Quantum information theory and quantum groups

• Perfect strategies for non-signalling games (with Laura Mancinska, Vern Paulsen, David Roberson, Giannicola Scarpa, Simone Severini, Ivan Todorov, Andreas Winter), Mathematical Physics, Analysis and Geometry, 23 (2020), no. 1, Paper No. 7, 31 pp.

• Nonlocal Games and Quantum Permutation Groups (with Laura Mančinska and David Robertson), Journal of Functional Analysis 279 (2020), no. 5, 108592, 44 pp.

Dynamical Systems

• The complexity of conjugacy, orbit equivalence, and von Neumann equivalence of actions of nonamenable groups (with Eusebio Gardella)

• Games orbits play and obstructions to Borel reducibility (with Aristotelis Panagiotopoulos), Groups, Geometry, and Dynamics,  12 (2018), no. 4, 1461--1483.

• Polish groupoids and functorial complexity, Transactions of the American Mathematical Society, 369 (2017), no. 9, 6683–6723

Combinatorics

• On Rado conditions for nonlinear Diophantine equations (with Jordan Barrett and Joel Moreira), European Journal of Combinatorics, 94 (2021), 103277, 20 pp.

• Actions on semigroups, and an infinitary Gowers--Hales--Jewett Ramsey theorem, Transactions of the American Mathematical Society, 371 (2019), no. 5, 3083-3116. 

• 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

Operator Algebras

• Definable K-homology of separable C*-algebras

• Group amenability and actions on Z-stable C*-algebras (with Eusebio Gardella), Advances in Mathematics 389 (2021), Paper No. 107931, 33 pp.

• A von Neumann algebra characterization of property (T) for groupoids, Journal of the Australian Mathematical Society, 108 (2020), no. 3, 363–386

• Rokhlin dimension for compact quantum group actions (with Eusebio Gardella and Mehrdad Kalantar), Journal of Noncommutative Geometry 13 (2019), no. 2, 711–767.

• Applications of model theory to C*-dynamics (with Eusebio Gardella), Journal of Functional Analysis,  275 (2018), no. 7, 1889–1942

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

• Actions of rigid groups on UHF-algebras (with Eusebio Gardella). Journal of Functional Analysis 275 (2018), no. 2, 381–421.

• The classification problem for operator algebraic varieties and their multiplier algebras (with Michael Hartz), Transactions of the American Mathematical Society,  370 (2018), no. 3, 2161–2180

• Representations of étale groupoids on Lp-spaces (with Eusebio Gardella), Advances in Mathematics, 318 (2017), 233–278.

• Conjugacy and cocycle conjugacy of automorphisms of $\mathcal{O}_2$ are not Borel (with Eusebio Gardella), Münster Journal of Mathematics 9 (2016), no. 1, 93–118.

• 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

Functional Analysis

• The Ramsey property for operator spaces and noncommutative Choquet simplices  (with Dana Bartosova, Jordi Lopez-Abad, and Brice Mbombo),  Journal of Functional Analysis 281 (2021), no. 9, Paper No. 109192, 39 pp.

• The Ramsey property for Grassmannians over R or C   (with Dana Bartosova, Jordi Lopez-Abad, and Brice Mbombo), Combinatorica, to appear

• The Ramsey property for Banach spaces and Choquet simplices (with Dana Bartosova, Jordi Lopez-Abad, and Brice Mbombo), Journal of the European Mathematical Society, to appear

• Dilation theory in finite dimensions and matrix convexity (with Michael Hartz), Israel Journal of Mathematics, to appear

• Fraïssé limits in functional analysis, Advances in Mathematics, 338 (2018), 93--174. 

• An intrinsic order-theoretic characterization of the weak expectation property, Integral Equations and Operator Theory, 90 (2018), no. 5, 90:55

• The Kirchberg--Wassermann operator system is unique, Journal of Mathematical Analysis and Applications, 459 (2018), no. 2, 1251–1259

• Boundary representations of operator spaces, and compact rectangular matrix convex sets (with Michael Hartz and Adam Fuller), Journal of Operator Theory, 79 (2018), no. 1,139–172

• Uniqueness, universality, and homogeneity of the noncommutative Gurarij space, Advances in Mathematics, 298 (2016), 286-324

• Operator space and operator system analogs of Kirchberg's embedding theorem, Journal of Mathematical Analysis and Applications 431 (2015), 47-56

Model Theory

• Model-theoretic aspects of the Gurarij operator system (with Isaac Goldbring), Israel Journal of Mathematics 226 (2018), no. 1, 87–118

• 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