Publications

On the arXiv
On MathScinet

In Progress

  1. Almost elementary dynamical systems in measure and the small boundary property (with Joan Bosa, Jianchao Wu, and Joachim Zacharias), 55 pp.

Preprints

  1. Ideals, quotients, and continuity of the Cuntz semigroup for rings (with Ramon Antoine, Pere Ara, Joan Bosa, and Eduard Vilalta), 38 pp. arXiv: 2411.00507
  2. The dynamical Cuntz semigroup and ideal-free quotients of Cuntz semigroups (with Joan Bosa, Jianchao Wu, and Joachim Zacharias), 49 pp. arXiv: 2409.16274
  3. Levels of cancellation for monoids and modules (with Pere Ara, Ken Goodearl, Pace P. Nielsen, Kevin C. O’Meara, and Enric Pardo), 32 pp. arXiv: 2409.06880
  4. Pure C*-algebras (with Ramon Antoine, Hannes Thiel, and Eduard Vilalta), 18 pp. arXiv: 2406.11052v2

Forthcoming

  1. Regular ring properties degraded through inverse limits (with Pere Ara, Ken R. Goodearl, Kevin C. O’Meara, and Enric Pardo), 23 pp., to appear in Journal of Algebra,
    arXiv: 2405.06837
  2. The Cuntz semigroup of a ring (with Ramon Antoine, Pere Ara, Joan Bosa, and Eduard Vilalta), 43 pp., to appear in Selecta Mathematica, arXiv: 2307.07266v1
  3. The modern theory of Cuntz semigroups of C*-algebras (with Eusebio Gardella), 82 pp., to appear in EMS Surveys in Mathematical Sciences,
    doi: 10.4171/EMSS/84 arXiv: 2212.02290v2
  4. The separativity problem in terms of varieties and diagonal reduction (with Pere Ara, Ken R. Goodearl, Pace P. Nielsen, and Enric Pardo), 28 pp., to appear in Proceedings of NonCommutative Rings and their Applications, VIII (A. Laghribi and A. Leroy, eds.), Contemporary Mathematics, arXiv: 2403.11837

Publications

  1. Traces on ultrapowers of C*-algebras (with Ramon Antoine, Leonel Robert, and Hannes Thiel), Journal of Functional Analysis, 286 (2024), 110341.
    doi: 10.1016/j.jfa.2024.110341 arXiv: 2303.01929v2
  2. C*-algebras of stable rank one and their Cuntz semigroups (with Ramon Antoine, Leonel Robert, and Hannes Thiel), Duke Mathematical Journal, 171 (2022), 33-99.
    doi: 10.1215/00127094-2021-0009 arXiv: 1809.03984
  3. Edwards’ condition for Quasitraces on C*-algebras (with Ramon Antoine, Leonel Robert, and Hannes Thiel), Proceedings of the Royal Society of Edinburgh, Section A, 151 (2021), 525-547.
    doi: 10.1017/prm.2020.26 arXiv: 1909.12787
  4. Cuntz semigroups of ultraproduct C*-algebras (with Ramon Antoine and Hannes Thiel), Journal of the London Mathematical Society, 102 (2020), 994-1029.
    doi: 10.1112/jlms.12343 arXiv: 1905.03208.
  5. Abstract bivariant Cuntz semigroups (with Ramon Antoine and Hannes Thiel), International Mathematics Research Notices, no. 17 (2020), 5342-5386.
    doi: 10.1093/imrn/rny143 arXiv:1702.01588.
  6. Abstract bivariant Cuntz semigroups II (with Ramon Antoine and Hannes Thiel), Forum Mathematicum, 32 (2020), 45-62.
    doi: 10.1515/forum-2018-0285 arXiv:1811.08689.
  7. Perforation conditions and almost algebraic order in Cuntz semigroups (with Ramon Antoine and Henning Petzka), Proceedings of the Royal Society of Edinburgh, Section A, 148 (2018), 669-702.
    doi: 10.1017/S0308210518000069 arXiv:1604.06718.
  8. Tensor products and regularity properties of Cuntz semigroups (with Ramon Antoine and Hannes Thiel), Memoirs of the American Mathematical Society, 251 (2018), no. 1199, 199 pp.
    doi: 10.1090/memo/1199 arXiv: 1410.0483.
  9. The Cuntz semigroup and stability of close C*-algebras (with Andrew S. Toms, Stuart White, and Wilhelm Winter), Analysis and PDE, 7 (2014), 929-952.
    doi: 10.2140/apde.2014.7.929 arXiv: 1210.4533.
  10. Recovering the Elliott invariant from the Cuntz semigroup (with Ramon Antoine, Marius Dadarlat, and Luis Santiago), Transactions of the American Mathematical Society, 366 (2014), no. 6, 2907-2922.
    doi: 10.1090/S0002-9947-2014-05833-9 arXiv: 1109.5803.
  11. Geometric structure of dimension functions of certain continuous fields (with Ramon Antoine, Joan Bosa, and Henning Petzka), Journal of Functional Analysis, 266 (2014), no. 4, 2403-2423.
    doi: 10.1016/j.jfa.2013.09.013 arXiv: 1305.7495.
  12. The Cuntz semigroup of continuous fields (with Ramon Antoine and Joan Bosa), Indiana University Mathematics Journal, 62 (2013), no. 4, 1105-1131.
    doi: 10.1512/iumj.2013.62.5071 arXiv: 1205.6608.
  13. The Cuntz semigroup, a Riesz type interpolation property, comparison and the ideal property (with Cornel Pasnicu), Publicacions Matemàtiques, 57 (2013), no. 2, 359-377.
    doi: 10.5565/PUBLMAT_5723_04 arXiv: 1012.5216.
  14. The corona factorization property, stability, and the Cuntz semigroup of a C*-algebra (with Eduard Ortega and Mikael Rørdam), International Mathematics Research Notices, 2012, no. 1, 34-66.
    doi: 10.1093/imrn/rnr013 arXiv: 0903.2917.
  15. Completions of monoids with applications to the Cuntz semigroup (with Ramon Antoine and Joan Bosa), International Journal of Mathematics, 22 (2011), no. 6, 837-861.
    doi: 10.1142/S0129167X11007057 arXiv: 1003.2874.
  16. The corona factorization property and refinement monoids (with Eduard Ortega and Mikael Rørdam), Transactions of the American Mathematical Society, 363 (2011), no. 9, 4505-4525.
    doi: 10.1090/S0002-9947-2011-05480-2 arXiv: 0904.0541.
  17. Pullbacks, C(X)-algebras, and their Cuntz semigroup (with Ramon Antoine and Luis Santiago), Journal of Functional Analysis, 260 (2011), no. 10, 2844-2880.
    doi: 10.1016/j.jfa.2011.02.016 arXiv: 1101.4776.
  18. Appendix: basic definitions and results for operator algebras (with Pere Ara and Fernando Lledó), in Aspects of operator algebras and applications, 157-168, Contemporary Mathematics, 534, American Mathematical Society, Providence, RI, 2011.
    doi: 10.1090/conm/534
  19. K-theory for operator algebras. Classification of C*-algebras (with Pere Ara and Andrew S. Toms), in Aspects of operator algebras and applications, 1-71, Contemporary Mathematics, 534, American Mathematical Society, Providence, RI, 2011.
    doi: 10.1090/conm/534 arXiv: 0902.3381.
  20. Purely infinite corona algebras of simple C*-algebras with real rank zero (with Dan Kucerovsky), Journal of Operator Theory, 65 (2011), no. 1, 131-144.
  21. Non-simple purely infinite rings (with Gonzalo Aranda Pino, Ken R. Goodearl, and Mercedes Siles Molina), American Journal of Mathematics, 132 (2010), no. 3, 563-610.
    doi: 10.1353/ajm.0.0119 arXiv: 0806.4156.
  22. Chain conditions for Leavitt path algebras (with Gene Abrams, Gonzalo Aranda Pino, and Mercedes Siles Molina), Forum Mathematicum, 22 (2010), no. 1, 95-114. doi: 10.1515/forum.2010.005
  23. Purely infinite corona algebras of simple C*-algebras (with Dan Kucerovsky and Ping Wong Ng), Mathematische Annalen, 346 (2010), no. 1, 23-40.
    doi: 10.1007/s00208-009-0382-0
  24. Computing the maximal algebra of quotients of a Lie algebra (with Matej Brešar, Juana Sánchez Ortega, and Mercedes Siles Molina), Forum Mathematicum, 21 (2009), no. 4, 601-620.
    doi: 10.1515/FORUM.2009.030
  25. Finitely generated antisymmetric graph monoids (with Pere Ara and Friedrich Wehrung), Journal of Algebra, 320 (2008), no. 5, 1963-1982.
    doi: 10.1016/j.jalgebra.2008.06.013
  26. The Cuntz semigroup, the Elliott conjecture, and dimension functions on C*-algebras (with Nate P. Brown and Andrew S. Toms), Journal für die Reine und Angewandte Mathematik, 621 (2008), 191-211.
    doi: 10.1515/CRELLE.2008.062 arXiv: math/0609182.
  27. Strongly non-degenerate Lie algebras (with Mercedes Siles Molina), Proceedings of the American Mathematical Society, 136 (2008), no. 12, 4115-4124.
    doi: 10.1090/S0002-9939-08-09558-0 arXiv: 0802.1591.
  28. Associative and Lie algebras of quotients (with Mercedes Siles Molina), Publicacions Matemàtiques, 52 (2008), no. 1, 129-149.
    doi: 10.5565/PUBLMAT_52108_06 arXiv: math/0509510.
  29. Non-stable K-theory for QB-rings (with Pere Ara), Mathematica Scandinavica, 100 (2007), no. 2, 265-300.
    doi: 10.7146/math.scand.a-15024
  30. Recasting the Elliott conjecture (with Andrew S. Toms), Mathematische Annalen, 338 (2007), no. 3, 669-702.
    doi: 10.1007/s00208-007-0093-3 arXiv: math/0601478.
  31. Inverse limits of rings and multiplier rings (with Gert K. Pedersen), Mathematical Proceedings of the Cambridge Philosophical Society, 139 (2005), no. 2, 207-228.
    doi: 10.1017/S0305004105008704 arXiv: math/0307385.
  32. Extensions and pullbacks in QB-rings (with Pere Ara and Gert K. Pedersen), Algebras and Representation Theory, 8 (2005), no. 1, 75-97.
    doi: 10.1007/s10468-004-5767-x arXiv: math/0107104.
  33. Simple Riesz groups of rank one having wild intervals (with Francisco Ortus and Enric Pardo), Journal of Algebra, 284 (2005), no. 1, 111-140.
    doi: 10.1016/j.jalgebra.2004.10.002 arXiv: math/0405035.
  34. AF-embeddings into C*-algebras of real rank zero (with Mikael Rørdam), Journal of Functional Analysis, 217 (2004), no. 1, 142-170.
    doi: 10.1016/j.jfa.2004.05.001 arXiv: math/0310340.
  35. Gromov translation algebras over discrete trees are exchange rings (with Pere Ara and Kevin C. O’Meara), Transactions of the American Mathematical Society, 356 (2004), no. 5, 2067-2079.
    doi: 10.1090/S0002-9947-03-03372-5
  36. Stable finiteness of group rings in arbitrary characteristic (with Pere Ara and Kevin C. O’Meara), Advances in Mathematics, 170 (2002), no. 2, 224-238.
    doi: 10.1006/aima.2002.2075
  37. A closure operation in rings (with Pere Ara and Gert K. Pedersen), International Journal of Mathematics, 12 (2001), no. 7, 791-812.
    doi: 10.1142/S0129167X01001039
  38. Ideal structure of multiplier algebras of simple C*-algebras with real rank zero, Canadian Journal of Mathematics, 53 (2001), no. 3, 592-630.
    doi: 10.4153/CJM-2001-025-2
  39. Algebraic aspects in the classification of C*-algebras, Irish Mathematical Society Bulletin, No. 45 (2000), 33-55.
  40. Extremal richness of multiplier and corona algebras of simple C*-algebras with real rank zero, Journal of Operator Theory, 44 (2000), no. 2, 413-431. arXiv: math/9906180.
  41. An infinite analogue of rings with stable rank one (with Pere Ara and Gert K. Pedersen), Journal of Algebra, 230 (2000), no. 2, 608-655.
    doi: 10.1006/jabr.2000.8330 arXiv: math/9910131.
  42. Multipliers of von Neumann regular rings (with Pere Ara), Communications in Algebra, 28 (2000), no. 7, 3359-3385.
    doi: 10.1080/00927870008827031
  43. Lifting units modulo exchange ideals and C*-algebras with real rank zero, Journal für die Reine und Angewandte Mathematik, 522 (2000), 51-62.
    doi: 10.1515/crll.2000.040 arXiv: math/9906181.
  44. The structure of countably generated projective modules over regular rings (with Pere Ara and Enric Pardo), Journal of Algebra, 226 (2000), no. 1, 161-190.
    doi: 10.1006/jabr.1999.8156
  45. Monoids arising from positive matrices over commutative C*-algebras, Mathematical Proceedings of the Royal Irish Academy, 99A (1999), no. 1, 75-84.
  46. The structure of positive elements for C*-algebras with real rank zero, International Journal of Mathematics, 8 (1997), no. 3, 383-405.
    doi: 10.1142/S0129167X97000196