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:
- Characterizations of information measures such as entropy (operational, algebraic, and topological characterizations).
- Dimension theory: relationship between fractal dimensions and information dimension.
- Probability measures with geometric structure, such as rectifiable measures and stratified measures.
- Magnitude and diversity as categorical generalizations of cardinality and entropy, respectively.
- Combinatorial (“microcanonical”) models for generalized entropies.
- Optimal transport and functional inequalities.