Research papers and preprints

• Actions of trees on semigroups, and an infinitary Gowers--Hales--Jewett Ramsey theorem

• Gowers' Ramsey theorem for generalized tetris operations, Journal of Combinatorial Theory, Series A, 149 (2017), 101–114.

• Approximate polynomial structure in additively large sets (with Mauro Di Nasso, Isaac Goldbring, Renling Jin, Steven Leth, Karl Mahlburg). Integers, 16 (2016), Paper No. A49, 11 pp.

• A monad measure space for logarithmic density (with Mauro Di Nasso, Isaac Goldbring, Renling Jin, Steven Leth, Karl Mahlburg), Monatshefte für Mathematik, 181 (2016), no. 3, 577–599.

• High density piecewise syndeticity of product sets in amenable groups (with Mauro Di Nasso, Isaac Goldbring, Renling Jin, Steven Leth, Karl Mahlburg), Journal of Symbolic Logic  81 (2016), no. 4, 1555–1562.

• Strongly productive ultrafilters on semigroups (with David J. Fernández Bretón), Semigroup Forum, 92 (2016), no. 1, 242–257

• High density piecewise syndeticity of sumsets (with Mauro Di Nasso, Isaac Goldbring, Renling Jin, Steven Leth, Karl Mahlburg), Advances in Mathematics, 278 (2015), 1–3

• On a sumset conjecture of Erdős (with Mauro Di Nasso, Isaac Goldbring, Renling Jin, Steven Leth, Karl Mahlburg), Canadian Journal of Mathematics 67 (2015), no. 4, 795-809

• Nonstandard Analysis and the sumset phenomenon in arbitrary amenable groups (with Mauro Di Nasso). Illinois Journal of Mathematics, 58 (2014), no. 1, Pages 11–25

• Rokhlin dimension for compact quantum group actions (with Eusebio Gardella and Mehrdad Kalantar)

• Cocycle superrigidity and group actions on stably finite C*-algebras (with Eusebio Gardella)

• Equivariant logic and applications to C*-dynamics (with Eusebio Gardella)

• The model theory of nuclear C*-algebras (with Ilijas Farah, Bradd Hart, Leonel Robert, Aaron P. Tikuisis, Alessandro Vignati, and Wilhelm Winter)

• Representations of étale groupoids on Lp-spaces (with Eusebio Gardella)

• The classification problem for operator algebraic varieties and their multiplier algebras (with Michael Hartz), Transactions of the American Mathematical Society, to appear

• Fraïssé limits of C*-algebras (with Christopher J. Eagle, Ilijas Farah, Bradd Hart, Boris Kadets, and Vlad Kalashnyk), Journal of Symbolic Logic, 81 (2016), no. 2, 755–773.

• Nonclassifiability of UHF Lp-operator algebras (with Eusebio Gardella), Proceedings of the American Mathematical Society, 144 (2016), no. 5, 2081–2091

• Borel complexity and automorphisms of C*-algebras (with David Kerr, and N. Christopher Phillips), Journal of Functional Analysis, 268 (2015), no. 12, 3767–3789

• Unitary equivalence of automorphisms of separable C*-algebras. Advances in Mathematics, 262 (2014), 1002–1034

• Boundary representations of operator spaces, and compact rectangular matrix convex sets (with Michael Hartz and Adam Fuller)

• Fraïssé limits in functional analysis 

• Model-theoretic aspects of the Gurarij operator system (with Isaac Goldbring), accepted for publication by the Israel Journal of Mathematics
• A López-Escobar theorem for metric structures, and the topological Vaught conjecture (with Samuel Coskey), Fundamenta Mathematicae, 234 (2016), no. 1, 55–72.
• Logic for metric structures and the number of universal sofic and hyperlinear groups. Proceedings of the American Mathematical Society, 142 (2014), no. 10, 3635–364

• The classification problem for automorphisms of C*-algebras, Bulletin of Symbolic Logic, volume 21, issue 04, pp. 402-424

• Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture (with Valerio Capraro, appendix by Vladimir Pestov). Lecture Notes in Mathematics vol. 2136, Springer
  

• Set theory and von Neumann algebras (with Asger Törnquist). Published in the volume "Appalachian Set Theory" by Cambridge University Press (2012), edited by James Cummings and Ernest Schimmerling.

• Borel complexity and automorphisms of C*-algebras, Oberwolfach Reports, Volume 11, Issue 1, 2014

• Gottschalk's surjuncitivity conjecture, Oberwolfach Reports, Volume 10, Issue 4, 2013.

• The complexity of the relation of unitary equivalence of automorphisms of separable C*-algebras, Oberwolfach Reports, Volume 9, Issue 4, 2012.