E-mail Natalia.Castellana@uab.cat
Position Associate Professor
Research interests Topology
Area Algebra, Geometry, Number Theory and Topology
Castellana Vila, Natalia

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.

I was the Coordinator of the Spanish Topology Netwok (2012).


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


Selected publications
  • 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.