Neil Lyall

Associate Professor of Mathematics, University of Georgia

Currently Teaching (Fall 2016):
Math 4100/6100

Research Interests:  Arithmetic Combinatorics and Harmonic Analysis

Graduate Students: 

Current:  Lauren Huckaba  Hans Parshall

  Alex Rice (Graduated August 2012, now at the University of Rochester)

    Some Recent Papers:

1. Product of simplices and sets of positive upper density in R^d (with Akos Magyar)

2. Simplices and sets of positive upper density in R^d (with Lauren Huckaba and Akos Magyar)
            to appear in Proc. Amer. Math. Soc.

3. Distances in dense subsets of Z^d (with Akos Magyar)

4. Polynomials and primes in generalized arithmetic progressions (with Ernie Croot and Alex Rice)
            Int. Math. Res. Not. (2015), no. 15, 6021-6043

5. A quantitative result on Diophantine approximation for intersective polynomials (with Alex Rice)
            INTEGERS Volume 15A (2015), Proceedings of Integers 2013: The Erdös Centennial Conference

6. A purely combinatorial approach to simultaneous polynomial recurrence modulo 1 (with Ernie Croot and Alex Rice)
Proc. Amer. Math. Soc. 143 (2015), no. 8, 3231-3238

7. Difference sets and polynomials (with Alex Rice)

8. Improved bounds on Sarkozy's theorem for quadratic polynomials (with Mariah Hamel and Alex Rice)
Int. Math. Res. Notices (2013), no. 8, 1761-1782

9. A new proof of Sarkozy's theorem
Proc. Amer. Math. Soc. 141 (2013), 2253-2264

10. Optimal polynomial recurrence (with Akos Magyar)
Canad. J. Math. 65 (2013), no. 1, 171-194     

11. Simultaneous polynomial recurrence (with Akos Magyar)
Bull. Lond. Math. Soc. 43 (2011), no. 4, 765-785

12. Polynomial configurations in difference sets (with Akos Magyar)
 J. Number Theory 129 (2009), 439-450

 Two expository notes:


1. Two theorems of Sarkozy (with Alex Rice)

In this note, we provide parallel expositions of two theorems of Sarkozy, the qualitative versions of which state that any set of natural numbers of positive upper density necessarily contains two distinct elements which differ by a perfect square, as well as two elements which differ by one less than a prime.

2. Ramsey Theory (Math 8440 course notes, Spring 2011)
The full collection: Preprints and expository notes

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