Hans Parshall

My current projects are focused on applying ideas from arithmetic combinatorics to obtain new density results in geometric Ramsey theory.

Publications

1. Spherical configurations over finite fields
(with Neil Lyall and Ákos Magyar)
submitted, preprint available upon request
• Large subsets of $$\mathbf{F}_q^{10}$$ contain isometric copies of all spherical quadrilaterals.

2. Simplices over finite fields (arXiv preprint)
Proc. Amer. Math. Soc. 145 (2017), 2323-2334
• Large subsets of $$\mathbf{F}_q^{k + 1}$$ contain isometric copies of all full rank $$k$$-simplices.

3. Small gaps between configurations of prime polynomials (arXiv preprint)
J. Number Theory 162 (2016), 35–53
• There are arbitrarily large affine subspaces in $$\mathbf{F}_q[t]$$ consisting of twin prime polynomials.

4. Primes represented by binary quadratic forms (PDF)
(with Pete L. Clark, Jacob Hicks, and Kate Thompson)
Integers 13 (2013), A37
• Primes represented by idoneal quadratic forms are determined by explicit congruence conditions.

I also have a few old expository notes on topics in arithmetic combinatorics.