U. Enstad, H. Thiel, E. Vilalta. Criteria for the existence of Schwartz Gabor frames over rational lattices, Int. Math. Res. Not. IMRN (to appear)
ArXiv preprint: arXiv:2408.03423

J. Bosa, E. Vilalta. Pure *-homomorphisms, J. Funct. Anal. 288 (2025), no. 3, 110739.
DOI: 10.1016/j.jfa.2024.110739 | ArXiv preprint: arXiv:2406.10949

R. Antoine, P. Ara, J. Bosa, F. Perera, E. Vilalta. The Cuntz semigroup of a ring, Selecta Math. 31 (2025), no. 6.
DOI: 10.1007/s00029-024-01002-9 | ArXiv preprint: arXiv:2307.07266

M. A. Asadi-Vasfi, H. Thiel, E. Vilalta. Ranks of soft operators in nowhere scattered C*-algebras,  J. Inst. Math. Jussieu  24 (2025), no. 2, 371-410.
DOI: 10.1017/S1474748024000318 | ArXiv preprint: arXiv:2310.00663

L. Cantier, E. Vilalta. Fraïssé Theory for Cuntz semigroups, J. Algebra 658 (2024), 319-364.
DOI: 10.1016/j.jalgebra.2024.05.052 | ArXiv preprint: arXiv:2308.15792

H. Thiel, E. Vilalta. Soft operators in C*-algebras, J. Math. Anal. Appl. 536 (2024), Article No. 128167, 35 pages.
DOI: 10.1016/j.jmaa.2024.128167 | ArXiv preprint: arXiv:2304.11644

E. Vilalta. Nowhere scattered multiplier algebras, Proc. Roy. Soc. Edinburgh Sect. A. (to appear, First View)
DOI: 10.1017/prm.2023.123 | ArXiv preprint: arXiv:2304.14007

H. Thiel, E. Vilalta. The Global Glimm Property, Trans. Amer. Math. Soc. 376 (2023), 4713-4744.
DOI: 10.1090/tran/8880 | ArXiv preprint: arXiv:2204.13059

H. Thiel, E. Vilalta. Nowhere scattered C*-algebras, J. Noncommut. Geom. 18 (2024), no. 1, 231-263
DOI: 10.4171/JNCG/526 | ArXiv preprint: arXiv:2112.09877

E. Vilalta. The Cuntz semigroup of unital commutative AI-algebras, Canad. J. Math. 75 (2023), no. 6, 1831-1868.
DOI: 10.4153/S0008414X22000542 | ArXiv preprint: arXiv:2104.08165

E. Vilalta. A local characterization for the Cuntz semigroup of AI-algebras, J. Math. Anal. Appl. 506 (2022), no. 1, 125612, 47 pages.
DOI: 10.1016/j.jmaa.2021.125612  |  ArXiv preprint: arXiv:2102.13557

H. Thiel, E. Vilalta. Covering dimension of Cuntz semigroups, Adv. Math. 394 (2022), 108016, 44 pages.
DOI: 10.1016/j.aim.2021.108016 | ArXiv preprint: arXiv:2101.04522

H. Thiel, E. Vilalta. Covering dimension of Cuntz semigroups II. Int. J. Math. 32 (2021), no. 14, 2150100, 27 pages.
DOI: 10.1142/S0129167X21501007 | ArXiv preprint: arXiv:2103.13062

U. Enstad, E. Vilalta. Z-stability of twisted group C*-algebras of nilpotent groups, 2025.
ArXiv preprint: arXiv:2503.18088

R. Antoine, P. Ara, J. Bosa, F. Perera, E. Vilalta.  Ideals, quotients, and continuity of the Cuntz semigroup for rings, 2024.
ArXiv preprint: arXiv:2411.00507

R. Antoine, F. Perera, H. Thiel, E. Vilalta. Pure C*-algebras, 2024.
ArXiv preprint: arXiv:2406.11052

The range problem and dimension theory for the Cuntz semigroup. My PhD thesis at Universitat Autònoma de Barcelona, under the supervision of Francesc Perera, 2022.

An overview of Uniform Roe Algebras: Asymptotic Dimension and Real Rank. My master thesis at Universitat Politècnica de Catalunya, under the supervision of Francesc Perera, 2019.

K-theory for C*-algebras: The hexagonal exact sequence, Reports@SCM (2021). Short introduction to K-theory for C*-algebras based on my bachelor thesis (as part of the Emmy Noether Prize, see my CV).

Teoria K per C*-àlgebres. My bachelor thesis (in catalan) at Universitat Autònoma de Barcelona, under the supervision of Francesc Perera, 2018.