Director of the Institute of Mathematics of the University of Barcelona (2010-2018). President of the European Solidarity Committee (2011-2016) and Publications Officer (1997-2002) of the European Mathematical Society. Member of the governing board of the Centre de Recerca Matemàtica (2003-2010). President of the Catalan Mathematical Society (2002-2006). Coordinator of the Spanish Network of Mathematical Institutes (2014-2015) and of the Spanish Topology Network (2008-2009). Director of the Algebra and Geometry Department of the University of Barcelona (2002-2006). Member of the editorial board of Springer Universitext since 2007 and of the Mediterranean Journal of Mathematics since 2003. Editor in chief of Advanced Courses in Mathematics CRM Barcelona (2009-2013).
- Implications of set-theoretical methods in algebraic topology
- Homotopical localizations in model categories
- Motivic homological localizations
- Reflective subcategories of triangulated categories
- Preservation of algebras over monads by idempotent transformations
- Definable orthogonality classes in accessible categories are small (with J. Bagaria, A. R. D. Mathias, and J. Rosický). Journal of the European Mathematical Society 17 (2015), 549-589.
- A generalization of Ohkawa’s theorem (with J. J. Gutiérrez and J. Rosický). Compositio Mathematica 150 (2014), 893-902.
- Are all localizing subcategories of stable homotopy categories coreflective? (with J. J. Gutiérrez and J. Rosický). Advances in Mathematics 252 (2014), 158-184.
- Localization of algebras over coloured operads (with J. J. Gutiérrez, I. Moerdijk, and R. M. Vogt). Proceedings of the London Mathematical Society 101 (2010), 105-136.
- Implications of large-cardinal principles in homotopical localization (with D. Scevenels and J. H. Smith). Advances in Mathematics 197 (2005), 120-139.