Books Published

Elemental methods in ergodic Ramsey theory. Lecture Notes in Mathematics, 1722. Springer-Verlag, Berlin, 1999. iv+160 pp. ISBN: 3-540-66809-8 

An ergodic IP polynomial Szemerédi theorem. Memoirs of the American Mathematical Society 146 (2000), viii+106 pp. (with V. Bergelson)

An Outline of Ergodic Theory, Cambridge University Press, 2010. ISBN: 0521194407. (with Steve Kalikow)

Refereed Journal Publications

IP-sets and polynomial recurrence. Ergodic Theory and Dynamical Systems 16 (1996), 963--974. (with V. Bergelson and H. Furstenberg)

A Roth theorem for amenable groups, American Journal of Mathematics 119 (1997), 1173--1211. (with V. Bergelson and Q. Zhang)

An infinitary polynomial van der Waerden theorem. Journal of Combinatorial Theory (Series A) 86 (1999), 214--231. 

The Gottschalk-Hedlund theorem. American Mathematical Monthly 106 (1999), 670--672. 

A half-commutative IP Roth theorem. Acta. Math. Univ. Comenian. (N.S.) 69 (2000), 19--39. 

Two new extensions of the Hales-Jewett theorem. Electronic Journal of Combinatorics  7 (2000), Research Paper 49, 18 pp. 

Aspects of uniformity in recurrence. Dedicated to the memory of Anzelm Iwanik. Colloquium Mathematicum 84/85 (2000), 549--576. (with V. Bergelson, B. Host and F. Parraeu)

VIP systems in partial semigroups. Discrete Mathematics 240 (2001), 45--70. (with N. Hindman)

An infinitary polynomial Hales-Jewett theorem. Israel Journal of Mathematics 121 (2001), 157--172.  

One sided ideals and Carlson's theorem. Proceedings of the American Mathematical Society 130 (2002), 2559--2567. (with N. Hindman)

A Sarkozy theorem for finite fields. Special issue on Ramsey theory. Combinatorics, Probability and Computing 12 (2003), 643--651. 

Partition theorems for left and right variable words. Combinatorica 24 (2004), 271--286. (with N. Hindman)

Polynomial Szemeredi theorems for countable modules over integral domains and finite fields. Journal D Analyse Mathematique 95 (2005), 243--296. (with V. Bergelson and A. Leibman)

Simultaneous Diophantine approximation and VIP systems. Acta Arithmetica  116 (2005), 13--23.  (with V. Bergelson and I.J.H. Knutson)

FVIP systems and multiple recurrence. Israel Journal of Mathematics 146 (2005), 157--188.

IP Systems, Generalized Polynomials and Recurrence. Ergodic Theory and Dynamical Systems 26 (2006), 999-1019. (with V. Bergelson and I.J.H. Knutson)

IP_r sets with polynomial weights and Szemeredi's theorem. Journal of Combinatorial Theory (Series A)  114 (2007), 167-174.  

Central sets and a Roth theorem for non-amenable groups, American Journal of Mathematics 129 (2007), 1251-1275. (with V. Bergelson)

Generalized polynomials and mild mixing, Canadian Journal of Mathematics 61 (2009), 656-673. (with A. Quas)

Idempotent ultrafilters, multiple weak mixing and Szemeredi's theorem for generalized polynomials, Journal D Analyse Mathematique 111 (2010), 77-130. (with V. Bergelson)

A variant of the density Hales-Jewett theorem. Bulletin of the London Mathematical Society 42 (2010), 974-980. 

The wildcard set's size in the density Hales-Jewett theorem. Electronic Journal of Combinatorics 18 (2011) #P114.

A concentration function estimate and intersective sets from matrices. Israel Journal of Mathematics 189 (2012), 413-436. (with P. Balister)

Monochromatic permutation quaduples--a Schur thing in S_n. American Mathematical Monthly 119 (2012), 342-343.

D sets and a Sarkozy theorem for finite fields Israel Journal of Mathematics 201 (2014), 123-146. (with A. Windsor)

A characteristic factor for the 3-term IP Roth theorem in Z_3^N. Electronic Journal of Combinatorics 21 (2014), P3.3. (with A. Windsor)

An Alpern tower independent of a given partition. Colloquium Mathematicum. 141 (2015), 119-124. (with J. Campbell, J. Collins, S. Kalikow and R. King) 

Recurrence and Primitivity for IP Systems with Polynomial Wildcards. Transactions of the American Mathematical Society. 368 (2016), 2697-2721. (with J. Campbell)

D sets and IP rich sets in Z. Fundamenta Mathematicae. 233 (2016), 71-82. (with J. Zhou)

D sets and IP rich sets in countable cancellative abelian semigroups. Semigroup Forum 96 (2018), 49-68. (with J.T. Campbell)

Independence and Alpern multitowers. Dynamical Systems: an International Journal 34 (2019), 239-243. (with J. Campbell and A. Windsor)

A Combinatorial Proof of a Stronger Dense Hindman Theorem. Colloquium Mathematicum. 162 (2020), 303-310.

On a no defeat evidence principle of Tal and Comesaña. Episteme. 16:237-240. 2019.

In favor of logarithmic scoring. Philosophy of Science. 86:286-303. 2019.

Regression to the mean and Judy Benjamin. Synthese. 197:1343-1355. 2020.

How to Co-exist with Nonexistent Expectations. Synthese. 198:2783-2799. 2021.

A Note on Verisimilitude and Accuracy. British Journal for the Philosophy of Science. 74:431-434. 2023.

Refereed Conference Publications

Three results in recurrence. Ergodic theory and its connections with harmonic analysis (Alexandria, 1993), 349--358, London Math. Soc. Lecture Note Ser., 205 Cambridge Univ. Press, Cambridge, 1995.  

Uniformity in polynomial Szemer'edi theorem, Ergodic Theory of Z^d-actions,  (Warwick, 1993--1994), 273--296, London Math. Soc. Lecture Note Ser., 228, Cambridge Univ. Press, Cambridge, 1996. (with V. Bergelson)

Recurrence for semigroup actions and a non-commutative Schur theorem. Topological dynamics and applications (Minneapolis, MN, 1995), 205--222, Contemporary Mathematics 215 Amer. Math. Soc., Providence, RI, 1998. (with V. Bergelson)

Notions of size and combinatorial properties of quotient sets in semigroups. Proceedings of the 1998 Topology and Dynamics Conference (Fairfax, VA). Topology Proceedings 23 (1998),  23--60. (with V. Bergelson and N. Hindman)

Weak VIP systems in commutative semigroups. Proceedings of the 14th Summer Conference on General Topology and its Applications (Brookville, NY, 1999). Topology Proceedings 24 (1999), 199--221.  (with N. Hindman)

Rhythmic functions and IP recurrence. Proceedings of the 18th Summer Conference on Topology and its Applications. Topology Proceedings 28 (2004), 617--637. 

Reading `A variant of the Hales-Jewett theorem' on its anniversary, Topology Proceedings 156 (2009), 2595-2599. (with D. Bond)

Presentations - Conference (refereed *)

3-95, Maryland-Penn State Workshop on Dynamical Systems and Related Topics, University of Maryland. "An IP polynomial Szemeredi theorem."

3-97, AMS Special Session on pointwise convergence in ergodic theory, Memphis TN. "The uniformity of multiple recurrence."

5-98, 30th CONE conference, Northampton, MA. "Sets of recurrence in semigroups and Ramsey theory."

9-98, AMS Special Session on ergodic theory, Chicago, IL (co-organizer). "An infinitary polynomial Hales-Jewett theorem."

10-98, Maryland-Penn State Workshop on Dynamical Systems and Related Topics, Penn State University. "Recurrence for amenable groups."

3-99, AMS Special Session on ergodic theory, Gainesville, FL. "Roth and van der Waerden theorems for amenable groups."

4-01, Ergodic theory mini-conference, University of Memphis. "FVIP systems and multiple recurrence."

4-02, Paul Erd"os Lecture Series, University of Memphis. "A Sarkozy theorem for finite fields."

4-03, AMS Special Session on ergodic theory, Bloomington, IN. "Mild mixing and generalized polynomials."

7-03, Summer Conference on Topology and Applications, Washington, DC (co-organizer). "VIP systems and recurrence in ergodic theory and topological dynamics."  

9-03, AMS Special Session on measurable dynamics, Chapel Hill, NC. "Polynomial recurrence for actions of modules over countable integral domains."  

1-04, AMS Special Session on ergodic theory, Phoenix, AZ. "Rhythmic functions and IP recurrence."  

12-05, National Meeting of the Canadian Mathematical Society, Victoria, BC. "A Roth theorem for non-amenable groups."

7-06, Summer Conference on Topology and its Applications, Statesboro, GA. "Central sets and generalized polynomials."    

10-06, AMS Special Session in ergodic theory, Cincinnati, OH. "Idempotence and polynomiality."   

5-08, International Conference on Interdisciplinary Mathematical and Statistical Techniques, Memphis, TN (co-organizer). "Idempotent ultrafilters in ergodic theory."    

7-08, Conference on Ramsey Theory and Topological Algebra, Oxford, OH. "Finite sums systems in ergodic theory" (plenary).

11-08, Semester in ergodic theory and additive combinatorics, MSRI, Berkeley, CA. "Concentration function estimates and intersective sets from matrices."       

3-09,  AMS Special Session on topological dynamics and ergodic theory, Urbana, IL. "Sets of recurrence from matrices."    

4-11, AMS Special session on interactions between dynamical systems, number theory and combinatorics, Worcester, MA. "On the size of the wildcard set in the IP Szemeredi theorem." 

6-13, Conference on ergodic theory with connections to arithmetic, Heraklion, Greece. "Some Problems Related to the T_ij Conjecture".

6-15, Ergodic Theory and Combinatorics Conference, Kristiansand, Norway. "In favor of cute little things."

7-15, Combinatorics meets ergodic theory, Banff, Alberta. "IP rich sets in Z."

7-16, The Stone Cech Compactification: Theory and Applications, Cambridge, UK. "D-sets without ultrafilters"

Appendix A

Appendix C