Neil Lyall

Some Recent Papers:

		1. Distance graphs and sets of positive upper density in R^d (with Akos Magyar) submitted
		2. Spherical configurations over finite fields (with Akos Magyar and Hans Parshall) to appear in Amer. J. Math.
		3. Product of simplices and sets of positive upper density in R^d (with Akos Magyar) Math. Proc. Cambridge Philos. Soc. 165 (2018), no. 1, 25-51
		4. Simplices and sets of positive upper density in R^d (with Lauren Huckaba and Akos Magyar) Proc. Amer. Math. Soc. 145 (2017), no. 6, 2335–2347

Some expository/unpublished notes:

1. A new proof of Bourgain's theorem on simplices in R^d (with Akos Magyar)

In this extract from Product of simplices and sets of positive upper density in R^d we present a new direct proof of the fact that any subset of R^d with positive upper Banach
density necessarily contains an isometric copy of all sufficiently large dilates of any fixed non-degenerate k-dimensional simplex provided d is greater than or equal to k+1.

2. Geometric squares and sets of positive upper density in R^d (with Akos Magyar)

In this note we present a proof of the simplest special case of the main result in Product of simplices and sets of positive upper density in R^d, namely that any subset of R^4
of positive upper Banach density necessarily contains an isometric copy of all sufficiently large geometric squares. In addition to this we also give a new direct proof of the fact
that the distance set of any subset of R^2 with positive upper Banach density necessarily contains all large numbers, a result originally due to Katznelson and Weiss.

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

4. Ramsey theory (Math 8440 course notes, Spring 2011)

The full collection: Preprints and expository notes

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