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You may have heard about DALL-E 2. According to its authors, it "is a new AI system that can create realistic images and art from a description in natural language." In concrete words, it is a machine learning model that has been trained to produce picture from text prompts. The results are astounding, and the release

Some time ago, I submitted a "Young Researcher" (JCJC) grant proposal to the French National Research Agency (ANR). I was listed as the scientific coordinator ("PI"), and I wrote the project in collaboration with Adrien Brochier, Yves Guiraud, and Christine Vespa. Logo of the French National Research Agency (ANR) We

My lecture notes Real Homotopy of Configuration Spaces: Peccot Lecture, Collège de France, March & May 2020 has now finished production and is available for sale. The publisher sent me several complimentary copies! A stack of books

Just for fun, I wrote a small $\LaTeX$ loop to define font-related single-letter commands, such as \cA = \mathcal{A} and so on. It is based on this answer by David Carlisle on TeX.SE. Here it is!It's not pretty but it's (in my opinion) a better alternative than writing down manually the $5 \times 26 = 130$ different co

I have been teaching for seven years now. Yet somehow, I started only recently using computer algebra software (CAS) to make live illustrations of mathematical concepts in class. And I have to say that it is quite useful!Previous attemptsAs you may know, I am/was a big proponent of free software, so I had only ever use

In 2020, the Collège de France awarded me the Peccot Lecture and Prize, which "\[rewards] promising mathematicians under 30 who have distinguished themselves in theoretical and applied mathematics." As part of the award, I was given the opportunity to hold a lecture at the Collège de France in front of a diverse audien

Happy new year everyone! I hope that 2022 will be better than 2020 and 2021. As of December 19th, my university has no name. The Conseil d'État (supreme court for administrative justice) has partially voided the decree of creation of "Université de Paris". They decided that, in choosing the same name as the two univer

For a reason I will explain below, I decided to count how many institutional email addresses I have. The answer? I have a whopping ten email addresses, as a result of the administrative mille-feuille that is French academia. Here are the domains of my email addresses (but not the addresses in full, for spam-related rea

For the past couple of months, I have been working on a side project with several colleagues from my department. In short, it's a web interface to our university's timetable system, the (infamous) ADE. For various reasons, we, the staff, are forbidden from accessing ADE, even though it is the authoritative source about

❗ This post is still a work-in-progress!After a long hiatus, here is the third part of my series of posts about Git for Mathematicians 🙂. I explain the basics of how one would go about using Git to write a math paper. If you have not read the previous parts of the series, you can find them there:Part 1: Preliminaries,

The paper "Boardman–Vogt resolutions and bar/cobar constructions of (co)operadic (co)bimodules", that Ricardo Campos, Julien Ducoulombier, and I wrote, has been accepted for publication in the journal Higher Structures! This technical part will serve as part of the foundation on which we are going to build in future wo

(Update 2021) With the switch to Gatsby, this chart doesn't work anymore; I will try to make it work with React but I cannot really give any ETA.Recently the French ministry for Higher Education and Research released some data on demographics among lecturers and professors in France. I was proctoring an exam yesterday

tl;dr: /a2b to get a .bib from arXiv entries. Update May 19th, 2021: New URL. Have you ever wanted to create a bib entry from an arXiv preprint? There are a few tools available, including one provided by arXiv (click on "NASA ADS" in the sidebar when viewing an entry), but none of them worked as I wanted. They all ha

With online teaching, I have to find ways to make many processes go faster, as otherwise teaching takes an inordinate amount of time compared to traditional teaching (and my salary doesn't change...). I have already written about automating exam production I've now taken to scanning my students' exams and grading them

This post is the first in a series in which I will try to explain how to use Git to write papers, with an audience of professional mathematicians in mind. I know that there are a lot of material online about learning Git, but as far as I can tell, none are tailored specifically for mathematicians' needs (which differ a

This post is the second in a series in which I will try to explain how to use Git to write papers, with an audience of professional mathematicians in mind. The first part, which was about why one would want to use Git, is here. Let us now dive into the second part, in which I explain a little what's going "under the ho

I have finished translation my notes for my Peccot Lecture to English. They have also been expanded, with a lot more new content. For the time being, you can find the notes here. They have been submitted for publication. I would like to thank again all the people who supported me. Update February 15th: As per the publ

My paper, "Formality of a higher codimensional Swiss-Cheese operad", has just been accepted for publication in Algebraic & Geometric Topology! This paper is part of my effort to try and apply rational homotopy theoretical methods to the computation of factorization homology and invariants of knot-like structures. As a

Like many people, I have been teaching online for some time now. In order to help students get an idea of how well they understand the material, I have been giving them and grading weekly homework (keep in mind that it is not common in French universities to give homework in math bachelors).I have been using the very n

In this post, I record a simple and probably well-known fact; but since I have to remake the computation again and again (because I forget it...) I thought it would be nice to have it in an accessible place. The fact is that for an odd $n \ge 3$, the usual action of the special orthogonal group $SO(n)$ on the sphere $

Several people have asked me for my LaTeX template to write letters, so I guess I might as well put it up on my webpage. It uses the scrlttr2 package. I think the markup is relatively self-explanatory.The template expects a copy of your signature and the logo of your university in the same folder, in images named signa

Update: The videos are now available on the Collège de France's website! Please go there for the third lecture and there for the fourth lecture. As some of you may know I was one of the people chosen this year to give a Peccot lecture at the Collège de France (see my first post about it). And as you all know for sure,

Thursday I'm giving a talk at the online Toric Topology research seminar. I was supposed to go there in person, but as you can guess, the current pandemic made that impossible. So I took the opportunity to prepare a little illustration to explain the connection between braids and configuration spaces!

Yesterday was my first Peccot lecture! I think it went okay. The video is going to be available soon on this webpage. I mainly talked about the background for my course: what are configuration spaces, why do we care about them, what do we know about them, and what we would like to know about them. I also got this meda

I am finishing to prepare my Peccot Lectures that start next week. I have prepared a small animation to illustrate the Fulton--MacPherson compactification using Blender, and I think it's relatively neat! I am not a 3D artist, obviously, but (with oral explanations) I think it explains the concept better than drawing on

Yesterday I received a letter from the Collège de France. I have been selected to give this year a Peccot Lecture, which "rewards each year young mathematicians under 30 who have been noticed in theoretical or applied mathematics" 😃. This is of course a great honor and I am very grateful! I still have to determine wha

This summer I've started to compile lecture notes for my class on homotopy theory in January/February. They are heavily inspired by Grégory Ginot's lecture notes from last year on the same subject, although I've reorganized them a bit; in particular I swapped the last two chapters. They are still missing the last chapt

It's official: the new University of Paris is born! For the moment, Paris Diderot University still exists, but it will merge with Paris Descartes and the new university on January 1st, 2020; the IPGP will remain a legally separate entity. (Yes, it's complicated.) We have a new logo that you can view on the university's

I dug up the tiny program I wrote to find minimal surfaces with fixed boundary in 2011 for the "grandes écoles" entrance exams. Ah, the memories... It's available here, along with some pictures. It's written in OCaml, of course! To compile it, install OCaml, OCamlBuild, and the OpenGL libraries for OCaml. Then run oca

I applied in January to a call by the math institute (Insmi) of the CNRS, entitled Projet Exploratoire Premier Soutien « Jeune chercheuse, jeune chercheur » (PEPS JCJC, roughly Exploratory Project, First Support: Young Researcher). These are small grants (3000--6000 €) for young researchers, in order to allow them to t

This week I am at the Centre international de rencontres mathématiques (CIRM) in Luminy. I am attending and speaking at the "Higher Structures" conference. The whole event is wonderful! I hope I am not too out of place among the big names in the speakers' list. I've learned a lot of new math during the talks, as well a

My second paper, The Lambrechts--Stanley Model of Configuration Space, has been accepted for publication in Inventiones Mathematicae! This is a great honor and I am very happy. The refeereing process was a bit above average (14 months for the first report, 7 for the final acceptancee), but I am thankful for it. The ano

I've been in Paris for almost a month now. It's been great! People at the math department and the math institute\[^1] have all been welcoming and have helped me a lot in getting settled. There have been a lot of administrative procedures to complete -- and I am unfortunately not done -- and it's great to have had peopl

One question people often ask is why the university is called "Paris 7", followed by the realization that there are (were!) thirteen universities in Paris, numbered from "Paris 1" to "Paris 13". Here's an attempt at explaining it (though I'm sure I can't cover all the reasons.) At the beginning Prior to the 70's, the

I finally got the confirmation from the ministry: I definitively got the job and I will be appointed in Paris-VII! A new life is about to begin... I've been at the Fields Institute (in Toronto) for a week now, to participate in the summer school on derived geometry and higher structures. The lectures and talks are del

Last week was life-changing, to say the least. I was interviewed for two maître de conférences1 positions, one in Université Paris Diderot, the other in Université Paris-Sud. And... I got ranked first for both jobs! So by all accounts I should have a permanent position next September. The difficult question I have to a

This is a cautionary tale, with the hope that this post could help future applicants for permanent academic positions in France. This past month, I've had the pleasure of applying for maître de conférences jobs -- roughly equivalent to something between assistant/associate professor. It turned out to be a singularly m

Many changes have happened in my life recently! I defended my doctorate on November 17th. I guess I'm a doctor now! There are too many people to thank for that, so please see the "Thanks" section of my thesis. I am now entering the scary world of job applications. I am discovering the wonderful "GALAXIE" web applicati

Hi! You may have noticed the new URL and the new design. Now everything (my home page + my blog) is in one place, powered by Hugo and its Academic theme. I was a bit fed up with Jekyll and its long building times, and I wanted something a bit more streamlined. The Academic theme is complete and easy to use; it took me

Last week I was at the Max Planck Institute for the Conference for Young researchers in homotopy theory and categorical structures (which was, by the way, a great conference -- thanks to the organizers), and I gave yet another talk about the Lambrechts--Stanley model for configuration spaces. So maybe it's time I write

My paper Swiss-Cheese operad and Drinfeld center has finally been accepted! It is going to appear in the Israel Journal of Mathematics. I've made the few corrections suggested by the referee (the new version is available on the arXiv), and I'm now waiting for the final proofs before the paper can be published. If you

I've been neglecting this blog a lot. Juggling research, teaching, organizing a seminar, and a personal life leaves little time for writing articles! (Wait, isn't that the same complaint as last time?) Most prominently I've been spending a lot of time working on my paper about the Lambrechts--Stanley model for configu

My first real post in a while! It turns out that writing an actual paper (cf. previous blog post) takes a lot of time and effort. Who knew? The Voronov product of operads is an operation introduced by Voronov in his paper The Swiss-cheese operad (he just called it "the product"). It combines an operad and a multiplica

I have uploaded a new preprint, The Lambrechts--Stanley Model of Configuration Spaces, which you can find on arXiv. Here is the abstract: We prove the validity over ℝ of a CDGA model of configuration spaces for simply connected manifolds with vanishing Euler characteristic, answering a conjecture of Lambrechts--Stanle

This week I was at the Young Topologists Meeting! It's gotten even bigger than two years ago, as there were more than 180 participants this year. The conference was quite interesting, and Copenhagen is a really nice city! The main theme was homological stability, about which I have learned a lot. The organizers should

Last week I was invited by Thomas Willwacher to ETH Zürich for a few days, during which I also had the opportunity to give a talk at the "Talks in Mathematical Physics" seminar. It was a very interesting few days, and I'm very grateful for this invitation! The main building of ETH It also explains why I've been slack

I just came back from the Mathematisches Forschungsinstitut Oberwolfach! The library I was there for the "Factorization Algebras and Functorial Field Theories" workshop. It was an incredible experience. The talks were all, of course, very interesting, and I learned a lot about QFT. But more than that, I learned a lot

The purpose of this post is to record the definition of ∞-operads and explain why it works like that. For this I'm using Lurie's definition of ∞-operads; there is also a definition by Cisinski--Moerdijk--Weiss using dendroidal sets, about which I might talk later. Indeed, the definition on an ∞-operad is a bit mysteri

Today I'm in Paris! I'm giving a talk at the Séminaire de Topologie of the Institut de Mathématiques de Jussieu--Paris Rive Gauche, about my preprint Swiss-Cheese operad and Drinfeld center. Here is the abstract of the talk (in French): Il est possible de construire, à partir des groupes de tresses, une opérade qui dé

This post is about the Milnor--Moore theorem, a powerful tool describing the structure of (co)commutative Hopf algebras. Like the Eckmann--Hilton argument, it shows that having multiple compatible operations on the same object can lead to unexpected results about the object. Briefly, the theorem says that as soon as th

My first article has been accepted for publication with minor revisions! Entitled "Opérades et structures commutatives à homotopie près" (yes, it's in French), it will appear in the Graduate Student Mathematical Diary, edited by the Mediterranean Institute For The Mathematical Sciences. The article is expository in nat

The theorem(s) of acyclic models are a rather powerful technique for proving that some functors defined on truncated chain complexes can be extended in higher dimensions, and that two such functors are homotopic, by proving it on a small class of "model" objects. For some reason I only discovered this last year, and I

This post is about something somewhat weird I noticed about infinitesimal bimodules over operads and their relationships with some $E\_n$ operads. I don't know if it's something significant, and I'd definitely be interested to hear more about it. Context: abelian bimodules As I said, this post is about abelian bimodu

As promised, this post is about the famous Eckmann--Hilton argument. This argument, on the surface, looks like a simple algebraic trick; but it has deep consequences, which I will now try to explain. This post is an expanded version of a math.SE answer I wrote some time ago. Some background When I was a first-year st