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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

Opening workshop of the OCHoTop project – Dec 10, 2019, EPFL (Lausanne)

Models for configuration spaces of manifolds
Abstract: Configuration spaces consist in ordered collections of pairwise disjoint points. The collection of all configuration spaces of a given manifold has the structure of a right module over some version of the little disks operad. In this talk, I will present algebraic models for the real or rational homotopy types configuration spaces and framed configuration spaces of manifolds as right modules. The proofs all rely on operad theory, more precisely Kontsevich's proof of the formality of the little disks operad and - for oriented surfaces - Tamarkin's proof of the formality of the little 2-disks operad. (Based on joint works with Campos, Ducoulombier, Lambrechts, and Willwacher.)

Journée Amiénoise de Topologie – Nov 14, 2019, Université de Picardie Jules Verne (Amiens)

Homotopie des espaces de configuration
Abstract: Les espaces de configuration sont des objets classiques en topologie algébrique, mais l'étude de leur type d'homotopie reste une question difficile. Après les avoir introduits, je présenterai des techniques de la théorie de l'homotopie rationnelle qui permettent d'obtenir des résultats concernant les espaces de configuration de variétés compactes, sans bord et à bord. J'expliquerai ensuite comment appliquer ces résultats pour calculer l'homologie de factorisation, un invariant des variétés inspiré par les théories des champs quantiques.

Séminaire de topologie algébrique – Jul 4, 2019, Université catholique de Louvain

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)
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.

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Teaching (2019–2020)

Algorithms and Programmation

L2 (S1) • exercises+labs • 42h

Elementary algebra and analysis & Mathematical Reasoning 1

L1 MIASHS (S1) • Lectures + Exercise sessions • 56.5h

Elementary algebra and analysis 2

L1 Chemistry (S2) • Exercise sessions • 36h

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Blog

Peccot Lecture – #math

Yesterday I received a letter from the Collège de France. I have been selected to give this year a Peccot Lecture, which “rewards each year young mathematicians under 30 who have been noticed in theoretical or applied mathematics” 😃. This is of course a great honor and I am very grateful! I still have to determine what the lecture will be about, but hopefully something about operads and configuration spaces. Together with my graduate course on homotopy theory, next semester will be interesting, teaching-wise!

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:

[… continue reading]
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…

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