Publications and Preprints
[-] Tracially complete C*-algebras (with Carrion, Evington, Gabe, Schafhauser, Tikuisis and White).
ArXiv.
[-] On topologically zero-dimensional morphisms (with R. Neagu).
Journal of Functional Analysis 286 (9) 110368. Journal, ArXiv.
[-] On tracial Z-stability of simple non-unital C*-algebras (with K. Li and G. Szabo).
Canadian Journal of Mathematics to appear. Journal, ArXiv.
[-] Stabilising uniform property Gamma (with S. Evington).
Proceedings of the American Mathematical Society 149 (2021), 4725-4737. Journal, ArXiv.
[-] Nuclear dimension of simple C*-algebras (with S. Evington, A. Tikuisis, S. White and W. Winter).
Inventiones Mathematicae 224 (2021), 245–290. Journal, ArXiv.
[-] Uniform property Gamma (with S. Evington, A. Tikuisis and S. White).
International Mathematical Research Notices 2022(13), 9864–9908. Journal, ArXiv.
[-] Classifying maps into uniform tracial sequence algebras (with S. Evington, A. Tikuisis and S. White).
Münster Journal of Mathematics 14 (2021), 265-281. Journal, ArXiv.
[-] Erratum to: Classifying maps into uniform tracial sequence algebras (with S. Evington, A. Tikuisis and S. White).
Münster Journal of Mathematics to appear. Journal.
[-] Nuclear dimension of simple stably projectionless C*-algebras (with S. Evington).
Analysis & PDE 13-7 (2020), 2205-2240. Journal, ArXiv.
[-] C*-algebras and their nuclear dimension.
Contemporary Mathematics 775 (2021), 41-64. Journal, ArXiv.
[-] Decomposable approximations and approximately finite C*-algebras.
Mathematical Proceedings of the Cambridge Philosophical Society, 162(1) (2017), 1-12. Journal, ArXiv.
In preparation
Coloured equivalence of C*-algebras (with James Gabe, Aaron Tikuisis and Stuart White). Preprint available upon request.
Coloured classification of simple Z-stable C*-algebras.
My papers on arXiv.
Talks
The non-unital Toms-Winter conjecture. Barcelona-Kiel operator algebra seminar. May 2022.
What is a C*-algebra? IMCU Colloquium, UNAM. April 2022.
VI Latin American Congress of Mathematicians. Uruguay 2021.
8th European Congress of Mathematics. Slovenia, 2021.
Property Gamma on von Neumann algebras and C* algebras. Noncommutative Harmonic Analysis at ICMAT-UAM, 2021.
Property Gamma. Quantum Symmetries Student Seminar. Ohio State University, 2020.
Stabilising uniform Property Gamma. Operator Algebra and Noncommutative Geometry Seminar. University of Wollongong , 2020.
The Toms-Winter conjecture. Functional Analysis Seminar. Université de Franche-Comté, 2020.
VI Latin American Congress of Mathematicians. Uruguay 2020.
Uniform property gamma. Functional Analysis Seminar, University of Oxford, 2020.
The Toms-Winter conjecture. Functional Analysis Seminar. IMPAN, 2020.
Spring Program on Operator Algebras. East China Normal University, 2020.
Non commutative Choquet-de Leeuw theorem. Working seminar. IMPAN, 2020.
Regularity properties of nuclear C*-algebras. East Coast Operator Algebras Symposium, Ohio State University, 2019.
Applications of CPoU and uniform property Gamma. Topology and Measure in Dynamics and Operator Algebras, Banff International Research Station, 2019.
Nuclear dimension of Z-stable C*-algebras. Operator Algebras Seminar. Institut de Mathématiques de Jussieu-Paris Rive Gauche, 2019.
An introduction to the Elliott intertwining. Operator Algebra Working Seminar. KU Leuven, 2019.
The Toms-Winter conjecture. Ring theory seminar. Universitat Autonoma Barcelona, 2018.
Classification of strict closures. Operator Algebra Working Seminar. KU Leuven, 2018.
A non-commutative topological dimension. Methusalem Symposium. KU Leuven, 2018.
Classification of strict closures. Analysis Seminar. University of Glasgow, 2018.
A non-commutative topological dimension. Casa Matematica Oaxaca BIRS. Mexico, 2018.
Structure and classification of C*-algebras. Methusalem Colloquia. KU Leuven, 2018.
The Toms-Winter conjecture. Operator Algebras Seminar. KU Leuven, 2017.
Partitions of unity and the Toms-Winter conjecture. Applications of the UCT for C*-algebras. University of Copenhagen, 2017.
An invitation to Operator Algebras. Mathematical Colloquium of Oaxaca. National Autonomous University of Mexico, 2017.
An invitation to Operator Algebras. Analysis Seminar. Technological University of the Mixteca, 2017.
Constructing order zero maps. Young Mathematicians in C*-algebras. University of Copenhagen, 2017.
Coloured isomorphic C*-algebras. Workshop on C*-algebras and dynamical systems. Centre de Reserca Matematica, UAB, 2017.
Coloured isomorphisms of C*-algebras. Operator Algebras Seminar. KU Leuven 2017.
Colours and order zero maps. Young Functional Analysts' Workshop. Queen's University Belfast, 2016.
Colouring C*-algebras. Scottish Operator Algebras Seminar. University of Aberdeen, 2016.
Coloured Equivalence of C*-algebras. Analysis Seminar. University of Newcastle, 2016.
Nuclear C*-algebras and Coloured Equivalence. KU Leuven, 2016.
Coloured Equivalence of C*-algebras. Kleines Seminar. University of Muenster, 2015.
Coloured Classification of C*-algebras. Young Mathematicians in C*-algebras. University of Copenhagen, 2015.
Classification of AF-algebras. University of Glasgow, 2015.
Covering Dimension. University of Glasgow, 2014.
Decomposable Approximations and nuclear dimension at most omega. CSTAR, University of Glasgow, 2014
The Jones Polynomial. University of Glasgow, 2014
Decomposable approximations and approximately finite C*-algebras. Young Functional Analysts' Workshop. Lancaster University, 2014
Non-smooth analysis. University of Glasgow, 2014
Theses
Decomposable approximations and coloured equivalence of C*-algebras. PhD thesis in Mathematics, University of Glasgow, 2016.
The topological algebra L(X) and subnormed spaces (in Spanish). Bachelor thesis in Mathematics, National Autonomous University of Mexico, 2010.