Professor of Mathematics, University of Georgia
Currently Teaching (Fall 2019):
Math 8100Research 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 |
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| 2. Distances
and trees in dense subsets of Z^d (with
Akos Magyar) to appear in Israel J. Math. |
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| 3. Distance graphs
and sets of positive upper density in R^d
(with Akos Magyar) to appear in Analysis and PDE |
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| 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 |
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| 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, 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Some expository/unpublished notes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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