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.

Arakelov geometry is an area of number theory which harnesses intuition and techniques from projective geometry for the study of arithmetic questions, especially diophantine problems. It relies on the interplay between algebraic geometry over Dedekind domains and complex differential geometry. In this talk, I will introduce its basic ideas by taking the simplest possible example: the « compactification » of line bundles over the ring of integers of a number field (aka fractional ideals). The resulting theory closely ressembles the study of line bundles on a smooth, projective curve, and one recovers from it the most classical results of algebraic number theory. Then, I will outline the next simplest case (due to Arakelov) of an arithmetic surface, where the compactification of line bundles is key to obtaining a satisfactory intersection theory for divisors.