# Juan Pablo Vigneaux

Mathematician

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.