# Research

Research papers and preprints

Combinatorics

*On Rado conditions for nonlinear Diophantine equations***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***Illinois Journal of Mathematics**, 58 (2014), no. 1, Pages 11–25

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***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

Quantum information 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.

Algebraic topology and homological algebra

*The classification problem for extensions of torsion abelian groups**The definable content of homological invariants I: Ext & lim1*(with Jeffrey Bergfalk and Aristotelis Panagiotopoulos*A definable Eilenberg--Mac Lane Universal Coefficient Theorem**The coherent category of towers of chain complexes*

Operator algebras

*Actions of nonamenable groups on Z-stable C*-algebras*, (with Eusebio Gardella),**Advances in Mathematics**, to appear*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***Münster Journal of Mathematics**9 (2016), no. 1, 93–118.*Fraïssé limits of C*-algebras***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 Anal****ysis**, to appear*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***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

Books

*Nonstandard methods in Ramsey Theory and Combinatorial Number Theory*(with Mauro Di Nasso and Isaac Goldbring).**Lecture Notes in Mathematics**vol. 2239, Springer (2019)*Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture***Lecture Notes in Mathematics**vol. 2136, Springer (2015)

Announcements, reviews, and surveys

*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***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*Fraïssé theory and the Poulsen simplex*,**Contributions to Discrete Mathematics**, to appear*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 (2015).*Recurrence and Szemerédi's theorem*. Master's thesis (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.