Carles Casacuberta

Prepublicacions

• Sketchable infinity categories, amb Javier J. Gutiérrez i David Martínez-Carpena.
  arxiv:2511.01497 [math.AT]


• Chordless cycle filtrations for dimensionality detection in complex networks via topological data analysis,
  Aina Ferrà Marcús, Robert Jankowski, Meritxell Vila Miñana, Carles Casacuberta, M. Ángeles Serrano.
  arXiv:2509.08350 [physics.soc-ph,cs.LG,math.AT]


• Homotopy reflectivity is equivalent to the weak Vopěnka principle, amb Javier J. Gutiérrez.
  arXiv:2410.21244 [math.AT]


• Attending to topological spaces: The Cellular Transformer,
  Rubén Ballester, Pablo Hernández-García, Mathilde Papillon, Claudio Battiloro, Nina Miolane, Tolga Birdal, Carles Casacuberta, Sergio Escalera, Mustafa Hajij.
  arXiv:2405.14094 [cs.LG]


• Classifying spaces of infinity groupoids, amb David Martínez-Carpena.


• Localizations of models of theories with arities, amb Aina Ferrà.


• Motivic homological localizations and stable cellularity, amb David White.


• Cohomological localization towers, amb Imma Gálvez-Carrillo i Andrew Tonks.

Articles i monografies

• Topological Data Analysis for Neural Networks,
  Rubén Ballester, Carles Casacuberta, Sergio Escalera.
  SpringerBriefs in Computer Science, Springer, Cham, 2026.
  DOI:10.1007/978-3-032-08283-1


• Escriure Matemàtiques a la Universitat, amb Artur Travesa.
  Serveis Lingüístics de la Universitat de Barcelona, 2025, accés obert.
  https://diposit.ub.edu/dspace/handle/2445/221818


• Reconstruction of univariate functions from directional persistence diagrams,
  Aina Ferrà Marcús, Carles Casacuberta, Oriol Pujol.
  Applicable Algebra in Engineering, Communication and Computing, 2026.
  arXiv:2203.01894 [math.AT]


• Higher-order molecular learning: The Cellular Transformer,
  Melih Barsbey, Rubén Ballester, Andac Demir, Carles Casacuberta, Pablo Hernández-García, David Pujol-Perich, Sarper Yurtseven, Sergio Escalera, Claudio Battiloro, Mustafa Hajij, Tolga Birdal.
  ICLR 2025 Workshop on Generative and Experimental Perspectives for Biomolecular Design.
  https://openreview.net/forum?id=GW3h79mxrF


• MANTRA: The Manifold Triangulations Assemblage,
  Rubén Ballester, Ernst Röell, Daniel Bin Schmid, Mathieu Alain, Sergio Escalera, Carles Casacuberta, Bastian Rieck.
  The Thirteenth International Conference on Learning Representations, ICLR 2025.
  https://openreview.net/forum?id=X6y5CC44HM


• Homotopies i homologies: de Poincaré fins avui.
  Discurs de presentació com a membre numerari de la Secció de Ciències i Tecnologia de l'Institut d'Estudis Catalans (2024), ISBN: 978-84-9965-752-3.
  DOI:10.2436/10.2000.81.1


• Predicting the generalization gap in neural networks using topological data analysis,
  Rubén Ballester, Xavier Arnal Clemente, Carles Casacuberta, Meysam Madadi, Ciprian A. Corneanu, Sergio Escalera.
  Neurocomputing 596 (2024), 127787, open access.
  DOI:10.1016/j.neucom.2024.127787


• Decorrelating neurons using persistence,
  Rubén Ballester, Carles Casacuberta, Sergio Escalera.
  2nd NeurIPS Workshop on Symmetry and Geometry in Neural Representations,
  Proceedings of Machine Learning Research 228:164-182 (2024), open access.
  https://proceedings.mlr.press/v228/ballester24a.html


• A topological classifier to characterize brain states: When shape matters more than variance,
  Aina Ferrà, Gloria Cecchini, Fritz-Pere Nobbe Fisas, Carles Casacuberta, Ignasi Cos.
  PLoS ONE (2023) 18(10):e0292049, open access.
  DOI:10.1371/journal.pone.0292049


• Importance attribution in neural networks by means of persistence landscapes of time series,
  Aina Ferrà, Carles Casacuberta, Oriol Pujol.
  Neural Computing and Applications (2023) 35:20143-20156, open access.
  DOI:10.1007/s00521-023-08731-6


• Cohomological localizations and set-theoretical reflection.
  Mathematics Going Forward: Collected Mathematical Brushstrokes, Lecture Notes in Mathematics 2313, Springer, Cham (2023), 167-181.
  DOI:10.1007/978-3-031-12244-6_13


• Influence in social networks through visual analysis of image memes,
  Carles Onielfa, Carles Casacuberta, Sergio Escalera.
  Artificial Intelligence Research and Development (CCIA, Sitges, 2022),
  Frontiers in Artificial Intelligence and Applications 356, IOS Press (2022), 71-80, open access.
  DOI:10.3233/FAIA220317


• Comparing localizations across adjunctions, amb Oriol Raventós i Andrew Tonks.
  Transactions of the American Mathematical Society 374 (2021), 7811-7865.
  DOI:10.1090/tran/8382


• Depth and simplicity of Ohkawa's argument.
  Bousfield Classes and Ohkawa's Theorem (Nagoya, 2015), Springer Proceedings in Mathematics & Statistics 309, Springer, Singapore (2020), 3-15.
  DOI:10.1007/978-981-15-1588-0_2


• Combinatorial homotopy categories, amb Jirí Rosický.
  Bousfield Classes and Ohkawa's Theorem (Nagoya, 2015), Springer Proceedings in Mathematics & Statistics 309, Springer, Singapore (2020), 89-101.
  DOI:10.1007/978-981-15-1588-0_4


• Localizations of abelian Eilenberg-Mac Lane spaces of finite type, amb José L. Rodríguez i Jin-yen Tai.
  Algebraic & Geometric Topology 16 (2016), 2379-2420.
  DOI:10.2140/agt.2016.16.2379


• Definable orthogonality classes in accessible categories are small, amb Joan Bagaria, A. R. D. Mathias i Jirí Rosický.
  Journal of the European Mathematical Society 17 (2015), 549-589.
  DOI:10.4171/JEMS/511


• A generalization of Ohkawa's theorem, amb Javier J. Gutiérrez i Jirí Rosický.
  Compositio Mathematica 150 (2014), 893-902.
  DOI:10.1112/S0010437X13007616


• Are all localizing subcategories of stable homotopy categories coreflective?, amb Javier J. Gutiérrez i Jirí Rosický.
  Advances in Mathematics 252 (2014), 158-184.
  DOI:10.1016/j.aim.2013.10.013


• Localization of algebras over coloured operads, amb Javier J. Gutiérrez, Ieke Moerdijk i Rainer M. Vogt.
  Proceedings of the London Mathematical Society 101 (2010), 105-136.


• Epireflections and supercompact cardinals, amb Joan Bagaria i Adrian R. D. Mathias.
  Journal of Pure and Applied Algebra 213 (2009), 1208-1215.


• Brown representability does not come for free, amb Amnon Neeman.
  Mathematical Research Letters 16 (2009), 1-5.


• Postnikov pieces of finite dimension, amb Manuel Castellet.
  L'Enseignement Mathématique 54 (2008), 61-63.


• Homotopy localization of groupoids, amb Marek Golasinski i Andrew Tonks.
  Forum Mathematicum 18 (2006), 967-982.


• The orthogonal subcategory problem in homotopy theory, amb Boris Chorny.
  An Alpine Anthology of Homotopy Theory (Arolla, 2004), Contemporary Mathematics 399, American Mathematical Society, Providence (2006), 41-53.


• Implications of large-cardinal principles in homotopical localization, amb Dirk Scevenels i Jeffrey H. Smith.
  Advances in Mathematics 197 (2005), 120-139.


• Homotopical localizations of module spectra, amb Javier J. Gutiérrez.
  Transactions of the American Mathematical Society 357 (2005), 2753-2770.


• Relative group completions, amb An Descheemaeker.
  Journal of Algebra 285 (2005), 451-469.


• On the existence of group localizations under large-cardinal axioms, amb Dirk Scevenels.
  Revista de la Real Academia de Ciencias, Serie A, Matemáticas 95 (2001), 163-170.


• A homotopy idempotent construction by means of simplicial groups, amb Gemma Bastardas.
  Israel Journal of Mathematics 121 (2001), 333-349.


• Homological localizations preserve 1-connectivity, amb Jérôme Scherer.
  Une Dégustation Topologique: Homotopy Theory in the Swiss Alps (Arolla, 1999), Contemporary Mathematics 265, American Mathematical Society, Providence (2000), 1-6.


• On structures preserved by idempotent transformations of groups and homotopy types.
  Crystallographic Groups and Their Generalizations (Kortrijk, 1999), Contemporary Mathematics 262, American Mathematical Society, Providence (2000), 39-68.


• On saturated classes of morphisms, amb Armin Frei.
  Theory and Applications of Categories 7 (2000), 43-46.


• Localizations as idempotent approximations to completions, amb Armin Frei.
  Journal of Pure and Applied Algebra 142 (1999), 25-33.


• Singly generated radicals associated with varieties of groups, amb José L. Rodríguez i Dirk Scevenels.
  Groups St Andrews 1997 in Bath, I, London Mathematical Society Lecture Note Series 260, Cambridge University Press, Cambridge (1999), 202-210.


• On Postnikov pieces of finite dimension.
  Collectanea Mathematica 49 (1998), 257-263.


• Models for torsion homotopy types, amb José L. Rodríguez i Luis J. Hernández Paricio.
  Israel Journal of Mathematics 107 (1998), 301-318.


• A universal space for plus-constructions, amb A. J. Berrick.
  Topology 38 (1999), 467-477.


• On weak homotopy equivalences between mapping spaces, amb José L. Rodríguez.
  Topology 37 (1998), 709-717.


• On towers approximating homological localizations, amb José L. Rodríguez.
  Journal of the London Mathematical Society 56 (1997), 645-656.


• On genus and embeddings of torsion-free nilpotent groups of class two, amb Charles Cassidy i Dirk Scevenels.
  Manuscripta Mathematica 92 (1997), 463-475.


• Extending localization functors, amb Armin Frei i Tan Geok Choo.
  Journal of Pure and Applied Algebra 103 (1995), 149-165.


• Extended genus of torsion-free finitely generated nilpotent groups of class two, amb Charles Cassidy i Youssef El From.
  Communications in Algebra 23 (1995), 3799-3814.


• Anderson localization from a modern point of view.
  The Cech Centennial: A Conference on Homotopy Theory (Boston, 1993), Contemporary Mathematics 181, American Mathematical Society, Providence (1995), 35-44.


• Recent advances in unstable localization.
  The Hilton Symposium 1993: Topics in Topology and Group Theory (Montréal, 1993), CRM Proceedings Lecture Notes 6, American Mathematical Society, Providence (1994), 1-22.


• On the rationalization of the circle.
  Proceedings of the American Mathematical Society 118 (1993), 995-1000.


• Localizing with respect to self maps of the circle, amb Georg Peschke.
  Transactions of the American Mathematical Society 339 (1993), 117-140.


• On finite groups acting on acyclic complexes of dimension two, amb Warren Dicks.
  Publicacions Matemàtiques 36 (1992), 463-466.


• Localization methods in the study of the homology of virtually nilpotent groups, amb Manuel Castellet.
  Mathematical Proceedings of the Cambridge Philosophical Society 112 (1992), 551-564.


• On nilpotent groups which are finitely generated at every prime, amb Peter Hilton.
  Expositiones Mathematicae 10 (1992), 385-401.


• A note on extensions of nilpotent groups, amb Peter Hilton.
  Adams Memorial Symposium on Algebraic Topology, Vol. 1 (Manchester, 1990), London Mathematical Society Lecture Note Series 175, Cambridge University Press, Cambridge (1992), 225-234.


• On orthogonal pairs in categories and localisation, amb Georg Peschke i Markus Pfenniger.
  Adams Memorial Symposium on Algebraic Topology, Vol. 1 (Manchester, 1990), London Mathematical Society Lecture Note Series 175, Cambridge University Press, Cambridge (1992), 211-223.


• Groups and spaces with all localizations trivial, amb A. J. Berrick.
  Algebraic Topology; Homotopy and Group Cohomology (Sant Feliu de Guíxols, 1990), Lecture Notes in Mathematics 1509, Springer-Verlag, Berlin, Heidelberg (1992), 20-29.


• The behaviour of homology in the localization of finite groups.
  Canadian Mathematical Bulletin 34 (1991), 311-320.


• Calculating the Mislin genus for a certain family of nilpotent groups, amb Peter Hilton.
  Communications in Algebra 19 (1991), 2051-2069.


• Sur la localisation dans les catégories avec une application à la théorie de l'homotopie, amb Georg Peschke i Markus Pfenniger.
  Comptes Rendus de l'Académie des Sciences de Paris, Série I, Mathématiques 310 (1990), 207-210.


• On special nilpotent groups, amb Peter Hilton.
  Bulletin de la Societé Mathématique de Belgique, Série B 41 (1989), 261-273.


• On the extended genus of finitely generated abelian groups, amb Peter Hilton.
  Bulletin de la Societé Mathématique de Belgique, Série A 41 (1989), 51-72.


• Localization of q-abelian groups.
  Archiv der Mathematik (Basel) 53 (1989), 424-435.

Llibres

• Simplicial Methods for Operads and Algebraic Geometry, amb Joachim Kock (editors).
  Advanced Courses in Mathematics CRM Barcelona, Birkhäuser, Basel (2010), ISBN 978-3-0348-0052-5.


• La formació del professorat de matemàtiques: d'infantil a la universitat, amb Jordi Deulofeu i Pili Royo (editors).
  Societat Catalana de Matemàtiques, filial de l'Institut d'Estudis Catalans, Barcelona (2006), ISBN 84-7283-854-4.


• Models matemàtics en la ciència i en la societat (editor).
  Aula de Ciència i Cultura núm. 13, Fundació Caixa de Sabadell, Sabadell (2002), ISBN 84-95166-37-2.


• Mathematical Glimpses into the 21st Century, amb Rosa M. Miró-Roig, Joaquín M. Ortega i Sebastià Xambó-Descamps (editors).
  Centre Internacional de Mètodes Numèrics en Enginyeria i Societat Catalana de Matemàtiques, filial de l'Institut d'Estudis Catalans, Barcelona (2001), ISBN 84-89925-85-2.


• European Congress of Mathematics, vol. II, amb Rosa M. Miró-Roig, Joan Verdera i Sebastià Xambó-Descamps (editors).
  Progress in Mathematics 202, Birkhäuser Verlag, Basel (2001), ISBN 3-7643-6418-1.


• European Congress of Mathematics, vol. I, amb Rosa M. Miró-Roig, Joan Verdera i Sebastià Xambó-Descamps (editors).
  Progress in Mathematics 201, Birkhäuser Verlag, Basel (2001), ISBN 3-7643-6417-3.


• Cohomological Methods in Homotopy Theory, amb Jaume Aguadé i Carles Broto (editors).
  Progress in Mathematics 196, Birkhäuser Verlag, Basel (2001), ISBN 3-7643-6588-9.


• Algebraic Topology: New Trends in Localization and Periodicity, amb Carles Broto i Guido Mislin (editors).
  Progress in Mathematics 136, Birkhäuser Verlag, Basel (1996), ISBN 3-7643-5333-3.


• Mathematical Research Today and Tomorrow; Viewpoints of Seven Fields Medalists, amb Manuel Castellet (editors).
  Lecture Notes in Mathematics 1525, Springer-Verlag, Berlin, Heidelberg (1992), ISBN 3-540-56011-4.


• Espais topològics amb accions P-locals.
  Tesi doctoral, Publicacions de la Universitat Autònoma de Barcelona (1988), ISBN 84-7488-403-9 (microforma).