# Research papers and preprints

## Algebraic topology and homological algebra

The classification problem for extension of torsion-free abelian groups, I

The classification problem for extensions of torsion abelian groups

The definable content of homological invariants II: cohomology and homotopy classication (with Jeffrey Bergfalk and Aristotelis Panagiotopoulos)

The definable content of homological invariants I: Ext & lim1 (with Jeffrey Bergfalk and Aristotelis Panagiotopoulos)

Applications of Borel-definable homological algebra to locally compact groups (with Jeffrey Bergfalk, Marco Moraschini, and Filippo sarti)

## 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

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

## Computability theory

Computable topological abelian groups (with Alexander Melnikov, Andre Nies). Journal of Algebra. To appear.

# Announcements, reviews, and surveys

Fraïssé theory and the Poulsen simplex, Contributions to Discrete Mathematics 16 (2021), no. 2, 23–35.

An invitation to model theory and C*-algebras, Bulletin of Symbolic Logic, 25 (2019), no. 5, 3083–3116.

The Ramsey property for Banach spaces and Choquet simplices, and applications (with Dana Bartosova, Jordi Lopez-Abad, and Brice Mbombo), Comptes Rendus Mathématique, 355 (2017), no. 12, 1242–1246

On the classification problem of free ergodic actions of nonamenable groups (with Eusebio Gardella), Comptes Rendus Mathématique, 355 (2017), no. 10, 1037–1040

Two papers on metrizable universal minimal flows, Bulletin of Symbolic Logic, volume 23, issue 02, pp. 201-203

The classification problem for automorphisms of C*-algebras, Bulletin of Symbolic Logic, volume 21, issue 04 (2015), pp. 402-424

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.

# Theses

Operator algebras and abstract classification. PhD thesis, York University (2015)

Recurrence and Szemerédi's theorem. Master's thesis, University of Pisa (2010)

# Conference Proceedings

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