After defending my PhD in 2012 at Universitat de Barcelona, I held several postdoctoral positions in Berlin, Münster and Barcelona, including a Marie Curie Fellowship at FU-Berlin and a research position as PI from the German Research Foundation at WWU-Münster. In 2019, I became Serra Húnter Lecturer at Universitat de Barcelona. Since June 2021, I am Vice-Dean of Research of the Faculty of Mathematics and Computer Science at UB. I am PI of the project "Homotopical methods in geometry", funded by the Spanish State Research Agency and a member of the French ANR project “Higher Algebra, Geometry, and Topology”.
Algebraic Topology and its interactions with Algebraic Geometry and Complex Geometry
Topology of algebraic varieties and mixed Hodge theory;
Multiplicative structures in homotopical algebra and cohomological operations;
Rational and p-adic homotopy theory, operads and formality;
Topology of complex and almost complex manifolds.
Homotopical methods in geometry (2021-2024)
PID2020-117971GB-C22, Agencia Estatal de Investigación
• Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces (with David Chataur)
Transactions of the American Mathematical Society. Published online December 2021.
• Dolbeault cohomology for almost complex manifolds (with Scott O. Wilson)
Advances in Mathematics. Volume 391 (2021).
• 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).
• 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).
• Mixed Hodge structures and formality of symmetric monoidal functors (with Geoffroy Horel)
Annales Scientifiques de l’École Normale Supérieure, 53(4):1071--1104 (2020).
• Almost Hermitian Identities (with Scott O. Wilson)
Mathematics, Special issue: Inequalities in Geometry and Applications, 8 1357 (2020) .
• Topological and geometric aspects of almost Kähler manifolds via harmonic theory (with Scott O. Wilson)
Selecta Mathematica 26, 35 (2020).
• 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).
• Sullivan minimal models of operad algebras (with Agustí Roig)
Publicacions Matemàtiques, 63, no 1, 125--154 (2019).
• Rational Homotopy and Intersection-Formality of Complex Algebraic Varieties (with David Chataur)
Revista Matemática Complutense, 31, no 2, 479--524 (2018).
• Derived A-infinity algebras and their homotopies (with Daniela Egas Santander, Muriel Livernet and Sarah Whitehouse)
Topology and its Applications, 235, 214--268 (2018).
• Rational homotopy of complex projective varieties with normal isolated singularities (with David Chataur)
Forum Mathematicum 29, no.1, 41--57 (2017).
• Homotopy theory of mixed Hodge complexes (with Francisco Guillén)
Tohoku Mathematical Journal 68, no.3, 349--375 (2016).
• Cofibrant models of diagrams: mixed Hodge structures in rational homotopy
Transactions of the American Mathematical Society 367, no.8, 5935--5970 (2015).
• Weight filtration on the cohomology of complex analytic spaces (with Francisco Guillén)
Journal of Singularities 8 , 83--99 (2014).
• E1-formality of complex algebraic varieties (with Francisco Guillén)
Algebraic & Geometric Topology 14, no.5, 3049--3079 (2014).
• Classification of isometries of spaces of constant curvature and invariant subspaces
Linear Algebra and Its Applications 450, 250--279 (2014).