Research

Research interests

• Functional analysis: linear and nonlinear geometry of Banach spaces and of operator spaces.

• Noncommutative geometry and operator algebras: uniform Roe algebras.

• Geometry of metric spaces: embeddings and large scale geometry.

• Logic: Descriptive set theory of Polish spaces and connections between set theory and operator algebras.

Papers either published or submitted for publication

39. On the uniform continuity of homeomorphisms between the spheres of ℓ_\infty^k and ℓ_1^k (joint with Chris Gartland, Gilles Lancien, Pavlos Motakis, Eva Pernecká, and Thomas Schlumprecht).

arXiv:2512.14966. PDF.

38. Descriptive set theory of separable Fréchet spaces (joint with Willian Corrêa and Valentin Ferenczi).

Submitted. arXiv:2508.09368. PDF.

37. A note on the quasi-local algebra of expander graphs (joint with Ján Špakula and Alessandro Vignati).

To appear in the Bulletin of the London Mathematical Society. arXiv:2508.07327. PDF.

36. Flows on uniform Roe algebras (joint with Alcides Buss and Ruy Exel). 

To appear in the Journal of the Mathematical Institute of Jussieu. arXiv:2411.06999. PDF.

35. KMS states of uniform Roe algebras (joint with Ruy Exel). 

Canadian Mathematical Communications , Volume 1 , 2025 , e1. PDF.

34. Asymptotic coarse Lipschitz equivalences (joint with Gilles Lancien). 

To appear in the Annales de l’Institut Fourier. arXiv:2302.12016. PDF.

33. On the expansiveness of coarse maps between Banach spaces and geometry preservation (joint with Gilles Lancien). 

Journal of Functional Analysis 288 (2025), no. 3, Paper No. 110724, 23 pp. PDF. 

32. On the small scale nonlinear theory of operator spaces (joint with Javier Alejandro Chávez-Domínguez). 

Comptes rendus de l'Académie des Sciences 362 (2024), 1893–1914. PDF.

31. Coarse equivalence versus bijective coarse equivalence of expander graphs (joint with Florent Baudier, Ilijas Farah, Alessandro Vignati, and Rufus Willett). 

Mathematische Zeitschrift, 307 (2024), no. 3, Paper No. 44, 24 pp. PDF.

30. Operator norm localization property for equi-approximable families of projections (joint with Ilijas Farah and Alessandro Vignati). 

Journal of Noncommutative Geometry, 18 (2024), no. 2, 657–680. PDF.

29. Embeddings of von Neumann algebras into quasi-local algebras (joint with Florent Baudier, Ilijas Farah, Alessandro Vignati, and Rufus Willett). 

Journal of Functional Analysis, 286 (2024), no. 1, Paper No. 110186, 37 pp. PDF.

28. Complete isomorphic embeddings into c0 and ℓ1-sums of operator spaces and their coarse geometry (joint with Timur Oikhberg). 

Mathematische Zeitschrift, 304 (2023), no. 3, Paper No. 52, 19 pp. PDF. 

27. Support expansion C∗-algebras (joint with Joseph Eisner and David Sherman). 

Journal of Operator Theory, 92 (2024), no. 2, 463–504. PDF.

26. Uniform Roe algebras of uniformly locally finite metric spaces are rigid (joint with Florent Baudier, Ilijas Farah, Ana Khukhro, Alessandro Vignati, and Rufus Willett). 

Inventiones Mathematicae, 230 (2022), no. 3, 1071–1100. PDF.

25. Towards a theory of coarse geometry of operator spaces. 

Israel Journal of Mathematics, 259 (2024), no. 2, 527–558. PDF.

24. Lipschitz geometry of operator spaces and Lipschitz-free operator spaces (joint with Javier Alejandro Chávez-Domínguez and Thomas Sinclair). 

Mathematische Annalen, 388 (2024), no. 1, 1053–1090. PDF.

23. Coarse quotients of metric spaces and embeddings of uniform Roe algebras. 

Journal of Noncommutative Geometry, 16 (2022), no. 4, 1337–1361. PDF.

22. A Gelfand-type duality for coarse metric spaces with property A (joint with Alessandro Vignati).

International Mathematics Research Notices, Vol. 00, No. 0, pp. 1–45. PDF.

21. Quantum uniform Roe algebras (joint with Joseph Eisner and David Sherman). 

Pacific Journal of  Mathematics 338 (2025), no. 1, 163–207. PDF.

20. Completely coarse maps are R-linear (joint with Javier Alejandro Chávez-Domínguez).

Proceedings of the American Mathematical Society 149 (2021), 1139-1149. PDF.

19. General uniform Roe algebra rigidity (joint with Ilijas Farah and Alessandro Vignati). 

Annales de l’Institut Fourier, 72 (2022), no. 1, 301–337. PDF.

18. On Banach algebras of band-dominated operators and their lattice structure.

Journal of Functional Analysis, Volume 280, Issue 9, 2021, 108958. PDF.

17. On Kalton’s interlaced graphs and nonlinear embeddings into dual Banach spaces (joint with Gilles Lancien, Colin Petitjean, and Antonín Procházka).

Journal of Topology and Analysis, Vol. 15, No. 2 (2023) 467–494. PDF.

16. Uniformly Factoring Weakly Compact operators and Parametrized Dualization (joint with Kevin Beanland and Leandro Antunes).

Forum of Mathematics, Sigma, 9 (2021), Paper No. e22, 27 pp. PDF.

15. The coarse Baum-Connes conjecture and rigidity of Roe algebras (joint with Yeong Chyuan Chung and Kang Li).

Journal of Functional Analysis, Volume 279 (2020), no. 9. PDF.

14. On the uniform Roe algebra as a Banach algebra and isomorphic embeddings of ℓp uniform Roe algebras (joint with Alessandro Vignati).

Bulletin of the London Mathematical Society 52 (2020), no. 5, 853–870. PDF.

13. Embeddings of uniform Roe algebras (joint with Ilijas Farah and Alessandro Vignati). 

Communications in Mathematical Physics 377 (2020), no. 3, 1853–1882. PDF.  

12. Uniform Roe coronas (joint with Ilijas Farah and Alessandro Vignati).

Advances in Mathematics 389, 8 October 2021, 107886. PDF.

11. On asymptotically uniformly smoothness and nonlinear geometry of Banach spaces. 

Journal of the Institute of Mathematics of Jussieu, 20 (2021), no. 1, 65–102. PDF.

10. On the rigidity of Roe algebras of uniformly discrete coarse spaces (joint with Ilijas Farah).

Transactions of the American Mathematical Society 374 (2021), no. 2, 1007–1040. PDF.

9. Nonlinear weakly sequentially continuous embeddings between Banach spaces.

International Mathematics Research Notices,  2020, no. 18, 5506–5533. PDF.

8. Coarse embeddings into superstable spaces (joint with Andrew Swift). 

Israel Journal of Mathematics, 232 (2019), no. 1, 1–39. PDF.

7. On weaker notions of nonlinear embeddings between Banach spaces.

Journal of Functional Analysis 274 (2018), no. 11, 3149-3169. PDF.

6. Asymptotic structure and coarse Lipschitz geometry of Banach spaces.

Studia Mathematica 237 (2017), no. 1, 71-97. PDF. 

5. Coarse and uniform embeddings.

Journal of Functional Analysis 272 (2017), no. 5, 1852-1875. PDF.

4. Duality on Banach spaces and a Borel parametrized version of Zippin’s theorem.

Annales de l’Institut Fourier 65 (2015), no. 6, 2413-2435. PDF.

3. On the complexity of some inevitable classes of separable Banach spaces.

Journal of Mathematical Analysis and Applications 431 (2015), no. 1, 682-701. PDF.

2. On the complexity of some classes of Banach spaces and non-universality.

Czechoslovak Mathematical Journal 64 (2014), no. 4, 1123-1147. PDF.

1. On the Hausdorff metric and some openings between Banach spaces as Borel functions.

Quaestiones Mathematicae 38 (2015), no. 3, 403-411. PDF.