One question people often ask is why the university is called “Paris 7”, followed by the realization that there are (were!) thirteen universities in Paris, numbered from “Paris 1” to “Paris 13”. Here’s an attempt at explaining it (though I’m sure I can’t cover all the reasons.)
Maître de conférences
I am Najib Idrissi, and I am a mathematician. I am mainly interested in operads and their applications to algebraic topology, more specifically the study of configuration spaces and their links to graph complexes.
I am maître de conférences (= permanent faculty, rank B) at Paris Diderot University in the Mathematics Department. I am part of the team-project Algebraic Topology & Geometry of the Institut de Mathématiques de Jussieu–Paris Rive Gauche (IMJ-PRG).
Between February and August 2018, I was postdoc at ETH Zürich in the group of Thomas Willwacher. In November 2017, I defended my doctoral thesis under the direction of Benoit Fresse at the University of Lille. You can find more info in my CV.
Najib Idrissi – Preprint, 32 pages, .PDF arXiv:1805.01853 hal-01786218
Najib Idrissi – Doctoral Thesis, Université Lille 1, .PDF Code University Defense
Najib Idrissi – Preprint, in revision, 50 pages, .PDF arXiv:1608.08054 hal-01438861
Najib Idrissi – Graduate J. Math. 1.1, pp. 9–17, .PDF Journal
Najib Idrissi – Master’s thesis, Université Paris 7, .
2018-06-20 – The Fields Institute, Toronto, CanadaTitle + Abstract Slides Video Article
Curved Koszul duality and factorization homology
Abstract: Koszul duality is a powerful tool that can be used to produce resolutions of algebras in many contexts. In this talk, I explain how to use curved Koszul duality for algebras over unital operads to compute the factorization homology of a closed manifold with values in the algebra of polynomial functions on a standard shifted symplectic space.
2018-06-05 – University of Regina, Regina, CanadaTitle + Abstract Slides
Configuration Spaces and Graph Complexes
Abstract: Configuration spaces of points are classical objects in algebraic topology that appear in a wide range of applications. Despite their apparent simplicity, they remain intriguing. Kontsevich proved in the 90's that they are intimately related to "graph complexes", combinatorial objects that can be used to explicitly describe the homotopy type of configuration spaces in a Euclidean space. After recalling the above story, I will explain a conjecture of Lambrechts and Stanley about configuration spaces of simply connected closed manifolds. I will then give an idea of the proof of this conjecture, using graph complexes similar to the ones appearing in the works of Kontsevich. I will also describe recent generalizations: for manifolds with boundary, and for so-called "framed" configuration spaces (j/w Campos, Ducoulombier, Lambrechts, and Willwacher). Finally, I will talk about applications of these results.
2018-05-24 – University of British Columbia, Vancouver, CanadaTitle + Abstract Slides Article
Configuration Spaces of Manifolds with Boundary
Abstract: We study the real homotopy type of configuration spaces of smooth compact manifolds with boundary. We built combinatorial model based on graph complexes for these configuration spaces. We have three different approaches: 1. the Swiss-Cheese operad naturally acts on colored configurations in the manifold, and we build models using Willwacher's graphical model for this operad; 1. the collection of configurations in a collar around the boundary of the manifold is naturally endowed with a homotopy associative algebra structure, by gluing, which naturally acts on the collection of configurations of the whole manifold, and we build models for this action; 3. under dimensionality and connectivity assumptions, we provide a small model inspired by the Lambrechts--Stanley model for configuration spaces of closed manifolds. (Joint work with Ricardo Campos, Pascal Lambrechts, and Thomas Willwacher)
2017-12-21 – Université de Nantes, Nantes, FranceTitle + Abstract Slides Article
Espaces de configuration de variétés compactes
Abstract: L'objet de cet exposé est le type d'homotopie réel des espaces de configuration de variétés compactes simplement connexes, avec ou sans bord. Sous certaines conditions, nous donnons un modèle réel explicite de ces espaces de configuration et qui ne dépend que du type d'homotopie réel de la variété donnée. De plus, nous étudions l'action des opérades des petits disques sur les espaces de configuration, et nous démontrons que le modèle est compatible avec cet action. Dans le cas des variétés à bord, nous démontrons aussi que le modèle est compatible avec l'action des opérades Swiss-Cheese.
This is a cautionary tale, with the hope that this post could help future applicants for permanent academic positions in France.
This past month, I’ve had the pleasure of applying for maître de conférences jobs – roughly equivalent to something between assistant/associate professor. It turned out to be a singularly more complicated process than I expected. The actual scientific part of the application was not too taxing, as I already had to do it when I applied for a chargé de recherche (“junior scientist”) job at CNRS in December, and my research statements, CV… didn’t change much since then. The administrative part was the kafkaesque part.