Neil Lyall

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Neil Lyall

Assistant Professor of Mathematics, University of Georgia

Research Interests: Arithmetic Combinatorics and Harmonic Analysis

Current Graduate Students: Alex Rice

lyall

Recent papers:

		1. Improved bounds on Sarkozy's theorem for quadratic polynomials (with Mariah Hamel and Alex Rice) to appear in the Int. Math. Res. Not.
		2. A new proof of Sarkozy's theorem to appear in the Proc. Amer. Math. Soc.
		3. Polynomial differences in the primes (with Alex Rice) submitted
		4. Simultaneous polynomial recurrence (with Akos Magyar) Bull. Lond. Math. Soc. 43 (2011), no. 4, 765-785
		5. Optimal polynomial recurrence (with Akos Magyar) to appear in the Canad. J. Math. Here is an exposition of the special case of squares: An optimal version of Sarkozy's theorem
		6. Arithmetic structure in sparse difference sets (with Mariah Hamel, Katherine Thompson and Nathan Walters) J. Number Theory 130 (2010), 1581-1589
		7. Polynomial configurations in difference sets (with Akos Magyar) J. Number Theory 129 (2009), 439-450 Here is an exposition of the special case of squares: Sarkozy's theorem

Recent 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)