Publications

In Progress

  1. The dynamical Cuntz semigroup and ideal-free quotients of Cuntz semigroups (with Joan Bosa, Jianchao Wu, and Joachim Zacharias), 41 pp.

Preprints

  1. The Cuntz semigroup of a ring (with Ramon Antoine, Pere Ara, Joan Bosa, and Eduard Vilalta), 43 pp. arXiv: 2307.07266v1
  2. The modern theory of Cuntz semigroups of C*-algebras (with Eusebio Gardella), 61 pp. arXiv: 2212.02290v2

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