lyall

Neil Lyall

Professor of Mathematics, University of Georgia

Currently Teaching (Fall 2019):
Math 8100
Research Interests:  Arithmetic Combinatorics and Harmonic Analysis

Graduate Students: 


Current:  Alex Newman
               Peter Woolfitt

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 Millsaps College)




















   
Some Recent Papers:



1. Weak hypergraph regularity and applications to geometric Ramsey theory (with Akos Magyar)
            submitted


2. Distances and trees in dense subsets of Z^d (with Akos Magyar)
            to appear in Israel J. Math.


3. Distance graphs and sets of positive upper density in R^d (with Akos Magyar)
            to appear in Analysis and PDE


4. Spherical configurations over finite fields (with Akos Magyar and Hans Parshall)
            to appear in Amer. J. Math.


5. 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


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Some expository/unpublished notes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


The full collection: Preprints and expository notes


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