Najib Idrissi’s math page


I am a maître de conférences at the mathematics department of Université Paris Cité. I am a member Institut de Mathématiques de Jussieu–Paris Rive Gauche (IMJ-PRG) and deputy head of the team-project “Algebraic Geometry & Topology” (TGA).

I am the scientific coordinator of the ANR Young Researcher project “Structure and Homotopy of Configuration Spaces” (SHoCoS).

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.



See also: arXiv, HAL, MathSciNet, zbMATH, ORCID.

Non-formality of Voronov's Swiss-Cheese operads

Najib Idrissi, Renato Vasconcellos Vieira. To appear in Q. J. Math. Online on . Updated on . Accepted on .

The Swiss-Cheese operads, which encode actions of algebras over the little $n$-cubes operad on algebras over the little $(n−1)$-cubes operad, comes in several variants. We prove that the variant in which open operations must have at least one open input is not formal in characteristic zero. This is slightly stronger than earlier results of Livernet and Willwacher. The obstruction

Configuration Spaces of Manifolds with Boundary

Ricardo Campos, Najib Idrissi, Pascal Lambrechts, Thomas Willwacher. To appear in Astérisque (Soc. Math. Fr., Paris) Online on . Updated on . Accepted 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 these configuration spaces using three different approaches.

Homotopy Prefactorization Algebras

Najib Idrissi, Eugene Rabinovich. Preprint v1, 34 pages. Online on .

We apply the theory of operadic Koszul duality to provide a cofibrant resolution of the colored operad whose algebras are prefactorization algebras on a fixed space $M$. This allows us to describe a notion of prefactorization algebra up to homotopy as well as morphisms up to homotopy between such objects. We make explicit these notions for several special $M$,

Curved Koszul duality of algebras over unital versions of binary operads

Najib Idrissi. J. Pure Appl. Algebra 227.3 (March 2023) Online on . Updated on . Accepted on .

We develop a curved Koszul duality theory for algebras presented by quadratic-linear-constant relations over unital versions of binary quadratic operads. As an application, we study Poisson $n$-algebras given by polynomial functions on a standard shifted symplectic space. We compute explicit resolutions of these algebras using curved Koszul duality. We use these resolutions to compute derived enveloping algebras and factorization

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. [![Cover of the book](]( ## 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 cobar construction of indecomposable elements. Dually, in the context of CDGAs, we perform similar

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 $\mathsf{CD}_{mn}$, associated to such configurations. The operad $\mathsf{CD}_{mn}$ is weakly equivalent to the operad of

Configuration Spaces of Surfaces

Ricardo Campos, Najib Idrissi, Thomas Willwacher. Preprint v2, 50 pages. Online on . Updated on .

We compute small rational models for configuration spaces of points on oriented surfaces, as right modules over the framed little disks operad. We do this by splitting these surfaces in unions of several handles. We first describe rational models for the configuration spaces of these handles as algebras in the category of right modules over the framed little disks

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 manifold. We moreover prove, if the dimension of the

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 modules, for compact smooth manifolds without boundary.

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 to the model that we would get

Opérades et Structures Commutatives à Homotopie Près

Najib Idrissi. In: Grad. J. Math. (2016) 1.1, pp. 9–17. Online on .

Nous donnons une introduction au domaine des opérades, des objets qui encodent les structures algébriques. Après les avoir définies, nous présentons plusieurs domaines d’application des opérades : espaces de lacets itérés, formalité, algèbres homotopiques, longs nœuds et groupe de Grothendieck--Teichmüller. --- Introductory work on operads based on my [Master's thesis](/research/m2).

Teaching for 2023−2024

Recent talks

Recent blog posts

Fun with DALL-E 2

Published .

You may have heard about [DALL-E 2]( According to its authors, it "is a new AI system that can create realistic images and art from a description in natural language." In concrete words, it is a machine learning model that has been trained to produce picture from text prompts. The results are astounding, and the release of the service

ANR Young researcher project “Structure and Homotopy of Configuration Spaces” (SHoCoS) selected!

Published .

Some time ago, I submitted a "Young Researcher" (JCJC) grant proposal to the French National Research Agency (ANR). I was listed as the scientific coordinator ("PI"), and I wrote the project in collaboration with [Adrien Brochier](, [Yves Guiraud](, and [Christine Vespa]( [![Logo of the French National Research Agency (ANR)](]( We recently learned that [the proposal has been accepted by

“Real Homotopy of Configuration Spaces” is out

Published .

My lecture notes *Real Homotopy of Configuration Spaces: Peccot Lecture, Collège de France, March & May 2020* has now finished production and [is available for sale]( The publisher sent me several complimentary copies! ![A stack of books](

LaTeX shenanigans

Published .

Just for fun, I wrote a small $\LaTeX$ loop to define font-related single-letter commands, such as `\cA = \mathcal{A}` and so on. It is based on [this answer by David Carlisle on TeX.SE]( Here it is! ```tex %%% Dark magic \makeatletter \def\font@loop#1{% define a loop \ifx\relax#1% if we get to \relax, do nothing \else% otherwise... % define \cA=\mathcal{A}, etc

Using math software for teaching calculus

Published .

I have been teaching for seven years now. Yet somehow, I started only recently using computer algebra software (CAS) to make live illustrations of mathematical concepts in class. And I have to say that it is quite useful! ## Previous attempts As you may know, I am/was a big proponent of free software, so I had only ever used