Photo
Najib Idrissi
Maître de conférences

Université de Paris
IMJ-PRG

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

I am mainly interested in operads and their applications to algebraic topology and homological algebra. I am especially interested in the study of configuration spaces of manifolds, their links to graph complexes, and the invariants they define.

I gave a Peccot lecture at the Collège de France in Spring 2020, you can find it here.

(Last updated on Jun 26, 2020)

Contact

Research

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Talks

Topology seminar – Oct 13, 2020, Northeastern University (online)
Slides

Real homotopy of configuration spaces
Abstract: Configuration spaces consist of ordered collected of pairwise 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 of manifolds, with or without boundary. 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.)

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

Real homotopy of configuration spaces
Abstract: Configuration spaces consist of ordered collected of pairwise 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 of manifolds, with or without boundary. 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.)

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.)

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Teaching (2020–2021)

Elementary algebra and analysis 2

L1 Chemistry (S2) • Exercise sessions • 36h

Homotopy II

M2 Fundamental Mathematics (S2) • Lectures • 24h

Elementary algebra and analysis & Mathematical Reasoning 1

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

Algorithms and Programming

L2 Maths (S1) • exercises+labs • 42h

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Blog

The action of \(SO(n)\) on \(S^{n-1}\) is not formal – #math
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.[… continue reading]
arXiv2BibLaTeX – #math #arxiv

tl;dr: a2b.idrissi.eu 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.

[… continue reading]
Peccot lecture & COVID-19 – Last updated on #math #peccot

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.

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