Preprints

• On the l-adic homotopy type of configuration spaces  (with Geoffroy Horel)

Preprint arxiv: 2606.31949[ math.AT]

• On the real homotopy type of compact complex surfaces
  Preprint arXiv: 2601.01958 [math.AT].
  
  

Publications

• Equivariant formality of the little disks operad (with Pedro Boavida and Geoffroy Horel)
  Forum of Mathematics, Pi (First Online 2026).
  [ Arxiv ] [ Journal (open access)]

• Formality of hypercommutative algebras of Kähler and Calabi-Yau manifolds (with Geoffroy Horel)
  Journal of the European Mathematical Society (First online 2026).
  [ Arxiv ] [ Journal ]

• An operadic proof of the BTT Theorem (with Geoffroy Horel)
  Philosophical Transactions A  (2026).
  [ Arxiv ] [ Journal ]

• Model category structures on truncated multicomplexes for complex geometry (with Muriel Livernet and Sarah Whitehouse)
  Bulletin of the London Mathematical Society, Vol. 57, Issue 12 (2025).
  [ Arxiv ] [ Journal (open access)]

• A-infinity structures for Bott-Chern and Aeppli cohomologies (with Roger Garrido-Vilallave and Anna Sopena-Gilboy)
  Complex Manifolds Volume 12 Issue 1 (2025).
  [Journal (open access)]

• Homotopy BV-algebras in Hermitian geometry (with Scott O. Wilson)
  Journal of Geometry and Physics, Vol 204, 105275 (2024).
  [ Arxiv ] [ Journal (open access)]

• Weight decompositions on algebraic models for mapping spaces and homotopy automorphisms (with Bashar Saleh)
  Mediterranean Journal of Mathematics, Vol. 21, art. nr. 156, (2024).
  [ Arxiv ] [ Journal ]

• Cup and Massey products on the cohomology of compact almost complex manifolds
  Rivista di Matematica della Università di Parma, Vol 13, n.2 (2022).
  [ Arxiv ] [ Journal ]

• Étale cohomology, purity and formality with torsion coefficients (with Geoffroy Horel)
  Journal of Topology, (2022).
    [ Arxiv ] [ Journal ] [ Correction ]

• Hodge-de Rham numbers of almost complex 4-manifolds (with Scott O. Wilson)
  Expositiones Mathematicae, (2022).
  [ Arxiv ] [ Journal (open access) ]

• Filtered A-infinity structures in complex geometry (with Anna Sopena-Gilboy)
  Proceedings of the American Mathematical Society 150 (2022), no. 9, 4067-4082.
  [ Arxiv ] [ Journal ]

• Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces (with David Chataur)
  Transactions of the American Mathematical Society 375, no. 02, 925-960 (2022).
  [ Arxiv ] [ Journal ]

• Dolbeault cohomology for almost complex manifolds (with Scott O. Wilson)
  Advances in Mathematics. Volume 391 (2021).
  [ Arxiv ] [ Journal (open access) ]

• Characterization of quantum entanglement via a hypercube of Segre embeddings (with Jordi Salvadó and Josep Taron)
  Quantum Information Processing 20, no. 7, Paper No. 252, 28 pp (2021).
  [Arxiv] [ Journal (open access) ]

• Model category structures and spectral sequences (with Daniela Egas Santander, Muriel Livernet and Sarah Whitehouse)
  Proceedings A of the Royal Society of Edinburgh, 150(6), 2815--2848 (2020).
  [ Arxiv ] [ Journal ]

• Mixed Hodge structures and formality of symmetric monoidal functors (with Geoffroy Horel)
  Annales Scientifiques de l’École Normale Supérieure, 53(4):1071--1104 (2020).
  [ Arxiv ] [ Journal ]

• Almost Hermitian Identities (with Scott O. Wilson)
  Mathematics, Special issue: Inequalities in Geometry and Applications, 8 1357 (2020) .
  [ Arxiv ] [ Journal (open access) ]

•  Topological and geometric aspects of almost Kähler manifolds via harmonic theory (with Scott O. Wilson)
  Selecta Mathematica 26, 35 (2020).
  [ Arxiv ] [ Journal ]

• Weight decompositions of Thom spaces of vector bundles in rational homotopy theory (with Urtzi Buijs and Federico Cantero)
  Journal of Homotopy and Related Structures, 15, 1--26 (2020).
  [Arxiv] [Journal]

• Sullivan minimal models of operad algebras (with Agustí Roig)
  Publicacions Matemàtiques, 63, no 1, 125--154 (2019).
  [ Arxiv ] [ Journal (open access) ]

• Rational Homotopy and Intersection-Formality of Complex Algebraic Varieties (with David Chataur)
  Revista Matemática Complutense, 31, no 2, 479--524 (2018).
  [ Arxiv ] [ Journal ]

• Derived A-infinity algebras and their homotopies (with Daniela Egas Santander, Muriel Livernet and Sarah Whitehouse)
  Topology and its Applications, 235, 214--268 (2018).
  [ Arxiv ] [ Journal ]

• Rational homotopy of complex projective varieties with normal isolated singularities (with David Chataur)
  Forum Mathematicum 29, no.1, 41--57 (2017).
  [ Arxiv ] [ Journal (open access) ]

• Homotopy theory of mixed Hodge complexes (with Francisco Guillén)
  Tohoku Mathematical Journal 68, no.3, 349--375 (2016).
  [ Arxiv ] [ Journal]

• Cofibrant models of diagrams: mixed Hodge structures in rational homotopy
  Transactions of the American Mathematical Society 367, no.8, 5935--5970 (2015).
  [ Arxiv ] [ Journal (open access) ]

• Weight filtration on the cohomology of complex analytic spaces (with Francisco Guillén)
  Journal of Singularities 8 , 83--99 (2014).
  [ Arxiv ] [ Journal (open access)]

•  E1-formality of complex algebraic varieties (with Francisco Guillén)
  Algebraic & Geometric Topology 14, no.5, 3049--3079 (2014).
  [ Arxiv ] [ Journal (open access) ]

• Classification of isometries of spaces of constant curvature and invariant subspaces
  Linear Algebra and Its Applications 450, 250--279 (2014).
  [ Arxiv ] [ Journal (open access) ]

Coauthors

• Pedro Boavida de Brito

• Urtzi Buijs

• Federico Cantero

• David Chataur

• Roger Garrido

• Daniela Egas Santander

• Francisco Guillén

• Geoffroy Horel

• Muriel Livernet

• Agustí Roig

• Bashar Saleh

• Jordi Salvadó

• Anna Sopena-Gilboy

• Josep Taron

• Sarah Whitehouse

• Scott Wilson

BiCoCalculator

• BiCoCalculator is a cool program for computing invariants of complex manifolds! (updates in progress)

Ongoing Funded Projects

• Homotopy Theory and Geometric Structures (PID2024-155646NB-I00), AEI, Spain (2025-2027)

Previous Funded Projects

• Homotopical Invariants of Almost Complex Manifolds. Europa Excelencia (EUR2023-143450), AEI, Spain.

• Geometry and Topology at Universitat de Barcelona (GiT-UB). Generalitat de Catalunya (AGAUR), Spain (SGR 00697), 2022-2024.

• Operadic methods in geometry (OMG). Centre National de la Recherche Scientifique, France 2023-2025. (with Geoffroy Horel).

• Homotopical methods in geometry. Agencia Estatal de Investigación, Spain (PID2020-117971GB-C22), 2021-2024. (with Javier Gutiérrez). 

Postdocs

• Haldun Özgür Bayindir Beatriu de Pinos fellowship (2025) / Ramon y Cajal (2026).

• Bashar Saleh, funded by the Knut and Alice Wallenberg Foundation (2020-2022).
  
  

PhD Students

• Jingyuan Zhu, Funded by The  Spanish National Agency of Research (2026 - ).
  Co-advised with Haldun Özgür Bayindir.

• Pedro Magalhães, funded by the Fundação para a Ciência e a Tecnologia, Portugal (2022 - 2026).
  Thesis title: Mixed Hodge Formality.

• Anna Sopena, funded by Generalitat de Catalunya - FI Fellowship Program (2022 - 2026).
  Thesis title: Pluripotential Operadic Calculus.
  Co-advised with Jonas Stelzig.

Master theses

• Micaela Mura (Università degli studi di Cagliari) - Massey Products on Spectral Sequences, 2026.

• Onofre Bisbal - An introduction to rational homotopy theory, 2024.

• Cesar Iglesias - E-infinity algebras in algebraic topology, 2021.

• Anna Sopena - Transferring Filtered Multiplicative Structures in Homotopy Theory, 2020.

• Marta Bustins - Computing Dolbeault cohomology for Lie algebras with almost complex structures, 2019.
  
  

Bachelor theses

• Irene Domenech - Singularitats de l'espaitemps, 2026.

• Elena Gijon Ruiz - A mathematical perspective on 0-dimensional Quantum Field Theory, 2025.

• Arnau Soler - Complexos cel.lulars, 2025.

• Arnau Lapena - Entanglement, Segre Embeddings and Quantum Teleportation, 2025.

• Roger Garrido - Homotopical aspects of hypercommutative algebras, 2024.

• Juan Fernández - A geometric approach to wormhole theory, 2024.

• Andrea Pérez - A Categorical Approach to Quantum Computation with Anyons, 2023.

• Marc Lladó - Introduction to complex geometry and Calabi-Yau manifolds motivated by physics, 2023.

• Martín de Muniategui Climente - The differential geometry behind Maxwell's equations, 2022.

• Daniel Guerrero - Introduction to Conformal Geometry and Penrose diagrams, 2022.

• Eric Gil - Cohomology theories of spacetimes, 2021.

• Gerard Ortega - Quantum algorithms for function optimization, 2021.

• Roberto Forbicia - Emergence of Causality from the Geometry of Spacetimes, 2020.

• Jaume Baixas - Topological Quantum Field Theories, 2020.

• Marcel Vilasís - A Geometric Approach to Quantum Entanglement Classification, 2020.

• Josep Lumbreras - Efficient unitary approximations in quantum computing: the Solovay-Kitaev Theorem, 2018.

Events 2027

• Women in Topology, ISTA, Viena, 25-29, January 2027.

• Colloquium in Hamburg, 19 January 2027

• Derived Geometry and Applications, Mainz, 5-9 April 2027.

• EUR MINT summer School on Homotopical methods in Geometry, Toulouse, 28 June - 3 July 2027.

Events 2026

• (Co-organizer) ALPE, Montpellier 23-24, March 2026.

• Workshop: Manifolds and Moduli, Lisboa, 14-16 April 2026.

• Workshop: higher structures, Roma, 17-18 September 2026.

• (Co-organizer) ALPE, Barcelona, 2-3 November 2026.

Past events that I co-organized

• Workshop Critical Math, Black Forest, 18-22 August 2025.

• ALPE, Barcelona 21-22 May 2025.

• Workshop Operadic Methods in Geometry II, Paris, 8-10 October 2024.

• Higher Algebra, Geometry, and Topology, CIRM, Luminy, 6-10 May 2024.

• Workshop: Operadic Methods in Geometry, Barcelona, 22-24 November 2023.

• Intensive Research Program on Higher Homotopical Structures at CRM, Barcelona, February - June 2021.

• Mini-workshop: Almost Complex Geometry, MFO Oberwolfach, 4-10 October 2020.

• Special Session Geometric Structures, BMD2020, Barcelona, 23-24 October 2020.

• Women in Homotopy Theory and Algebraic Geometry II - Berlin, 20-22 March 2019.

• Workshop on infinity-operads and applications, Osnabrück, 12-14 July 2017.

• Women in Homotopy Theory and Algebraic Geometry, Berlin, 13-15 September 2016.

Events 2025

• Workshop: BCN-Face(t)s of Symplectic Geometry, UPC, Barcelona 28-31 January 2025.

• Workshop: Complex Geometry in Aarhus, Aarhus University, Denmark. 19-21 February 2025.

• Informal Workshop in Paradiso, Paradiso, Italy. 31 March - 2 April 2025.

• Workshop: Beyond the telescope conjecture, Isaac Newton Institute, UK. 16-20 June 2025.

•  Lecture Series at European Autumn School in Topology, Utrecht, 15-19 September 2025.

• MdM Closing Conference, CRM Bellaterra 18 November 2025.

Events 2024

• Workshop: Alps 2024, Sainte-Foy-Tarentaise, France. 8-12 January 2024.

• Homotopy Theory in Stockholm Stockholm, Sweden. 10-14 June 2024.

• Conference Geometry and Physics (GAP): Moduli spaces and higher structures, Rome, Italy. 9-13 September 2024.

• Workshop Generalized complex structures and homological methods, Hamburg 23-27 September 2024.

• Workshop: Maths Somma Junior Meeting, CRM, Barcelona. 2-4 October 2024.

• ALPE, Montpellier 9 - 10 December 2024.

Events 2023

• Homotopical methods in algebraic geometry, Paris, France. 1-3 March 2023.

• Complex Geometry and Lie Groups, Lecce, Italy. 22-26 May 2023.

• Generalised Lie algebras in Derived Geometry, Utrecht, the Netherlands. 29 May - 2 June 2023.

• ANR meeting HightAGT, Strasbourg, France. 30 May - 2 June 2023.

• Conference in Homotopy Theory, Trondheim, Norway. 26-30 June 2023.

• Moduli and Friends, Bucharest, Rumania. 11-15 September 2023.

• Conference CATS-7: Categories and stacks in algebraic geometry and algebraic topology, Luminy, France. 16-23 October 2023.

Events 2022

• Mittag-Leffer Program: higher algebraic structures in algebra, topology and geometry, Stockholm, Sweden, 17-23 January 2022.

• Conference and mini-course Geometric Analysis conference at Rutgers, New Jersey, USA, 16-20 May 2022.

• Barcelona Conference on Higher Structures, Universitat de Barcelona, Barcelona, 13-17 June 2022.

• Twinned Conference on Homotopy Theory with Applications to Arithmetic and Geometry, MPIM Bonn, Germany, 27-30 June 2022.

Events 2021

• Joint meeting of the Spanish and Mexican Mathematical societies. June 2021. (online)

• Midterm workshop OCHoTop. Lille, 5-7 July 2021. (online)

• Cohomology of Complex Manifolds and Special Structures, II. Levico Terme (Trento), July 2021. (online)

• SFB Lecture Higher Invariants. Regensburg, July 2021.(online)

• XXVII Spanish Topology Meeting, Sevilla, 22-23 October 2021.

• Colloque du GDR: Topologie Algebrique et Applications, Strasbourg, 26-29 October 2021.
  
  

Events 2020

• Geometry and TACoS Cohomology and Characteristic Classes of (Almost) Complex Manifolds, 7-21 July 2020. (online)

Events 2019

• Conference on Higher Homotopy Algebras in Topology - MPIM Bonn, 9-10 May 2019.

• Escuela JAE de Matematicas - Madrid, 10-22 June 2019.

• BGSMath Junior meeting - Berlin, 26-28 June 2019.

• Workshop in Homotopy Theory - MFO Oberwolfach, 4-10 August 2019.

• Women in Geometry and Topology - CRM Bellaterra, Spain, 25-27 September 2019.

• Bridging the Gap between Kahler and non-Kahler Complex Geometry - Banff, Canada, 27 October - 1 November 2019.

• Hyperplane Arrangements and Singularities - Tokyo, Japan, 2-6 December 2019.