Department of Mathematical Sciences
University of Memphis
Memphis, TN 38152
(901)-678-2693
rmcctchn@memphis.edu
Selected Papers:
Three results in recurrence.Ergodic theory and its connections with
harmonic analysis (Alexandria, 1993),
349-358, London Math. Soc. Lecture Note
pdf
Uniformity in polynomial Szemer'edi theorem (jointly with V. Bergelson), Ergodic
Theory of Z^d-actions, (Warwick, 1993-1994), 273-296, London Math. Soc. Lecture Note Ser.,
228, Cambridge Univ. Press, Cambridge, 1996.
pdf
IP-sets and polynomial recurrence (jointly with V. Bergelson and H. Furstenberg),
Ergodic Theory Dynam. Systems16 (1996), 963-974.
pdf
A Roth theorem for amenable groups
(jointly with V. Bergelson and Q. Zhang),
Amercan Journal of Mathematics119 (1997), 1173-1211
pdf
Recurrence for semigroup actions and a non-commutative Schur theorem
(jointly with V. Bergelson),
Topological dynamics and applications
Contemporary Mathematics, 215 (1998),
205-222,
Amer. Math. Soc., Providence, RI
pdf
Notions of size and combinatorial
properties of quotient sets in semigroups (jointly with V. Bergelson and N. Hindman),
Proceedings of the 1998 Topology and Dynamics Conference (Fairfax, VA). Topology Proc.23 (1998), Spring, 23-60.
pdf
The Gottschalk-Hedlund theoremAmer. Math. Monthly106 (1999), 670-672.
pdf
An infinitary polynomial van der Waerden theorem.J. Combin. Theory Ser. A86 (1999), 214-231.
pdf
Two new extensions of the Hales-Jewett theorem, Electron. J. Combin.
7 (2000), Research Paper 49, 18 pp.
pdf
An ergodic IP polynomial Szemeredi theorem
(jointly with V. Bergelson),
Mem. Amer. Math. Soc146 (2000), viii+106pp.
pdf
VIP systems in partial semigroups (jointly with N. Hindman), Discrete Math.240
(2001), 45-70. pdf
An infinitary polynomial Hales-Jewett theorem, Israel J. Math.121 (2001),
157-172. pdf
1
Rhythmic functions and IP recurrence, Proceedings of the 18th Summer Conference on
Topology and its Applications, Topology Proc.28 (2004), 617-637.
pdf
Partition theorems for left and right variable words (jointly with N. Hindman), Combinatorica24 (2004), 271-286.
pdf
Polynomial Szemeredi theorem
for countable modules over integral domains and finite fields
(jointly with V. Bergelson and A. Leibman),
Journal d'Analyse Mathematique95 (2005), 243-296.
pdf.
Simultaneous Diophantine approximations and VIP systems
(jointly with V. Bergelson and I. Haaland),
Acta Arithmetica116 (2005), 13-23.
pdf
FVIP systems and multiple recurrence, Israel J. Math.146 (2005), 157-188.
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IP Systems, generalized polynomials and recurrence
(jointly with V. Bergelson and I.J. Haaland Knutson),
Ergodic Theory and Dynamical Systems26 (2006), 999-1019.
pdf
IP_r sets with polynomial weights and
Szemeredi's theorem, Journal of
Combinatorial Theory (Series A) 114 (2007), 167-174.
pdf
Central sets and a non-commutative Roth theorem
(jointly with V. Bergelson), American Journal Math.129
(2007), 1227-1250.
pdf
Generalized polynomials and mild mixing (jointly with A. Quas),
Canadian Journal of Mathematics61 (2009), 656-673.
pdf
Recurrence (jointly with N. Franzikinakis),
Encyclopedia of Complexity and System Science, Springer, 2009.
pdf
Reading "A variant of the Hales-Jewett theorem" on its
anniversary (jointly with D. Bond), Topology Proceedings.
156 (2009), 2595-2599.
pdf
Idempotent ultrafilters, multiple weak mixing and Szemeredi's
theorem for generalized polynomials (jointly with V. Bergelson),
Journal d'Analyse Mathematique111 (2010), 77-130.
pdf
A variant of the density Hales-Jewett theorem. Bulletin of the
London Mathematical Society42 (2010), 974-980.
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The wildcard set's size in the density Hales-Jewett theorem. Electronic
Journal of Combinatorics 18(1) (2011), Research Paper 114. 12 pages.
pdf
A concentration function estimate and intersective sets
from matrices (jointly with P. Balister). Israel Journal of Mathematics189
(2012), 413-436.
pdf
Monochromatic permutation quadruples--a Schur thing in S_n. American Mathematical
Monthly119 (2012), 342-343.
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D sets and IP rich sets in Z (jointly with J. Zhou). Preprint. pdf
The logarithmic scoring rule of decision theory. Preprint. pdf