My research interests lie primarily in the field of arithmetic combinatorics, a rapidly developing area with close connections to number theory, combinatorics, harmonic analysis, and ergodic theory. Specifically, I am most interested in applying analytic and combinatorial techniques to show the existence of certain arithmetic structures in sufficiently dense sets of integers.
Courses Offered (subject to change)
- MTH 141 Calculus I
- MTH 142 Calculus II
- MTH 165 Linear Algebra
- MTH 218 Math Modeling for the Life Sciences
- MTH 238 Combinatorics
- MTH 263 Qualitative Theory of ODEs
- Difference Sets and Polynomials (with Neil Lyall), submitted.
- Polynomials and Primes in Generalized Arithmetic Progressions (Revised Version) (with Ernie Croot and Neil Lyall), Int. Math. Res. Not. (2015), no. 15, 6021-6043.
- A Quantitative Result on Diophantine Approximation for Intersective Polynomials (with Neil Lyall), INTEGERS Volume 15A (2015), Proceedings of Integers 2013: The Erdös Centennial Conference.
- A Purely Combinatorial Approach to Simultaneous Polynomial Recurrence Modulo 1, (with Ernie Croot and Neil Lyall), Proceedings of the AMS 143 (2015), no. 8, 3231-3238.
- Sárközy’s Theorem for P-Intersective Polynomials, Acta Arithmetica 157 (2013), no. 1, 69-89.
- Improved Bounds on Sárközy’s Theorem for Quadratic Polynomials (with Mariah Hamel and Neil Lyall), Int. Math. Res. Not. (2013), no.8, 1761-1782.
- Polynomial Differences in the Primes (with Neil Lyall), Combinatorial and Analytic Number Theory 2011-2012, Springer Proceedings of Mathematics and Statistics vol. 101 (2014), 129-146
- Improvements and Extensions of Two Theorems of Sárközy (Ph. D. Thesis)