• Ph.D. in Geometry and Topology
  Universidade de Santiago de Compostela (Spain)
  Title of Thesis: LS-category of foliations (in Spanish)
• Bachelor and Master in Mathematics
  Universidade de Santiago de Compostela (Spain)

My CV in PDF format.

I am a pure mathematician working in the area of algebraic topology. The central topic of my research is Lusternik-Schnirelmann theory. Specific Topics: Groupoids, orbifolds, group actions.

My current interest is in developing a LS-theory for orbifolds (Satake-manifolds).

• On the 1-homotopy type of Lie groupoids.
• Lusternik-Schnirelmann theory for orbifolds as groupoids.
• The foliated Whitehead and Ganea formulation of tangential LS category.
• A homotopy notion for Hilsum-Skandalis maps.

• Lusternik-Schnirelmann category of orbifolds.
  http://www.abdn.ac.uk/~wpe006/conference/skye/booklet.pdf, 2005.
• Transverse Lusternik-Schnirelmann category of Riemannian foliations.
  Topology and its Applications, 2004.
• LS-category of compact-Hausdorff foliations. With S. Hurder.
  Trans. Amer. Math. Soc., 2004.
• Equivariant LS-category for finite group actions.
  Contemporary Mathematics, 2002.
• Tangential Lusternik-Schnirelmann category of foliations. With E. Macias.
  Journal of the London Mathematical Society, 2002.
• Tangential LS category and cohomology for foliations. With S. Hurder.
  Proceedings of the AMS: Lusternik-Schnirelmann Category in the New Millennium, 2002.
• LS-Categories for foliated manifolds.
  Proceedings of Foliations: Geometry and dynamics, World Scientific Publishing, 2002.
• Transverse Lusternik-Schnirelmann category of foliated manifolds. With E. Macias.
  Topology, 2000.
• Categoría LS en foliaciones.
  Pub. del Dep. de Topología y Geometría, Universidade de Santiago de Compostela, 1998.
• Local Fibrewise Category.
  C.R. Acad. Sci. Paris, 1997.

• Abel Symposium, Oslo, Norway, August 2007
• Postnikov Memorial Conference, Bedlewo, Poland, June 2007
• Algebra Seminar, Universidade de Santiago de Compostela, Spain, June 2007
• IV Seminar on Categories and Applications, Barcelona, Spain, June 2007
• Homology Theories, K-Theory and Homotopy Theory, Tbilisi, Georgia, May 2007
• University of Chicago Algebraic Topology Seminar, January 2007
• Fields Institute, Toronto, Canada, January/May 2007
• Groups in Geometry and Topology, ICM2006 satellite, Málaga, Spain, September 2006
• UAB Topology Seminar, Universitat Autònoma de Barcelona, Spain, July-August 2006
• XVth Oporto Meeting on Geometry, Topology and Physics ICM2006 satellite, Portugal, June 2006
• British Mathematical Colloquium, University of Newcastle, Newcastle, UK, April 2006
• Stringy Topology in Morelia, Morelia, Mexico, January 2006
• Colloquium, Harold Washington College, Chicago, 2005
• International Conference on Pure and Applied Topology, Isle of Skye, Scotland, 2005
• Colloquium, University of Sheffield, Sheffield, UK, 2005
• International Conference on Foliations, Ryukoku University, Kyoto, Japan, 2003
• AMS Conference: Riemannian foliations, Sevilla, 2003
• Geometry and Topology Seminar, University of Illinois at Chicago, 1999, 2001, 2002
• AMS Lusternik-Schnirelmann category in the new millennium, Mount Holyoke, 2001
• Topology Seminar, University of Sheffield, September-November 2000
• Foliations, Stefan Banach International Mathematical Center, Warsaw, 2000

Calculus and Linear Algebra.

My teaching statement in PDF format.

My art page at the School of the Art Institute of Chicago.