Research
Research Interests
My research interests include functional analysis, operator algebras, noncommutative geometry, metric space geometry, and descriptive set theory.
Papers
Flows on uniform Roe algebras (joint with Alcides Buss and Ruy Exel).
Preprint.
On the small scale nonlinear theory of operator spaces (joint with Javier Alejandro Chávez-Domínguez).
arXiv:2404.19092. PDF.
Coarse equivalences versus bijective coarse equivalences of expander graphs (joint with Florent Baudier, Ilijas Farah, Alessandro Vignati, and Rufus Willett).
To appear in Mathematische Zeitschrift. PDF
KMS states on uniform Roe algebras (joint with Ruy Exel).
arXiv:2304.05873. PDF.
On the expansiveness of coarse maps between Banach spaces and geometry preservation (joing with Gilles Lancien).
arXiv:2310.05684. PDF.
Asymptotic coarse Lipschitz equivalences (joing with Gilles Lancien).
arXiv:2302.12016. PDF.
Embeddings of von Neumann algebras into uniform Roe algebras (joint with Florent Baudier, Ilijas Farah, Alessandro Vignati, and Rufus Willett).
To appear in the Journal of Functional Analysis. PDF.
Operator norm localization property for equi-approximable families of projections (joint with Ilijas Farah and Alessandro Vignati).
To appear in the Journal of Noncommutative Geometry. arXiv:2211.02775. PDF.
Complete isomorphic embeddings into c_0 and l_1-sums of operator spaces and their coarse geometry (joint with Timur Oikhberg).
To appear in the Mathematische Zeitschrift. PDF.
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 Mathematica, 28 July 2022. arXiv:2106.11391. PDF.
Support expansion C*-algebras (joint with Joseph Eisner and David Sherman)..
To appear in the Journal of Operator Theory. PDF.
Towards a theory of coarse geometry of operator spaces
To appear in the Israel Journal of Mathematics. arXiv:2106.15022. PDF.
Lipschitz geometry of operator spaces and Lipschitz-free operator spaces (joint with Javier Alejandro Chávez-Domínguez and Thomas Sinclair)
To appear in Mathematische Annalen. arXiv:2104.02714. PDF.
Coarse quotients of metric spaces and embeddings of uniform Roe algebras
Journal of Noncommutative Geometry, 16 (2022), no. 4, 1337–1361. PDF.
A Gelfand-type duality for coarse metric spaces with property A (joint with Alessandro Vignati)
International Mathematics Research Notices, 18 May 2022. PDF.
Quantum uniform Roe algebras (joint with Joseph Eisner and David Sherman)
Preprint.
Completely coarse maps are ℝ-linear (joint with Javier Alejandro Chávez-Domínguez)
Proceedings of the American Mathematical Society 149 (2021), 1139-1149. PDF.
On Banach algebras of band-dominated operators and their order structure
Journal of Functional Analysis, Volume 280, Issue 9, 2021, 108958. PDF.
General uniform Roe algebra rigidity (joint with Ilijas Farah and Alessandro Vignati)
Annales de l'Institut Fourier, 72 (2022), no. 1, 301–337. PDF.
On Kalton's interlaced graphs and nonlinear embeddings into dual Banach spaces (joint with Gilles Lancien, Antonín Procházka and Colin Petitjean)
Journal of Topology and Analysis, Vol. 15, No. 2 (2023) 467–494. doi: 10.1142/S1793525321500345. PDF.
Coarse Baum-Connes conjecture and rigidity for Roe algebras (joint with Yeong Chyuan Chung and Kang Li)
Journal of Functional Analysis, 279 (2020), no. 9. PDF.
Uniformly Factoring Weakly Compact operators and Parametrized Dualization (joint with Leandro Antunes and Kevin Beanland)
Forum of Mathematics, Sigma, 9, E22. doi:10.1017/fms.2020.68. PDF.
On the uniform Roe algebra as a Banach algebra and embeddings of ℓp uniform Roe algebras (joint with Alessandro Vignati)
Bulletin of the London Mathematical Society 52 (2020), no. 5, 853-870. PDF.
Embeddings of uniform Roe algebras (joint with Ilijas Farah and Alessandro Vignati)
Communications in Mathematical Physics, 377 (2020), 1853–1882. PDF.
Uniform Roe coronas (joint with Ilijas Farah and Alessandro Vignati)
Advances in Mathematics, Volume 389, 8 October 2021, 107886. doi: 10.1016/j.aim.2021.107886. PDF.
On asymptotic uniform smoothness and nonlinear geometry of Banach spaces
Journal of the Institute of Mathematics of Jussieu (2019), 1-38. doi: 10.1017/S1474748019000124. PDF.
On the rigidity of uniform Roe algebras over uniformly locally finite coarse spaces (joint with Ilijas Farah)
Transactions of the American Mathematical Society 374 (2021), no. 2, 1007-1040. PDF.
Nonlinear weakly sequentially continuous embeddings between Banach spaces
International Mathematics Research Notices, rny181, doi: 10.1093/imrn/rny181. PDF.
Coarse embeddings into superstable spaces (joint with Andrew Swift)
Israel Journal of Mathematics (2019), 1–39. doi: 10.1007/s11856-019-1862-x. PDF.
On weaker notions of nonlinear embeddings between Banach spaces
Journal of Functional Analysis, 274 (2018), no. 11, 3149-3169. PDF.
Asymptotic structure and coarse Lipschitz geometry of Banach spaces
Studia Mathematica 237 (2017), no. 1, 71-97. PDF.
Coarse and uniform embeddings
Journal of Functional Analysis 272 (2017), no. 5, 1852-1875. PDF.
On the complexity of some inevitable classes of Banach spaces
Journal of Mathematical Analysis and Applications 431 (2015) 682-701. PDF.
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.
On the complexity of some classes of Banach spaces and non-universality
Czechoslovak Mathematical Journal 64 (2014), no. 4, 1123–1147. PDF.
On the Hausdorff metric and some openings between Banach spaces as Borel functions
Quaestiones Mathematicae 38 (2015), 403-411. PDF.
Research Notes
