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

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.

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 $M$,

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

* 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](https://cdn.idrissi.eu/main/research/peccot-cover.webp)](https://doi.org/10.1007/978-3-031-04428-1) ## About This volume provides a unified and accessible

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

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

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

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

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.

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

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).

## Recent blog posts

You may have heard about [DALL-E 2](https://openai.com/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

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](https://abrochier.org/), [Yves Guiraud](https://webusers.imj-prg.fr/~yves.guiraud/), and [Christine Vespa](https://irma-web1.math.unistra.fr/~vespa/). [![Logo of the French National Research Agency (ANR)](https://cdn.idrissi.eu/main/logos/anr.svg)](https://anr.fr/) We recently learned that [the proposal has been accepted by

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](https://link.springer.com/book/10.1007/978-3-031-04428-1). The publisher sent me several complimentary copies! ![A stack of books](https://cdn.idrissi.eu/main/post/peccot-books.webp)

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](https://tex.stackexchange.com/a/359201/14965). 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

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