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 Hilbert scheme is an object that answers positively one of the most optimistic questions (algebraic) geometers posed themselves throughout the centuries: can there be one geometric object that parametrizes “sub-objects” Z inside some fixed object X?
Apart from their existence, which was established in the sixties, Hilbert schemes are wild beasts about which we don’t know much. Even considering only those Z with dimension zero (i.e. a bunch of points), the corresponding Hilbert scheme can be highly nontrivial: we call such a thing a “Hilbert scheme of points”. Starting from the 80’s and 90’s up until today, these objects started attracting more and more interest. 

In this talk, I will introduce what a Hilbert scheme of points is, focusing on its intuitive, yet deceptively rich combinatorial nature, brought to light by the Hilbert-Chow morphism.