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) submitted
		3. Product of simplices and sets of positive upper density in R^d (with Akos Magyar) to appear in Math. Proc. Cambridge Philos. Soc.
		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Some expository/unpublished notes: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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