Git for Mathematicians (1/3): Preliminaries #code Discuss

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 bit from programmers' needs). Here, I will try to explain why one would even be interested in Git to begin with.

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Peccot Lecture: Notes #math #peccot Discuss

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 (see the PDF file for names 😉).

Exam Template for Pandoc #teaching #latex Discuss

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 nice exam LaTeX class for some time. It works well, but I found it annoying to copy/paste my template each time I want to create a new exam. I decided to write a small template to be used with Pandoc, so that I can also write my exams in Markdown rather than LaTeX. It was not completely trivial since the exam class requires bullet items to use the questions and parts environment, and the \question and \part commands, which I did not want to retype manually all the time. I thus wrote a little Pandoc filter to save some time.

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The action of \(SO(n)\) on \(S^{n-1}\) is not formal #math Discuss

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 \(S^{n-1}\) is not formal over \(\mathbb{Q}\) in the sense of rational homotopy theory, even though both spaces are formal. This was first told to me by Thomas Willwacher, and it is mentioned as Remark 9.5 in his paper “Real models for the framed little (n)-disks operads” (arXiv:1705.08108) with Anton Khoroshkin.

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arXiv2BibLaTeX #math #arxiv Discuss

tl;dr: to get a .bib from arXiv entries.

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 had quirks and problems (like displaying some URL twice, putting “arXiv” as in the journal field even though it doesn’t belong there, no biblatex support, etc). In the end, I always had to fix things by hand, and it took almost as long as writing the entry myself.

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Peccot lecture & COVID-19 – Last updated on #math #peccot Discuss

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, normal life came to a halt a couple of months ago when the number of COVID-19 cases exploded in France (and the world) and the French government ordered a lockdown. While I was able to give my first two lectures before the lockdown started, the last two had to be postponed.

Thankfully, the number of cases is now diminishing and the lockdown is progressively being lifted. I was thus able to record my third lecture yesterday; it should appear online in a few days. The experience was somewhat surreal: I gave a two-hour lecture to a large classroom that was completely empty except for the cameraman and me. I had to give some online classes during the lockdown, but even then there was a certain sense of interactivity, whereas I was almost literally talking to wall yesterday, which was a bit destabilizing. But still, I’m happy that I was able to record the lecture, and I’d like to thank the Collège de France again for the opportunity! The current situation is extremely difficult for everyone, and I’m not the worst one off: it’s a very small sacrifice in the face of the public health crisis.

I hope people will still find it interesting and that the video will not feel too strange. I could not take questions during the lecture, obviously, but I will be happy to answer any you might have via email.

Video #math #peccot #animation Discuss

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 the board, since drawing moving 3D pictures is not an easy task… The animation is available here, and here it is in all its glory:

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Peccot Lecture #math #peccot Discuss

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 what the lecture will be about, but hopefully something about operads and configuration spaces. Together with my graduate course on homotopy theory, next semester will be interesting, teaching-wise!

Lecture Notes #math #class Discuss

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 chapter on \(\infty\)-categories, and they probably need a lot of polishing – I am mainly planning to use them as a memory aid during the lectures – but in case you are interested, they’re available here. If you take a look at them, don’t hesitate to let me know about any remarks you might have (typos, errors…)

Faculty in France over the past 20 years Discuss

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 and couldn’t do anything too mentally taxing (because students might cheat 😟) so I compiled the data in a somewhat interactive chart. You can select which groups you want to see, and whether you only want to see lecturers (MCF), professors (PR) or both. You can also normalize the data so that each section starts at 100 in 1998, to compare the evolutions. I might add the total of the two later, but I fear I’ve already wasted enough time on this… Here it is:

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New University of Paris #job Discuss

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 new website. We also have new statutes that govern the internal structure of the new university. And most importantly… all the staff got pots and seeds to plant in them! Very symbolic.

Digging Discuss

I dug up the tiny program I wrote to find minimal surfaces in 2011 for the “grandes écoles” entrance exams. It’s available in the miscellaneous section of my website, along with some pictures. It’s written in OCaml, of course! Ah, memories…

Grant: PEPS JCJC #grant Discuss

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 travel and/or invite people, and incite them to apply to larger grants in the followings years, such as the ones from the French ANR, or even the ERC (one can dream). I just got the answer: it’s a yes! So my project is now funded in 2019, for the amount of 3500 €. It’s comfortable, especially considering that the application and the administrative requirements are lightweight. Time to get to work!

Higher Structures at the CIRM #trip Discuss

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 as to speak with people who I hadn’t had the chance to meet yet, or that I am not able to see very often. I’d like to thank Bruno Vallette and all the organizers for giving me this opportunity.

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Paper accepted in Inventiones! #paper #conf-spaces Discuss

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 anonymous referee had many remarks and questions that greatly improved my paper. Most of the comments were about the presentation of the paper, and thanks to the referee’s suggestions, I believe it has been improved quite a bit. Since I use techniques from several areas of mathematics – algebraic topology, differential geometry, mathematical physics, and of course operad theory – these suggestions helped make the paper more accessible (hopefully) to a broader audience. So, I’d like to thank the referee, as well as many people (see the acknowledgments on my paper): Ricardo Campos, Ivo Dell’Ambrogio, Julien Ducoulombier, Matteo Felder, Benoit Fresse, Ben Knudsen, Pascal Lambrechts, Antoine Touzé, Thomas Willwacher. Anyway, time to celebrate! (And tomorrow’s my birthday 😃)

A Picture #job Discuss

Today is a holiday, it’s raining and cold, and I’m too tired to do anything meaningful. So I took half an hour to make a picture to go with my earlier post about the organizational structure I belong to now. This picture explains why the signature on my latest article was so long: Université Paris Diderot, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne Paris Cité, CNRS, Sorbonne Université, F-75013 Paris, France.

Life in Paris #job #paper Discuss

I’ve been in Paris for almost a month now. It’s been great! People at the math department and the math institute1 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 people being able to guide me. And I finally found an apartment in Paris! It was unexpectedly hard: faculty salaries are not very high compared to the cost of living, and the first year is technically on “probation”, meaning I could theoretically get fired next August… Landlords in Paris have very rigid expectations and this made me fall outside them.

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Why is it called “Paris 7”? #job Discuss

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.)

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Next Stop: Paris! #job Discuss

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 delightful! This whole conference is impressive! Hopefully my own talk yesterday was not out of place. I also learned that some people actually do read my blog! I was a bit surprised. So now I have the moral obligation to flesh out my posts a little. Here’s something that I hope people will find interesting.

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An Eventful Week #job Discuss

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 answer soon is which one. As they correspond to rather different profiles and expectations, this is not an easy choice.

I am of course extremely happy and I feel extremely lucky. This would not have been possible without the support of many people, foremost my former advisor Benoit Fresse, who gave me a lot of advice on how to navigate the French academic maze. My current supervisor, Thomas Willwacher, has also been a great support, and I thank him too.

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Kafka in the stars #job Discuss

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 more complicated process than I expected. The actual scientific part of the application was not too taxing, as I already had to do it when I applied for a chargé de recherche (“junior scientist”) job at CNRS in December, and my research statements, CV… didn’t change much since then. The administrative part was the kafkaesque part.

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Defense, postdoc, new paper #job #conf-spaces #paper Discuss

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 application – fellow French job applicants know my pain.

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New design #blog Discuss

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 about one hour to setup the new blog, and one hour to migrate the blog posts to the new format (most of which was spent trying to work out the interactions between Mathjax and the Markdown format… I settled on shortcodes, like in this article). Building a whole website from scratch was fun, but time-consuming, and a theme seemed like an okay compromise.

A Model for Configuration Spaces of Closed Manifolds #math #conf-spaces Discuss

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 a little bit about it on this blog. I’ll write a first post about the model itself, and later I will explain how the Fulton–MacPherson operad is involved in all this.

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Configuration Spaces Woes #conf-spaces #paper Discuss

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 configuration spaces (see my previous post). The good news is, I’m done (or as done as one can be with a paper). I’ve just uploaded the third version of the paper on the arXiv, and I’ve submitted it. I’ve finally managed to remove this bothersome hypothesis about the Euler characteristic of the manifold, and I’ve fixed an issue about my use of the propagator (PA forms are hard).

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The Voronov Product of Operads #math #operads #swiss-cheese Discuss

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 multiplicative operad to yield a new colored operad; the main example I know is the homology of the Swiss-cheese operad. This is a construction that I use in my preprint Swiss-Cheese operad and Drinfeld center, where as far as I know I coined the name “Voronov product” – I haven’t seen this operation at all outside of Voronov’s paper. I wanted to advertise it a bit because I find it quite interesting and I’m eager to see what people can do with it.

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Young Topologists Meeting 2016 #trip Discuss

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 be applauded, because I can’t imagine how hard it must have been to plan a conference this big.

Now that I’ve done all my (math-related) travelling for the summer, I hope I’ll be able to post actual content here…

New Domain Name #blog Discuss

Maybe you (I don’t know who reads this anyway) haven’t noticed, but this blog has a new URL:! I splurged and got a domain name. The blog is (for now) still accessible via the old GitHub URL, but this may change at some point… Maybe more details on this later.

Update: And now the old Github URL shouldn’t work anymore. Hehe.

Infinity-Operads Demystified #math #algtop #operads #higher-cat Discuss

The purpose of this post is to record the definition of \(\infty\)-operads and explain why it works like that. For this I’m using Lurie’s definition of \(\infty\)-operads; there is also a definition by Cisinski–Moerdijk–Weiss using dendroidal sets, about which I might talk later.

Indeed, the definition on an \(\infty\)-operad is a bit mysterious taken “as-is” – see [HA, §]. My goal is to explain how to reach this definition, mostly for my own sake. Most of what follows is taken either from the book Higher Algebra, the \(n\)Lab, or the semester-long workshop about hgiher category theory in Lille in 2015.

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The Milnor–Moore Theorem #math #algtop Discuss

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 the Hopf algebra is cocommutative and connected, then it is isomorphic to the universal enveloping algebra of a Lie algebra (and a similar dual statement is true for commutative Hopf algebras).

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Paper Accepted! #paper Discuss

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 nature, it contains a general introduction to the theory of operads, and then some applications of the theory, mostly in relation with the little disks operads. I’m psyched!

Now let’s hope that my preprint Swiss-Cheese operad and Drinfeld center meets the same fate… ☺

Acyclic Models #math #algtop Discuss

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 always find myself forgetting the precise hypotheses and conclusion… Hopefully writing this blog post will fix them in my mind. My main reference will be:

  • Samuel Eilenberg and Saunders MacLane. “Acyclic models”. In: Amer. J. Math. 75 (1953), pp. 189–199. ISSN: 0002-9327. JSTOR: 2372628. MR0052766.
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