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Najib Iᴅʀɪꜱꜱɪ
Maître de conférences

Université de Paris
IMJ-PRG

I am a maître de conférences at the University of Paris (formerly Université Paris Diderot). I am part of the team-project Algebraic Topology & Geometry of the Institut de Mathématiques de Jussieu–Paris Rive Gauche. 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 one of the organizers of the Topology Seminar of the IMJ-PRG. You can find more info in my CV.

(Last updated on Jul 17, 2019)

Contact

Research

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Talks

Séminaire de topologie algébrique – Jul 4, 2019, Université Catholique de Louvain, Louvain-la-Neuve, Belgium

Homologie de factorisation et espaces de configuration
Abstract: L’homologie de factorisation est une théorie homologique pour les variétés structurées (orientées, parallélisées…) qui trouve ses origines dans les théories topologique et conformes des champs (Beilinson–Drinfeld, Salvatore, Lurie, Ayala–Francis, Costello–Gwilliam…). Après l’avoir définie et donné une idée de ses propriétés, j’expliquerai comment on peut la calculer sur ℝ grâce au modèle de Lambrechts–Stanley des espaces de configuration et/ou grâce à des complexes de graphes dans le cas des variétés fermées parallélisées, des variétés fermées orientées, et des variétés à bord parallélisées. [En partie en collaboration avec R. Campos, J. Ducoulombier, P. Lambrechts, T. Willwacher]

Séminaire de Topologie – May 14, 2019, Institut de Mathématiques de Jussieu-Paris Rive Gauche

Homologie de factorisation et espaces de configuration
Abstract: L’homologie de factorisation est une théorie homologique pour les variétés structurées (orientées, parallélisées…) qui trouve ses origines dans les théories topologique et conformes des champs (Beilinson–Drinfeld, Salvatore, Lurie, Ayala–Francis, Costello–Gwilliam…). Après l’avoir définie et donné une idée de ses propriétés, j’expliquerai comment on peut la calculer sur ℝ grâce au modèle de Lambrechts–Stanley des espaces de configuration et je concluerai par quelques applications.

Higher Homotopy Algebras in Topology – May 9, 2019, Max Planck Institute for Mathematics (MPIM), Bonn, Germany
Slides

Curved Koszul duality for algebras over unital operads
Abstract: Koszul duality is a powerful tool that can be used to produce resolutions of algebras in many contexts. In particular, Koszul duality of operads is the tool of choice to define the notion of “homotopy algebras”. In this talk, I will present a framework to study curved Koszul duality for algebras over certain kinds of unital operads (i.e. satisfying $P(0) = \Bbbk$). I will explain how to use it in order to compute the factorization homology of a closed manifold with values in the algebra of polynomial functions on a standard shifted symplectic space.

Higher Structures – Jan 23, 2019, Centre international de rencontres mathématiques (CIRM), Luminy, France
Slides

Configuration spaces and operads
Abstract: Configuration spaces consist of tuples of pairwise distinct points in a given space. Studying the homotopy type of configuration spaces of manifolds is a classical problem in algebraic topology. In this talk, I will explain how to use the theory of operads - more precisely, Kontsevich’s proof of the formality of the little disks operads - to obtain results on the real homotopy type of configuration spaces of simply connected closed smooth manifolds. I will also talk about generalizations and applications: manifolds with boundary, framed configuration spaces, factorization homology, and work in progress on complements of submanifolds.

Stockholm Topology Seminar – Dec 11, 2018, Stockholm University + Royal Institute of Technology (KTH), Stockholm, Sweden
Slides

Configuration spaces and Operads
Abstract: Configuration spaces of manifolds are classical objects in algebraic topology, but studying their homotopy type is a difficult task. In this talk, I will explain how to use ideas coming from the theory of operads (and more precisely Kontsevich’s proof of the formality of the little disks operads) to obtain results on the real homotopy type of configuration spaces of compact manifolds. I will also talk about recent applications.

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Blog

Lecture Notes – #math #class

This summer I’ve started to compile lecture notes for my class on homotopy theory in January/February. They are heavily inspired by Grégory Ginot’s lecture notes from last year on the same subject, although I’ve reorganized them a bit; in particular I swapped the last two chapters. They are still missing the last chapter on \(\infty\)-categories, and they probably need a lot of polishing – I am mainly planning to use them as a memory aid during the lectures – but in case you are interested, they’re available here. If you take a look at them, don’t hesitate to let me know about any remarks you might have (typos, errors…)

Faculty in France over the past 20 years –

Recently the French ministry for Higher Education and Research released some data on demographics among lecturers and professors in France. I was proctoring an exam yesterday and couldn’t do anything too mentally taxing (because students might cheat 😟) so I compiled the data in a somewhat interactive chart. You can select which groups you want to see, and whether you only want to see lecturers (MCF), professors (PR) or both. You can also normalize the data so that each section starts at 100 in 1998, to compare the evolutions. I might add the total of the two later, but I fear I’ve already wasted enough time on this… Here it is:

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New University of Paris – #job

It’s official: the new University of Paris is born! For the moment, Paris Diderot University still exists, but it will merge with Paris Descartes and the new university on January 1st, 2020; the IPGP will remain a legally separate entity. (Yes, it’s complicated.) We have a new logo that you can view on the university’s new website. We also have new statutes that govern the internal structure of the new university. And most importantly… all the staff got pots and seeds to plant in them! Very symbolic.

Digging –

I dug up the tiny program I wrote to find minimal surfaces in 2011 for the “grandes écoles” entrance exams. It’s available in the miscellaneous section of my website, along with some pictures. It’s written in OCaml, of course! Ah, memories…

Grant: PEPS JCJC – #grant

I applied in January to a call by the math institute (Insmi) of the CNRS, entitled Projet Exploratoire Premier Soutien « Jeune chercheuse, jeune chercheur » (PEPS JCJC, roughly Exploratory Project, First Support: Young Researcher). These are small grants (3000–6000 €) for young researchers, in order to allow them to travel and/or invite people, and incite them to apply to larger grants in the followings years, such as the ones from the French ANR, or even the ERC (one can dream). I just got the answer: it’s a yes! So my project is now funded in 2019, for the amount of 3500 €. It’s comfortable, especially considering that the application and the administrative requirements are lightweight. Time to get to work!

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