lyall

Neil Lyall

Associate Professor of Mathematics, University of Georgia

Currently Teaching (Fall 2017):
Math 4100/6100
Research Interests:  Arithmetic Combinatorics and Harmonic Analysis

Graduate Students: 


Former:
  Hans Parshall      (Graduated August 2017, now at The Ohio State University)
               Lauren Huckaba  (Graduated August 2016, now at the NSA)
               Alex Rice            (Graduated August 2012, now at Millsap College)
              




















   
Some Recent Papers:



1. Spherical configurations over finite fields (with Akos Magyar and Hans Parshall)
            submitted


2. Product of simplices and sets of positive upper density in R^d (with Akos Magyar)
           
to appear in Math. Proc. Cambridge Philos. Soc.


3. Simplices and sets of positive upper density in R^d (with Lauren Huckaba and Akos Magyar)
            Proc. Amer. Math. Soc. 145 (2017), no. 6, 23352347

Some expository/unpublished notes:

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.   

     
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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