Séminaire Betty B.

J'ai créé ce séminaire en pensant aux mathématicien·ne·s, et notamment aux plus jeunes. J'y demande à des collègues de présenter le contexte mathématique de certains exposés du Séminaire de mon aïeul, N. Bourbaki, pour les rendre plus accessibles ; ils pourront aussi en introduire quelques outils ou des motivations plus lointaines. — Betty B., Nancago, Janvier 2018.

27 mars 2021

Le Séminaire Betty B. a lieu en principe à l'Institut Henri Poincaré (IHP) mais cette séance sera à distance. — [iCal] [Affiche] [Résumés]

15h00
Sarah Peluse — An introduction to Gowers norms
In this talk, I will define the Gowers uniformity norms, discuss the role they play in Gowers's proof of Szemerédi's theorem, and state a couple of versions of the inverse theorem for these norms, including the “local” version used in Gowers's proof. As a warm-up for thinking about the inverse theory of the Gowers norms, I will also present a proof of the “99% inverse theorem”, which concerns a model case of the inverse problem.

Séminaire N. Bourbaki

27 mars 2021

Le Séminaire N. Bourbaki a lieu en principe à l'Institut Henri Poincaré (IHP) mais cette session aura lieu à distance. — [iCal] [Affiche] [Résumés]

16h30
Thomas Bloom — Quantitative inverse theory of Gowers uniformity norms after F. Manners [PDF]
Gowers uniformity norms are the central object of higher-order Fourier analysis, one of the cornerstones of additive combinatorics, and play an important role in both Gowers' proof of Szemerédi's theorem and the Green–Tao theorem. The inverse theorem states that if a function has a large uniformity norm, which is a robust combinatorial measure of structure, then it must correlate with a nilsequence, which is a highly structured algebraic object. This was proved in a qualitative sense by Green, Tao, and Ziegler, but with a proof that was incapable of providing reasonable bounds. In 2018 Manners achieved a breakthrough by giving a new proof of the inverse theorem. Not only does this new proof give a wealth of new insights but it also, for the first time, provides quantitative bounds, that are at worst only doubly exponential. This talk will give a high-level overview of what the inverse theorem says, why it is important, and the new proof of Manners.

Sessions antérieures :

Session de janvier 2020

Session de novembre 2019

Session de juin 2019

Vous pouvez aussi ajouter à vos calendriers électroniques les agendas hébergés sur le portail Indico : Séminaire Betty B. et Séminaire Bourbaki (format iCalendar)

Remerciements

Une subvention du CNRS couvre une partie des frais d'organisation de ce Séminaire.

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Association des collaborateurs de Nicolas Bourbaki
Institut Henri Poincaré
11 rue Pierre-et-Marie-Curie
75231 Paris cedex 05, FRANCE
Courriel : association@bourbaki.fr
Twitter : @Betty_Bourbaki