Research

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

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

3. "The Median Largest Prime Factor."

2. "The Average Largest Prime Factor."

1. "Integers with a Predetermined Prime Factorization."

** "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"