Research papers and notes

Research

Classical analysis

• "On contractive families and a fixed-point question of Stein", Mathematika 52 (2005), no. 1-2, 115--129
• "A pair of non-homeomorphic product measures on the Cantor set", Math. Proc. Cambridge Philos. Soc. 142 (2007), no. 1, 103--110

Exchangeable random variables and related extremal combinatorics

• "On the testability and repair of hereditary hypergraph properties", with Terence Tao, Random Struct. Alg. 36 (2010), no. 4, 373--463

Ergodic theory and related arithmetic combinatorics

• "On the norm convergence of nonconventional ergodic averages", Ergodic Theory and Dynamical Systems 30 (2010), no. 2, 321--338
• "Deducing the multidimensional Szemeredi Theorem from an infinitary removal lemma", J. Anal. Math 111 (2010), 131--150
• "Deducing the Density Hales-Jewett Theorem from an infinitary removal lemma". J. Theoret. Probab. 24 (2011), no. 3, 615--633
• "Relatively finite measure-preserving extensions and lifting multipliers by Rokhlin cocycles", with Mariusz Lemanczyk, J. Fixed Point Theory Appl. 6 (2009), no. 1, 115--131
• "Extensions of probability-preserving systems by measurably-varying homogeneous spaces and applications", Fund. Math. 210 (2010), no. 2, 133--206
• "Pleasant extensions retaining algebraic structure, I". Preprint.
• "Pleasant extensions retaining algebraic structure, II". Preprint.
• "Nonconventional ergodic averages and multiple recurrence for von Neumann dynamical systems", with Tanja Eisner and Terence Tao, Pacific J. Math. 250 (2011), no. 1, 1--60
• "Norm convergence of continuous-time polynomial multiple ergodic averages". Dedicated to the memory of Dan Rudolph. To appear, Ergodic Theory and Dynamical Systems.
• "Ergodic-theoretic implementations of the Roth density-increment argument" (2011) Preprint.
• "Equidistribution of joinings under off-diagonal polynomial flows of nilpotent Lie groups " (2011) Preprint.

Geometry of groups and their actions, cohomology, topological algebra

• "The Euclidean distortion of the lamplighter group", with Assaf Naor and Alain Valette, Discrete and Computational Geometry 44 (2010), no. 1, 55--74
• "The wreath product of Z with Z has Hilbert compression exponent 2/3", with Assaf Naor and Yuval Peres, Proc. Amer. Math. Soc. 137 (2009), no. 1, 85--90
• "A CAT(0)-valued pointwise ergodic theorem", J. Topology and Analysis 3 (2011), no. 2, 145--152.
• "Amenable groups with very poor compression into Lebesgue spaces", Duke Mathematical Journal 159 (2011), no. 2, 187--222.
• "Rational group ring elements with kernels having irrational dimension" (2009). Preprint.
• "Sharp quantitative nonembeddability of the Heisenberg group into superreflexive Banach spaces", with Assaf Naor and Romain Tessera. To appear, Groups, Geometry and Dynamics.
• "Continuity properties of measurable group cohomology" (2010), with Calvin C. Moore. Preprint.
• "On discontinuities of cocycles in cohomology theories for topological groups" (2011) Preprint.

Applied stochastic processes

• "The emergence of the deterministic Hodgkin-Huxley equations as a limit from the underlying stochastic ion-channel mechanism", Ann. App. Probab. 18 (2008), no. 4, 1279--1325

Survey articles

• "On exchangeable random variables and the statistics of large graphs and hypergraphs", Probability Surveys 5 (2008), 80--145

Some unpublished notes

• "Multiple recurrence and the structure of probability-preserving systems" (2010). This is a slightly re-written version of my thesis.
• "An alternative ending to ``Pleasant extensions retaining algebraic structure'' " (2010).
• "For what number of cars must self organization occur in the Biham-Middleton-Levine traffic model from any possible starting configuration?" (2006), with Itai Benjamini
• "On the geometry of a class of invariant measures and a problem of Aldous" (2008)
• "Razborov flag algebras as algebras of measurable functions" (2008)
• "A counterexample in von Neumann algebra dynamics" (2008): pdf.
• "Entropy and Probability Theory" (2007): pdf. These notes were written to accompany a talk to sixth-form students at Winchester College (UK).
• "Entropy and Sinai's Theorem" (2006): pdf. These notes were written loosely to accompany a pair of graduate seminars at UCLA.
• "Phase transitions" (2005): pdf
• "Spectral measures without the spectrum" (2004): pdf
• "On coordinate-permutation-invariant signed Radon measures on Cartesian powers of compact Hausdorff spaces: a look at de Finetti's theorem" (2003): pdf

Tim Austin,
Office no. 111, tel. +1 (401) 863 1127
Department of Mathematics, Brown University, Box 1917, 151 Thayer Street, Providence, RI 02912, U.S.A.
timaustin AT math DOT brown DOT edu