Université Paris Diderot - CNRS
Laboratoire SPHERE, UMR 7219
bâtiment Condorcet, case 7093
5 rue Thomas Mann
75205 Paris cedex 13

office 396A
email :

Gathered thoughts

A view to mathematics


Things about me

I'm a french researcher in mathematics.

The mathematics I can understand are limited to what I can picture, so I qualify myself as a geometer.

However, since geometry is about a thousand different things in maths, one geometer is always the non-geometer of another.

Here some mathematical interests of mine:

  • Higher category theory, which is both the minimal structure underlying to all mathematical objects, and the "space-time" of mathematics, where all mathematics are done.
  • Algebraic geometry, which I understand as the study of spaces by means of different kinds of commutative algebras of functions over them.
  • Topos theory, which the kind of algebraic geometry studying those spaces with enough functions int the space of homotopy types.
    • Goodwillie calculus, which is differential calculus on topoi.
    • Verdier duality, which is measure theory on topoi.
  • Symplectic geometry, a.k.a. the geometry of lagrangian correlations, which is arguably the most intriguing hierarchy of geometries in the classification of Lie groups.
  • Mathematization of Physics, which is (symplectic) geometry used as a metaphor for natural phenomena.
  • Philosophical reflection on mathematics, which I understand as trying to extract the ideas behind mathematical formalisms and trying to understand the relationship of maths with other sciences and Nature.



Things with theorems

- An application of the previous paper to Goodwillie theory (joint work with G. Biedermann, E. Finster and A. Joyal).

- A paper on the Blakers-Massey theorem (joint work with G. Biedermann, E. Finster and A. Joyal).

- A paper on the cofree coalgebra over a cooperad.

- My book with André Joyal on Sweedler theory of (co)algebras and the bar-cobar constructions.

- More on arXiv



Things with ideas

- Slides about the sequel of our work on left exact localizations of topos and Goodwillie calculs (talk at YaMCATS & PSSL 103).

- Slides from a course on topoi in Nice (in french):

- The slides from a talk about Why higher categories are useful (in french).

- An introduction to the ideas of Derived Geometry.

- More slides of our work with André Joyal on bar-cobar constructions.

- Slides of André Joyal's talk at the AMS meeting (Boston 2012) on our work on bar-cobar constructions

- A note about why deformations are cohomological

- Introductory notes to derived categories (in french)



Things for fun

- Slides from a popularization talk about Cross-multiplication (in french).



Things for philosophers

- Slide of a talk at the seminar Semiomath explaining how homotopy theory is a substitute for set theory.

- Slide of a talk at the seminar (Id)entification::(Id)entit้ about the mathematics of identification (in french).


all pictures are copyrighted