Neil Lyall

of Mathematics, University of Georgia
Graduate Coordinator
Double Dawgs Program Advisor

Research Interests:  Arithmetic Combinatorics and Harmonic Analysis

Currently Teaching: Math 8100
Graduate Students: 

Current:  Alex Newman
               Peter Woolfitt

  Hans Parshall      (Graduated August 2017, now at Western Washington University)
               Lauren Huckaba  (Graduated August 2016, now at the NSA)
               Alex Rice            (Graduated August 2012, now at Millsaps College)

Some Recent Papers:

1. The discrete spherical maximal function: A new proof of l^2-boundedness (with Akos Magyar, Alex Newman, and Peter Woolfitt)
            to appear in the Proc. Amer. Math. Soc.

2. Multilinear maximal operators associated to simplices (with Brian Cook and Akos Magyar)
            to appear in the Journal of the LMS

3. Weak hypergraph regularity and applications to geometric Ramsey theory (with Akos Magyar)
            to appear in Trans. Amer. Math. Soc.

4. Distances and trees in dense subsets of Z^d (with Akos Magyar)
            Israel J. Math., 240, 769-790 (2020)

5. Distance graphs and sets of positive upper density in R^d (with Akos Magyar)
            Analysis and PDE, Vol. 13 (2020), No. 3, 685-700

6. Spherical configurations over finite fields (with Akos Magyar and Hans Parshall)
            Amer. J. Math. Volume 142, Number 2, April 2020, 373-404

7. 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

8. 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Some expository/unpublished notes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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