Things about me

I'm a French researcher in mathematics, currrently working in Steve Awodey's group in Carnegie Mellon University.

I'm a geometer with various interests:

• ∞-category theory, the set theory of the XXI Century;
• algebraic geometry, the study of spaces by means of algebras of functions;
• ∞-topos theory, the algebraic geometry of functions with values in ∞-groupoids;
• categorical logic and its relationships to topology and geometry;
• symplectic geometry and its use in the mathematization of physics;
• philosophical reflections on mathematics.

Things with theorems

- A paper about the relation of choice axioms and Postnikov completeness (2024, joint work with R. Barton)

- A paper about smooth and proper maps (2024, joint work with J. Weinberger).

- My series of papers with G. Biedermann, E. Finster and A. Joyal about ∞-topoi and Goodwillie calculus

- Goodwillie and Weiss Towers (ongoing Draft, 2024)
- III. The Acyclic Product (2023)
- II. Grothendieck topologies for ∞-topoi (2022)
- I. Higher Sheaves (2021)

- A paper on the category of π-finite spaces (2021)

- A paper of derived symplectic geometry about the reduction of critical loci (2021, joint work with D. Calaque).

- A paper about the small object argument for unique factorization systems with applications to left-exact localizations of topoi (2020, joint work with C. Leena Subramaniam).

- Some work around exponentiable ∞-topoi (Version 2, 2019, substantial rewrite from the arXiv version, joint work with D. Lejay).

- 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 a talk about choice axioms and Postnikov completeness (HoTT-UF conference, 2024)

- Slides of a talk about type theory and geometry (HoTT conference, 2023)

- Slides of a talk on well-pointed ∞-endofunctors (jww Simon Henry, MURI meeting, 2021)

- Slides of a talk on an example of elementary ∞-topos (CMU-HoTT seminar, 2021)

- Slides of some talks on enveloping ∞-topoi (MURI meeting 2020, EPFL 2021, CRM 2021)

- 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)

- Two books I have edited with Gabriel Catren on New Spaces in Mathematics and New Spaces in Physics (Cambridge University Press, 2021)

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 ∞-topoi and Goodwillie calculus (2018, talk at YaMCATS & PSSL 103)

- Slides from three lectures on topoi in Nice (2018, in french)

- 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 (2014)

- 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 the HoTT/UF conference (Leuven) on Choice axioms and Postnikov completeness (2024)

- Video from a talk at the CIRGET seminar (Montreal) on the topology of non-separated spaces (2022)

- Video from my talk at the Seminar on Higher Homotopical Structures, CRM, UA Barcelona The enveloping ∞-topos of a presheaf 1-topos (2021)

- Video from my talk at the Oktoberfest, in Baltimore Small object argument for unique factorization systems (2019)

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

- Videos from three lectures in Nice about Topos theory Part 1 Part 2 Part 3 (2018)

- Video from a talk in IHES about Topoi 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)

- News article about a Promenade avec la Règle de Trois (2017)

Things for fun

- Text from a popularization talk about The ten dimension bike (2010, in french)

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

Things for philosophers

- Slides of a talk at the seminar PhilMath Intersem 2022 about the spaces of logic (2022)

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

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