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 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.

(Updated on Jan 15, 2021)

Contact

Université de Paris, IMJ-PRG • Bâtiment Sophie Germain • 8 place Aurélie Nemours • F-75013 Paris • France

Office SG-7032

Research

Real Homotopy of Configuration Spaces.

Peccot Lecture, 162 pages, submitted, .
Info  PDF

Boardman–Vogt resolutions and bar/cobar constructions of (co)operadic (co)bimodules.

Ricardo Campos, Julien Ducoulombier, [N.I.]. Preprint v2, 68 pages, .
Info  PDF arXiv:1911.09474  Source

A model for framed configuration spaces of points.

Ricardo Campos, Julien Ducoulombier, [N.I.], Thomas Willwacher. Preprint v1, 27 p., .
Info  PDF arXiv:1807.08319  Source

Configuration Spaces of Manifolds with Boundary.

Ricardo Campos, [N.I.], Pascal Lambrechts, Thomas Willwacher. Preprint v1, 107 p., .
Info  PDF arXiv:1802.00716  Source

Talks

Topology and Geometry seminar – May 9, 2021, University of Haifa (online).

Event

Configuration Spaces of Surfaces
Abstract: Framed configuration spaces of a surface form a right module over the framed little disks operad. This rich algebraic structure has important consequences, for example for the computations of manifold calculus or factorization homology. Determining the homotopy type of this operadic right module remains however a difficult task. In this talk, I will explain how to compute the rational homotopy type for oriented compact surfaces. The end result is a finite-dimensional purely combinatorial model. The proof involves several ingredients: Kontsevich’s formality, Tamarkin’s formality, and the cyclic formality of the framed little disks operad. (Joint work with Ricardo Campos and Thomas Willwacher.)

Topology Seminar – Mar 15, 2021, MIT (Online).

Event  Slides

Configuration Spaces of Surfaces
Abstract: Framed configuration spaces of a surface form a right module over the framed little disks operad. This rich algebraic structure has important consequences, for example for the computations of manifold calculus or factorization homology. Determining the homotopy type of this operadic right module remains however a difficult task. In this talk, I will explain how to compute the rational homotopy type for oriented compact surfaces. The end result is a finite-dimensional purely combinatorial model. The proof involves several ingredients: Kontsevich’s formality, Tamarkin’s formality, and the cyclic formality of the framed little disks operad. (Joint work with Ricardo Campos and Thomas Willwacher.)

Research Seminar on Algebraic Topology – Feb 15, 2021, Universität Hamburg (online).

Event  Slides

Configuration spaces of surfaces
Abstract: Framed configuration spaces of a surface form a right module over the framed little disks operad. This rich algebraic structure has important consequences, for example for the computations of manifold calculus or factorization homology. Determining the homotopy type of this operadic right module remains however a difficult task. In this talk, I will explain how to compute the rational homotopy type for oriented compact surfaces. The end result is a finite-dimensional purely combinatorial model. The proof involves several ingredients: Kontsevich’s formality, Tamarkin’s formality, and the cyclic formality of the framed little disks operad. (Joint work with Ricardo Campos and Thomas Willwacher.)

Séminaire Algèbre et topologie – Jan 19, 2021, Université de Strasbourg (online).

Event  Slides

Espaces de configuration de surfaces
Abstract: Les espaces de configuration de points à repère dans une variété lisse orientée forment un module à droite sur l’opérade des petits disques à repères. Cette structure opéradique a des applications importantes, par exemple dans le calcul des plongements ou pour l’homologie de factorisation. Il reste cependant difficile de déterminer explicitement le type d’homotopie de ce module opéradique, même dans des cas simples. Dans cet exposé, nous expliquerons comment calculer le type d’homotopie rationnel de ce module dans le cas des surfaces orientées. La preuve fait intervenir divers ingrédients (formalité de Kontsevich, formalité de Tamarkin, formalité cyclique de l’opérade des petits disques à repères). Cet exposé est basé sur un article en collaboration avec Ricardo Campos et Thomas Willwacher.

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

Event  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.)

Teaching (2020–2021)

Elementary algebra and analysis 2

L1 Chemistry (S2) • Exercise sessions • 36h

Homotopy II

M2 Fundamental Mathematics (S2) • Lectures • 24h •  PDF Video

Elementary algebra and analysis & Mathematical Reasoning 1

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

Algorithms and Programming

L2 Maths (S1) • exercises+labs • 42h •  Video

Blog

Git for Mathematicians (2/3): The Theory

Published on #code Discuss

This post is the second 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. The first part, which was about why one would want to use Git, is here. Let us now dive into the second part, in which I explain a little what’s going “under the hood” of Git.

While it is not strictly necessary to know all this to use Git, I think that understanding the mechanics helps in actually using it correctly and efficiently. Commands like git push or git pull are actually a bit complex and it is useful to know what words like “commit”, “branch”, “remote”, etc. refer to, especially when there is a conflict between branches.

Select-Exams

Published on • Updated on #code#teaching Source Discuss

With online teaching, I have to find ways to make many processes go faster, as otherwise teaching takes an inordinate amount of time compared to traditional teaching (and my salary doesn’t change…). I have already written about automating exam production I’ve now taken to scanning my students' exams and grading them directly on my touchscreen computer. This way I avoid all the issues that come with physical exams: I’m not scared to death of bringing them home anymore – losing them means redoing the whole exam 😨, I have a backup, I can give more detailed feedback to students, give it to them earlier and more often, etc.

Git for Mathematicians (1/3): Preliminaries

Published on • Updated on #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.

Peccot Lecture: Notes

Published on #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 😉).