Publications [7]

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 algebr

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 uni

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

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

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

Preprints [3]

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

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

Theses [2]