lyall

Neil Lyall

Associate Professor of Mathematics, University of Georgia

Currently Teaching (Spring 2017):
Math 2260 and Math 3100
Research Interests:  Arithmetic Combinatorics and Harmonic Analysis

Graduate Students: 

Current:  Hans Parshall (Graduation August 2017, expected)

Former:
  Alex Rice (Graduated August 2012, now at the University of Rochester)
              
Lauren Huckaba (Graduated August 2016, now at the NSA)




















   
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)
            to appear in Proc. Amer. Math. Soc.


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


Some expository/unpublished notes: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. Ramsey theory (Math 8440 course notes, Spring 2011)


The full collection: Preprints and expository notes


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