Séminaires : Séminaire des Thésards

Equipe(s) : doctorants,
Responsables :Andrei Bengus-Lasnier, Eleonora Di Nezza, Ilias Ftouhi, Mario Gonçalves, Mahya Mehrabdollahi, Romain Petrides, Arnaud Vanhaecke
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Description

Le séminaire des thésards est l'occasion pour les doctorants de présenter des résultats et des problématiques dignes d'intérêt devant un public de non-spécialistes. L'ambiance y est informelle ; poser des questions naïves est encouragé, et les questions moins naïves sont bienvenues dans la mesure où elles n'entravent pas le bon déroulement de l'exposé.

Un mercredi sur deux à 17 h, en alternance entre Jussieu et Sophie Germain.


Orateur(s) Daniel Lopez - IMJ-PRG,
Titre Knot polynomials and knot homology
Date05/06/2019
Horaire18:00 à 19:00
Résume

A knot is a piece of chord whose ends have been glued together in some way. Given a knot one asks : is it possible to untangle the knot without breaking the chord ? You may have asked yourself this question before when taking your headphones from your pocker.

To answer this question one construct "invariants" of knots, that is, quantities (numbers, polynomials, groups) that are unchanged through deformations of the knot that don't break the chord. If a given invariant of a knot is non-trivial then the knot cannot be untangled, but the converse is often not true.

In this talk we will introduce the simplest polynomial invariant of a knot, the Alexander polynomial, which comes from classical algebraic topology. We will then motivate a more recent and powerful construction from 2002 due to Ozsvath-Szabo and Rasmussen : an invariant taking the form of a (Floer) homology theory whose Euler characteristic is the Alexander polynomial and which contains deep topological information of the knot. In particular, if this homology is trivial, then the knot can indeed be untangled.

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