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.

Intersection theory, which aims at understanding precisely how algebraic varieties intersect, is an old research subject in algebraic geometry, and it is nowadays well understood. However, it does not generalize well to the arithmetic case. Arithmetic intersection theory, developed by Gillet and Soulé in the 90s, strikingly mixes the previous algebraic objects at finite places, and complex analytic objects called Green currents. This asymmetry motivates the search for non-Archimedean Green currents, with the objective of unifying both finite and infinite places.

During this presentation, I will present the basic constructions of classical intersection theory, then discuss in more detail the notion of Green currents and the arithmetic theory. Finally, I will briefly present ongoing approaches that tend towards a non-Archimedean version.