lyall

Neil Lyall

Professor
of Mathematics
Associate Dean, Franklin College of Arts and Sciences
University of Georgia


Research Interests:  Arithmetic Combinatorics and Harmonic Analysis

 
Graduate Students: 


Current:  Peter Woolfitt

Former:
  Alex Newman      (Graduated December 2022)        
               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. Discrete multilinear maximal operators and pinned simplices (with Akos Magyar, Alex Newman, and Peter Woolfitt)
            submitted


2. The discrete spherical maximal function: A new proof of l^2-boundedness (with Akos Magyar, Alex Newman, and Peter Woolfitt)
            Proc. Amer. Math. Soc. 149 (2021), no.12, 5305-5312.


3. Multilinear maximal operators associated to simplices (with Brian Cook and Akos Magyar)
            J. London Math. Soc., Volume 104, Issue 4, November 2021, pp1491-1514


4. Weak hypergraph regularity and applications to geometric Ramsey theory (with Akos Magyar)
            Trans. Amer. Math. Soc. Ser. B 9 (2022), 160-207


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


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


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


8. 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


9. 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Some expository/unpublished notes
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


The contents and opinions expressed on this web page do not necessarily reflect the views of nor are they endorsed by the university system of georgia