##### 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.

(Last updated on Jan 15, 2021)

## Research

PDF
##### Formality of a higher-codimensional Swiss-Cheese operad. To appear in Algebr. Geom. Topol., 47 p., 2020.
PDF arXiv Source Journal
PDF arXiv Source
PDF arXiv Source
##### The Lambrechts–Stanley Model of Configuration Spaces. In: Invent. Math 216.1, pp. 1–68, 2019.
PDF DOI arXiv MR Zbl Source
PDF arXiv Source
PDF arXiv Source
PDF arXiv Source
##### Swiss-Cheese Operad and Drinfeld Center. In: Israel J. Math 221.2, pp. 941–972, 2017.
PDF DOI arXiv MR Zbl Source
PDF MR Journal

## Talks

TBA

##### Topology Seminar– Mar 15, 2021, MIT (Online)
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)
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)
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)
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 (1/3): Preliminaries– Apr 13, 2021 #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– Apr 6, 2021 #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 😉).

##### “Formality of a higher codimensional Swiss-Cheese operad” accepted in Algebraic & Geometric Topology– Dec 8, 2020 #math #paper Discuss

My paper, “Formality of a higher codimensional Swiss-Cheese operad”, has just been accepted for publication in Algebraic & Geometric Topology! I am very grateful to the editorial committee for this, as well as to the anonymous referees who provided many suggestions to improve the paper, especially the exposition.

##### Exam Template for Pandoc– Nov 20, 2020 #teaching #latex Discuss

Like many people, I have been teaching online for some time now. In order to help students get an idea of how well they understand the material, I have been giving them and grading weekly homework (keep in mind that it is not common in French universities to give homework in math bachelors).

I have been using the very nice exam LaTeX class for some time. It works well, but I found it annoying to copy/paste my template each time I want to create a new exam. I decided to write a small template to be used with Pandoc, so that I can also write my exams in Markdown rather than LaTeX. It was not completely trivial since the exam class requires bullet items to use the questions and parts environment, and the \question and \part commands, which I did not want to retype manually all the time. I thus wrote a little Pandoc filter to save some time.

##### The action of $$SO(n)$$ on $$S^{n-1}$$ is not formal– Sep 17, 2020 #math Discuss
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. This was first told to me by Thomas Willwacher, and it is mentioned as Remark 9.5 in his paper “Real models for the framed little (n)-disks operads” (arXiv:1705.08108) with Anton Khoroshkin.