Paper accepted in Inventiones!
#paper #conf-spaces

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

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

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”?

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!

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

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

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
#math #job #conf-spaces #paper

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

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

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
#math #conf-spaces #paper

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

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
#math #trip

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

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

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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List of Facts

I just started a list of facts, mainly rather classical facts that I don’t want to forget. Before, that list lived on sheets of papers strewn across my desk, which was clearly not optimal. Now it’s in a more permanent form.

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The Milnor–Moore Theorem
#math #algtop

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!
#math #paper

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

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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About Abelian Bimodules
#math #algtop #operads

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.

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