Najib Idrissi’s math page

Intro

I am a maître de conférences at the math department of Université Paris Cité. I am also a member of the team-project Algebraic Topology & Geometry of the Institut de Mathématiques de Jussieu–Paris Rive Gauche (IMJ-PRG). I am one of the organizers of the Topology Seminar of the IMJ-PRG.

You can find more information in my CV.

My main mathematical interests are in the fields of operads, as well as in 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.


Research (more details)

See also: ArXiv, MathSciNet, zbMATH.

Real Homotopy of Configuration Spaces: Peccot Lecture, Collège de France, March & May 2020

Najib Idrissi. Lecture Notes in Mathematics 2303 (CEMPI subseries). Cham: Springer, 2022. 210 pp. ISBN: 978-3-031-04427-4. Online on . Updated on . Accepted on .

Provides an in-depth discussion of the connection between operads and configuration spaces Describes a unified and accessible approach to the use of graph complexes Based on 4 lectures held in the framework of the Peccot Lecture and Prize by the Collège de France. About This volume provides a unified and accessible

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

Ricardo Campos, Julien Ducoulombier, Najib Idrissi. In: High. Struct. 5.1, pp. 293–366 (2021), 74 pages. Online on . Updated on . Accepted on .

In this paper we develop the combinatorics of leveled trees in order to construct explicit resolutions of (co)operads and (co)operadic (co)bimodules. We construct explicit cofibrant resolutions of operads and operadic bimodules in spectra analogous to the ordinary Boardman--Vogt resolutions and we express them as a cob

Formality of a higher-codimensional Swiss-Cheese operad

Najib Idrissi. In: Algebr. Geom. Topol. 22.1 (2022), pp. 55–111 Online on . Updated on . Accepted on .

We study bicolored configurations of points in the Euclidean $n$-space that are constrained to remain either inside or outside a fixed Euclidean $m$-subspace, with $n - m \ge 2$. We define a higher-codimensional variant of the Swiss-Cheese operad, called the complementarily constrained disks operad $\mathsf{CD}{mn}$, a

The Lambrechts–Stanley Model of Configuration Spaces

Najib Idrissi. In: Invent. Math. (2019) 216.1, pp. 1–68. Online on . Updated on . Accepted on .

We prove the validity over ℝ of a commutative differential graded algebra model of configuration spaces for simply connected closed smooth manifolds, answering a conjecture of Lambrechts--Stanley. We get as a result that the real homotopy type of such configuration spaces only depends on the real homotopy type of the m

A model for framed configuration spaces of points

Ricardo Campos, Julien Ducoulombier, Najib Idrissi, Thomas Willwacher. Preprint v1, 27 p. Online on .

We study configuration spaces of framed points on compact manifolds. Such configuration spaces admit natural actions of the framed little discs operads, that play an important role in the study of embedding spaces of manifolds and in factorization homology. We construct real combinatorial models for these operadic modu

Configuration Spaces of Manifolds with Boundary

Ricardo Campos, Najib Idrissi, Pascal Lambrechts, Thomas Willwacher. Preprint v1, 107 p. Online on .

We study ordered configuration spaces of compact manifolds with boundary. We show that for a large class of such manifolds, the real homotopy type of the configuration spaces only depends on the real homotopy type of the pair consisting of the manifold and its boundary. We moreover describe explicit real models of thes

Swiss-Cheese Operad and Drinfeld Center

Najib Idrissi. In: Israel J. Math. (2017) 221.2, pp. 941–972. Online on . Updated on . Accepted on .

We build a model in groupoids for the Swiss-Cheese operad, based on parenthesized permutations and braids, and we relate algebras over this model to the classical description of algebras over the homology of the Swiss-Cheese operad. We extend our model to a rational model for the Swiss-Cheese operad, and we compare it


Teaching for 2021−2022 (see more)


Recent talks (see more)

Barcelona Conference on Higher Structures @ Universitat de Barcelona, Centre de Recerca Matemàtica

On . Title: Formality and non-formality of Swiss-Cheese operads and variants.

Configuration spaces consist in ordered collections of points in a given ambient manifold. Kontsevich and Tamarkin proved that the configuration spaces of Euclidean n-spaces are rationally formal, i.e., that their rational homotopy type is completely encoded by their cohomology. Their proofs use ideas from the theory o


Recent blog posts (see more)

Peccot Lecture notes accepted in Lecture Notes in Mathematics (CEMPI subseries)

Published . #algtop #class #conf-spaces #math #operads #paper #swiss-cheese

In 2020, the Collège de France awarded me the Peccot Lecture and Prize, which "\[rewards] promising mathematicians under 30 who have distinguished themselves in theoretical and applied mathematics." As part of the award, I was given the opportunity to hold a lecture at the Collège de France in front of a diverse audien