Things about me

I'm a french researcher in mathematics currrently working in Steve Awodey's group in CMU.

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 in 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 (2017, joint work with G. Biedermann, E. Finster and A. Joyal).

- A paper on the Blakers-Massey theorem (2017, joint work with G. Biedermann, E. Finster and A. Joyal)

- A paper on the cofree coalgebra over a cooperad (2014)

- My book with André Joyal on Sweedler theory of (co)algebras and the bar-cobar constructions (2013)

- More on arXiv

Things with ideas

- Slides of my lectures HoTT 2019 -- Summer School (Lecture I) (August 2019)

- Slides of my HoTTEST seminar Univalence & Descent (May 2019)

- Slides of a talk on What is a space? (April 2019, 6th workshop on formal topology)

- Table of contents of a book I'm editing with Gabriel Catren on New Spaces in Mathematics and Physics -- Formal and Conceptual Reflections (to be edited this year by Cambridge University Press)

Two chapters for the book:
- Introduction to the geometric aspects of topos theory: Topo-logie (2019, written with André Joyal)
- An introduction to Derived Geometry: The geometry of ambiguity (2016)

- Slides about the sequel of my joint work with Georg Biederman, Eric Finster and André Joyal on left exact localizations of topos and Goodwillie calculus (2018, talk at YaMCATS & PSSL 103)

- Slides from a course on topoi in Nice (2018, in french):

• Cours 1 - L'intuition géométrique des topos
• Cours 2 - Les topos en analogie avec les anneaux commutatifs 1/2
• Cours 3 - Les topos en analogie avec les anneaux commutatifs 2/2

- The slides from a talk about Why higher categories are useful (2017, in french)

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

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

- A note about why deformations are cohomological (2010)

- Introductory notes to derived categories (2010, in french)

Things to watch

- Video from my talk at HoTTEST seminar on Univalence & Descent (2019)

- Video from a talk in IHES about Toposes as commutative rings (2015)

- Video from a conference in IHP about Derived geometry (2015)

- Video from a workshop in Paris 7 about the evolution of homological algebra beyond the vision of Grothendieck (2015, in french)

- Video from a workshop in Paris 7 about Ambiguity in Mathematics (2014)

Things for fun

- Slides from a popularization talk about Cross-multiplication (2017, in french)

Things for philosophers

- Slide of a talk at the seminar Semiomath explaining how homotopy theory is a substitute for set theory: The homotopy quotient (2018)

- Slide of a talk at the seminar (Id)entification::(Id)entité about the mathematics of identification (2016, in french)