Federico Cantero Morán

Federico Cantero Morán

Federico Cantero
PhD in Mathematics from the University of Barcelona
Researcher at UB

Personal webpage

email: federico.cantero@ub.edu

Biosketch

I am a postdoctoral researcher in mathematics at the BGSMath. Previously I was a postdoc in the Topology group at the Université catholique de Louvain and in the Topology group at WWU Münster. I obtained my PhD at University of Barcelona under the supervision of Carles Casacuberta and Oscar Randal-Williams.

My main scientific achievements are on the field of homology stability, where I have extended results of Harer and Madsen–Weiss to spaces of embedded surfaces. Together with Martin Palmer, I have developed new techniques to prove homological stability for configuration spaces in closed manifolds.

My research is about algebraic and geometric topology, particularly the homotopy theory of moduli spaces of submanifolds, to which I have applied the techniques of homological stability. The prominent examples of such moduli spaces are configuration spaces (when the submanifolds have dimension 0) and knot spaces (when the submanifolds have dimension 1).

Prizes, awards, honors and distinctions

Best poster of the Spanish Topology Meeting in 2011 and 2013.

 

Research Interests

My research is about algebraic and geometric topology, particularly the homotopy theory of moduli spaces of submanifolds, to which I have applied the techniques of homological stability. The prominent examples of such moduli spaces are configuration spaces (when the submanifolds have dimension 0) and knot spaces (when the submanifolds have dimension 1).

 

Selected publications

  • Homological stability for spaces of surfaces, under revision in Geometry and Topology after a positive referee report and available as a preprint at arXiv:1304.3006 (2013), joint with Oscar Randal-Williams.
  • On homological stability for configuration spaces in closed background manifolds, Documenta Mathematica 20, 753-805 (2015), joint with Martin Palmer.
  • A note on hyperspaces and the compact-open topology, arXiv:, 1412.4249 (2014).
  • The space of merging submanifolds in Rn, under revision in Homology, Homotopy and Applications after a positive referee report and available as a preprint at arXiv:1412.4938 (2014).
  • A metric for the space of submanifolds of Galatius and Randal-Williams, submited to Proceedings of the AMS and available as a preprint at arXiv:1512.06849 (2015).