Najib Iᴅʀɪꜱꜱɪ
Maître de conférences

I am a maître de conférences at the University of Paris (formerly Université Paris Diderot). I am part 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)

Research

PDF arXiv
PDF arXiv
The Lambrechts–Stanley Model of Configuration Spaces. In: Invent. Math 216.1, pp. 1–68, 2019.
PDF DOI arXiv MR Zbl
PDF arXiv
PDF arXiv
PDF arXiv
PDF arXiv
Swiss-Cheese Operad and Drinfeld Center. In: Israel J. Math 221.2, pp. 941–972, 2017.
PDF DOI arXiv MR Zbl

Talks

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)

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)

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.

Séminaire de topologie algébrique– Jul 4, 2019, Université catholique de Louvain

Homologie de factorisation et espaces de configuration
Abstract: L’homologie de factorisation est une théorie homologique pour les variétés structurées (orientées, parallélisées…) qui trouve ses origines dans les théories topologique et conformes des champs (Beilinson–Drinfeld, Salvatore, Lurie, Ayala–Francis, Costello–Gwilliam…). Après l’avoir définie et donné une idée de ses propriétés, j’expliquerai comment on peut la calculer sur ℝ grâce au modèle de Lambrechts–Stanley des espaces de configuration et/ou grâce à des complexes de graphes dans le cas des variétés fermées parallélisées, des variétés fermées orientées, et des variétés à bord parallélisées. [En partie en collaboration avec R. Campos, J. Ducoulombier, P. Lambrechts, T. Willwacher]

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

Video– Feb 28, 2020 #math

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:

Peccot Lecture– Sep 24, 2019 #math

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!

Lecture Notes– Sep 11, 2019 #math #class

This summer I’ve started to compile lecture notes for my class on homotopy theory in January/February. They are heavily inspired by Grégory Ginot’s lecture notes from last year on the same subject, although I’ve reorganized them a bit; in particular I swapped the last two chapters. They are still missing the last chapter on $$\infty$$-categories, and they probably need a lot of polishing – I am mainly planning to use them as a memory aid during the lectures – but in case you are interested, they’re available here. If you take a look at them, don’t hesitate to let me know about any remarks you might have (typos, errors…)

Faculty in France over the past 20 years– Jun 21, 2019

Recently the French ministry for Higher Education and Research released some data on demographics among lecturers and professors in France. I was proctoring an exam yesterday and couldn’t do anything too mentally taxing (because students might cheat 😟) so I compiled the data in a somewhat interactive chart. You can select which groups you want to see, and whether you only want to see lecturers (MCF), professors (PR) or both. You can also normalize the data so that each section starts at 100 in 1998, to compare the evolutions. I might add the total of the two later, but I fear I’ve already wasted enough time on this… Here it is: