I am an Associate Professor at the UAB since 2010. I was a EPSRC postdoc, Aberdeen University, from 2000 and 2001; and a visiting professor in Purdue University in 2005.

I have participated in several research programmes: Mittag-Leffler Insitute (2006)(2022), Bernouilli Centre (2005), Max-Planck Institut fur Mathematik (2001)(2022), Fields Institute (2020), Banff International Research Centre (2022), Haussdorff Institute (2022), ICTS Bangalore (2023) and several workshops at Matematisches Forschunginstitut Oberwolfach.

My research is mainly focused on understanding homotopy properties of p-completed classifying spaces of compact Lie groups and fusion systems in general. Recently I am also working on understand cohomological properties by its translation in the stable homotopy theory of geometric cochains, specially from the point of view of tensor-triangular geometry.

My research is mainly focused on understanding homotopy properties of p-completed classifying spaces of compact Lie groups and fusion systems in general by means of p-local group information, specially focused o maps between p-completed classifying spaces. I am also interested on having a better understanding of homotopy idempotent functors and homotopy generalizations of classifying spaces of groups. Recently I am also working on understand cohomological properties by its translation in the stable homotopy theory of geometric cochains, specially the point of view of tensor-triangular geometry of Quillen stratification results.

I have been PI of research project:

• MTM2010-20692: Análisis local en grupos y espacios topológicos
• MTM2013-42293-P: Teoría de homotopía de espacios clasificadores y espacios de funciones
• MTM2016-80439-P Teoría de homotopía de estructuras algebraicas

• On stratification for spaces with Noetherian mod p cohomology, amb Tobias Barthel, Drew Heard and Gabriel Valenzuela.  American Journal of Mathematics 144 (2022) no 4.
• Stratification and duality for homotopical groups, amb Tobias Barthel, Drew Heard and Gabriel Valenzuela. Advances in Mathematics 354 (2019)
• Noetherian loop spaces, amb Joan A. Crespo, Jérôme Scherer. Journal of the European Mathematical Society 13 (2011), no. 5, 1225–1244.
• Deconstructing Hopf spaces amb Crespo, Juan A.; Scherer, Jérôme . Inventiones Mathematicae 167 (2007), no. 1.
• Homology decompositions for p-compact groups amb Levi, Ran; Notbohm, Dietrich Homology decompositions for p-compact groups. Adv. Math. 216 (2007), no. 2.
• Wreath products and representations of p-local finite groups amb Libman, Assaf. Advances in Mathematics 221 (2009), no. 4.
• Subgroup families controlling p-local finite groups amb Broto, Carles; Grodal, Jesper; Levi, Ran; Oliver, Bob. Proceedings of the London Mathematical Society (3) 91 (2005), no. 2.