Najib Idrissi's page

Najib Idrissi

Maître de conférences

Hello! I am a maître de conférences at the math department of the University of Paris and a member of the team-project Algebraic Topology & Geometry of the Institut de Mathématiques de Jussieu–Paris Rive Gauche. I am mainly interested in operads and their applications to algebraic topology, more specifically the study of configuration spaces and their links to graph complexes.

I am one of the organizers of the Topology Seminar of the IMJ-PRG. You can find more info in my CV.

(Last updated on Jul 17, 2019)

Contact

najib.idrissi-kaitouni@imj-prg.fr
(+33) 01 57 27 91 16
Université de Paris, IMJ-PRG • Bâtiment Sophie Germain • 8 place Aurélie Nemours • F-75013 Paris • France
Office SG-7032

Research

Configuration Spaces of Surfaces. Ricardo Campos, [N.I.], Thomas Willwacher. Preprint v2, 50 pages, 2019.

PDF arXiv

Boardman–Vogt resolutions and bar/cobar constructions of (co)operadic (co)bimodules. Ricardo Campos, Julien Ducoulombier, [N.I.]. Preprint v1, 61 pages, 2019.

PDF arXiv

The Lambrechts–Stanley Model of Configuration Spaces. In: Invent. Math 216.1, pp. 1–68, 2019.

PDF DOI arXiv MR Zbl

Formality of a higher-codimensional Swiss-Cheese operad. Preprint v2, 49 p., 2018.

PDF arXiv

A model for framed configuration spaces of points. Ricardo Campos, Julien Ducoulombier, [N.I.], Thomas Willwacher. Preprint v1, 27 p., 2018.

PDF arXiv

Curved Koszul Duality for Algebras over Unital Operads. Preprint v2, 32 p., 2018.

PDF arXiv

Configuration Spaces of Manifolds with Boundary. Ricardo Campos, [N.I.], Pascal Lambrechts, Thomas Willwacher. Preprint v1, 107 p., 2018.

PDF arXiv

Swiss-Cheese Operad and Drinfeld Center. In: Israel J. Math 221.2, pp. 941–972, 2017.

PDF DOI arXiv MR Zbl

Talks

Toric Topology Research Seminar (online) – Apr 23, 2020, Fields Institute (online)

Slides

Real homotopy of configuration spaces
Abstract: Configuration spaces consist of ordered collected ofpairwise distinct points in a given manifold. In this talk, I will present several algebraic models for the real/rational homotopy types of (possibly framed) configuration spaces. These models canbe used to establish real/rational homotopy invariance of configuration spaces under dimensionality and connectivity assumptions. Moreover, the collection of all configuration spacesof a given manifold has the structure of a right module over some version of the little disks operad, and the algebraic models are compatible with this extra structure. The proofs all use ideas from the theory of operads, namely Kontsevich’s proof of the formality of the little disks operad and – for oriented surfaces – Tamarkin’s proof of the formality of the little 2-disks operad.(Based on joint works with Campos, Ducoulombier, Lambrechts, and Willwacher.)

Málaga & Topology Meeting – Feb 5, 2020, Universidad de Málaga

Real homotopy of configuration spaces
Abstract: I will present several algebraic models for the real/rational homotopy types of (ordered) configuration spaces of points and framed points in a manifold. These models can be used to establish real/rational homotopy invariance of configuration spaces under dimensionality and connectivity assumptions. Moreover, the collection of all configuration spaces of a given manifold has the structure of a right module over some version of the little disks operad, and the algebraic models are compatible with this extra structure. The proofs all use ideas from the theory of operads, namely Kontsevich’s proof of the formality of the little disks operad and – for oriented surfaces – Tamarkin’s proof of the formality of the little 2-disks operad. (Based on joint works with Campos, Ducoulombier, Lambrechts, and Willwacher.)

Seminar – Jan 17, 2020, Aarhus Universitet

Factorization homology and configuration spaces
Abstract: Factorization homology is a homology theory for structured manifolds (e.g. oriented or parallelized) which finds its roots in topological and conformal field theory (cf. Beilinson–Drinfeld, Salvatore, Lurie, Ayala–Francis, Costello–Gwilliam among others). After defining factorization homology, I will explain how to compute it for simply connected closed manifolds over the real numbers using the Lambrechts–Stanley model of configuration spaces.

Opening workshop of the OCHoTop project – Dec 10, 2019, EPFL (Lausanne)

Notes

Models for configuration spaces of manifolds
Abstract: Configuration spaces consist in ordered collections of pairwise disjoint points. The collection of all configuration spaces of a given manifold has the structure of a right module over some version of the little disks operad. In this talk, I will present algebraic models for the real or rational homotopy types configuration spaces and framed configuration spaces of manifolds as right modules. The proofs all rely on operad theory, more precisely Kontsevich’s proof of the formality of the little disks operad and - for oriented surfaces - Tamarkin’s proof of the formality of the little 2-disks operad. (Based on joint works with Campos, Ducoulombier, Lambrechts, and Willwacher.)

Journée Amiénoise de Topologie – Nov 14, 2019, Université de Picardie Jules Verne (Amiens)

Notes

Homotopie des espaces de configuration
Abstract: Les espaces de configuration sont des objets classiques en topologie algébrique, mais l’étude de leur type d’homotopie reste une question difficile. Après les avoir introduits, je présenterai des techniques de la théorie de l’homotopie rationnelle qui permettent d’obtenir des résultats concernant les espaces de configuration de variétés compactes, sans bord et à bord. J’expliquerai ensuite comment appliquer ces résultats pour calculer l’homologie de factorisation, un invariant des variétés inspiré par les théories des champs quantiques.

Teaching (2019–2020)

Real homotopy of configuration spaces

Collège de France • Peccot Lecture • 8h

Elementary algebra and analysis 2

L1 Chemistry (S2) • Exercise sessions • 36h

Introduction to Homotopy Theory

M2 Fundamental Mathematics (S2) • Lectures • 24h

Elementary algebra and analysis & Mathematical Reasoning 1

L1 Maths (S1) • Lectures + Exercise sessions • 56.5h

Algorithms and Programmation

L2 Maths (S1) • exercises+labs • 42h

Blog

Peccot lecture & COVID-19 – May 25, 2020 #math #peccot

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.

Braid video – Apr 21, 2020 #math #talk #animation

Thursday I’m giving a talk at the online Toric Topology research seminar. (I was supposed to go there in person, but you can probably expect, 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!

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First Peccot lecture – Mar 5, 2020 #math #peccot

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.

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Video – Feb 28, 2020 #math #peccot

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 – Sep 24, 2019 #math #peccot

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!