I am what people call an algebraic topologist. My research is focus on the interactions between Group Theory and Homotopy Theory, and it follows different lines:

Homotopy theory of loop spaces: By homotopy theory of loop spaces I mean "homotopy group theory", "p-compact groups", or "p-local finite groups", and related stuff as cohomology of groups. This implies that sometimes I have to work with honest groups. I develop this research as part of the Barcelona Algebraic Topology Group.

Homotopy invariants and self homotopy equivalences: This is a more classical branch of Algebraic Topology in which I am also interested. I have a special interest in the LS-category of spaces and related (or dual) concepts. This research is developed jointly with Cristina Costoya, Antonio Garvín and Aniceto Murillo.

Geometrical and Topological methods in Economy, Robotics and Theoretical Physics: This is a brave new interest for me! I try to apply the Algebraic Topology technics to "real world" problems.

• 2009SGR-1092 - Grup de Topologia Algebraica de Barcelona

• Homotopy uniqueness of classifying spaces of compact Lie groups

• Homological algebra on graded posets
Student: Ramos, Antonio Díaz