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.

From a vector space with an endomorphism, classical linear algebra allows one to extract numerous invariants: eigenvalues, characteristic polynomial, eigenspaces, Jordan form… The Hitchin system is a « globalization » of this story : that is, we allow all of this to continuously depend on a single parameter living in a geometric object, like a Riemann surface.

Rather than starting from a vector space, we start with a family of vector spaces - a vector bundle. The endomorphism gets replaced by an object called a Higgs field. When we take the characteristic polynomial in this context, we obtain a map known as the Hitchin fibration, which possesses a remarkably rich geometric structure. From there, all the usual notions of linear algebra can be translated and yield geometric objects. 

Along the way, we will encounter several concepts from algebraic geometry, which we will describe in an informal manner.