Research Group in Algebraic Topology

Current Project

  • Homotopical methods in geometry (2021-2024)

    PID2020-117971GB-C22, Agencia Estatal de Investigación

Description and Members

The main research lines of the present research proposal include the study of operadic algebras, higher categories and higher operads, and the development of homotopical methods to address open questions on the geometry and topology of complex and almost complex manifolds. We also plan to incorporate techniques from simplicial homotopy to solve the inverse problem for smooth functions in topological data analysis and to contribute in the development of virtual reality software aimed at the visualization of geometric figures.

This is a coordinated research project with a partner team at Universidad de Sevilla.

Past Projects

  • Algebraic and low-dimensional topology (2017-2020)
    MTM2016-76453-C2-2-P, Agencia Estatal de Investigación
  • Enhanced homotopy (2014-2016)
    MTM2013-42178-P, Ministerio de Economía y Competitividad
  • Higher homotopy in algebra and geometry (2010-2013)
    MTM2010-15831, Ministerio de Ciencia e Innovación
  • Higher homotopical structures (2007-2010)
    MTM2007-63277, Ministerio de Educación y Ciencia
  • Localizations in simplicial model categories (2004-2007)
    MTM2004-03629, Ministerio de Educación y Ciencia
  • Universal constructions in stable and unstable homotopy (2001-2004)
    BFM2001-2031, Ministerio de Ciencia y Tecnología
  • Homological and homotopical localizations (1998-2001)
    PB97-0202, Dirección General de Enseñanza Superior