Najib Idrissi’s math page

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

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

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

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

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

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

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

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

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

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

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

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

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

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 diffi

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 diffi

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

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

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

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!It's not pretty but it's (in my opinion) a better alternative than writing down manually the $5 \times 26 = 130$ different co

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 attemptsAs you may know, I am/was a big proponent of free software, so I had only ever use