Professor of Mathematics, University of Georgia
Department Head
Research Interests: Arithmetic Combinatorics and Harmonic Analysis
Currently Teaching: Math 8100
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 |
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| 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. |
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| 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 |
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| 4. Weak
hypergraph regularity and applications to
geometric Ramsey theory (with
Akos Magyar) Trans. Amer. Math. Soc. Ser. B 9 (2022), 160-207 |
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| 5. Distances
and trees in dense subsets of Z^d (with
Akos Magyar) Israel J. Math., 240, 769-790 (2020) |
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| 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 |
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| 7. Spherical configurations
over finite fields (with Akos Magyar and
Hans Parshall) Amer. J. Math. Volume 142, Number 2, April 2020, 373-404 |
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| 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 |
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| 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Some expository/unpublished notes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.
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.
The full collection: Preprints and expository notes
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