Juan Pablo Vigneaux



Currently, I am an Olga Taussky and John Todd Instructor in Mathematics at Caltech, mentored by Matilde Marcolli. We co-organize the Information, Geometry, and Physics Seminar.

Previously, I was a postdoctoral researcher at the Max Planck Institute for Mathematics in the Sciences. In 2019, I obtained my Ph.D. in Mathematics at the University of Paris under the supervision of Daniel Bennequin.

I’m broadly interested in the concept of information. My work deals with:

  • Information topology and, more generally, the algebraic characterization of information measures.
  • Rectifiable and stratified measures, and the relation between geometric and entropic dimensions.
  • Categorical magnitude and diversity as generalizations of cardinality and entropy, respectively.
  • Combinatorial (“microcanonical”) models for generalized entropies.
  • Optimal transport and functional inequalities.

selected publications


  1. Journal
    Typicality for stratified measures
    Juan Pablo Vigneaux
    IEEE Transactions on Information Theory, 2023
  2. Journal
    A formula for the categorical magnitude in terms of the Moore-Penrose pseudoinverse
    Stephanie Chen, and Juan Pablo Vigneaux
    Bulletin of the Belgian Mathematical Society - Simon Stevin, 2023
    To appear in Vol. 30, Issue 3


  1. Journal
    Information structures and their cohomology
    Juan Pablo Vigneaux
    Theory and Applications of Categories, 2020


  1. Journal
    Information theory with finite vector spaces
    Juan Pablo Vigneaux
    IEEE Transactions on Information Theory, 2019