Séminaires : Phd Seminar - Séminaire des doctorant.e.s

Le séminaire des doctorant.e.s est l'occasion pour les doctorant.e.s 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.

Chaque jeudi à 18h, en alternance entre Jussieu et Sophie Germain.

The PhD seminar is an opportnuity for PhD students to present results and topics worthy of interest in front of a non-specialist audience. The mood is informal ; asking naive questions is highly encouraged and less naive questions are also welcomed, as long as they don't intefere with the smoothness of the talk.

Every Thursday at 6pm, alternating between Jussieu and Sophie Germain.

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.