My name is Juan Pablo Vigneaux, and I am a first-year doctoral student at Institut de Mathématiques de Jussieu - Paris Rives Gauche (IMJ-PRG).
My advisor is Daniel Bennequin, and the subject of my thesis is "Cohomology, geometric quantization and quantum information" (you can find the -rather technical- details here).
Prof. Bennequin also supervised my master thesis (see 'Files'), where I investigated the relation between the information cohomology recently defined by him in a paper with P. Baudot, and the general topos cohomology introduced in SGA IV.
I am interested in geometry in a wide sense (differential and topological manifolds, varieties, schemes, topos, stacks...) and its interaction with mathematical physics, information theory and other"applied" areas, as well as logic. A nice example is the concept of topos, that provides a fantastic unification of geometry and logic.
Universitè Paris Diderot - host of (one half of) the IMJ-PRG.