Higher Structures
~2019-01-21Centre international de rencontres mathématiques (CIRM), Luminy, France

Stockholm Topology Seminar
2018-12-11Stockholm University + Royal Institute of Technology (KTH), Stockholm, Sweden
Slides

Configuration spaces and Operads
Abstract: Configuration spaces of manifolds are classical objects in algebraic topology, but studying their homotopy type is a difficult task. In this talk, I will explain how to use ideas coming from the theory of operads (and more precisely Kontsevich's proof of the formality of the little disks operads) to obtain results on the real homotopy type of configuration spaces of compact manifolds. I will also talk about recent applications.

Geometry & Topology Seminar
2018-11-08Institut de Mathématiques de Jussieu-Paris Rive Gauche, Paris, France
Slides

Espaces de configuration et Opérades
Abstract: Les espaces de configuration de points sont des objets classiques en topologie algébrique. L'étude de leur type d'homotopie engendre de nombreuses questions et applications dans différents domaines des mathématiques. Dans cet exposé, je présenterai des idées qui viennent de la théorie des opérades et qui permettent d'obtenir des résultats concernant le type d'homotopie rationnel des espaces de configuration de variétés.

Derived Geometry and Higher Categorical Structures in Geometry and Physics
2018-06-20Fields Institute, Toronto, Canada
Slides Video

Curved Koszul duality and factorization homology
Abstract: Koszul duality is a powerful tool that can be used to produce resolutions of algebras in many contexts. In this talk, I explain how to use curved Koszul duality for algebras over unital operads to compute the factorization homology of a closed manifold with values in the algebra of polynomial functions on a standard shifted symplectic space.

Departmental colloquium
2018-06-05University of Regina, Regina, Canada
Slides

Configuration Spaces and Graph Complexes
Abstract: Configuration spaces of points are classical objects in algebraic topology that appear in a wide range of applications. Despite their apparent simplicity, they remain intriguing. Kontsevich proved in the 90's that they are intimately related to "graph complexes", combinatorial objects that can be used to explicitly describe the homotopy type of configuration spaces in a Euclidean space. After recalling the above story, I will explain a conjecture of Lambrechts and Stanley about configuration spaces of simply connected closed manifolds. I will then give an idea of the proof of this conjecture, using graph complexes similar to the ones appearing in the works of Kontsevich. I will also describe recent generalizations: for manifolds with boundary, and for so-called "framed" configuration spaces (j/w Campos, Ducoulombier, Lambrechts, and Willwacher). Finally, I will talk about applications of these results.

…more talks »

#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 😃)

#job

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.

#job #paper

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 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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#job

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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#job

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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