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.

One of the core problems of number theory is to determine wether a system of polynomial equations with rational or integer coefficients has rational or integer solutions. A historically significant and fruitful strategy to study this problem is the local-global principle, or Hasse principle, which consists in comparing the existence of solutions in Q to that in every completion of Q : R and the p-adic fields Q_p. For some varieties, known as homogeneous spaces, the existence of rational points has been fully caracterized in local-global terms, using the Brauer-Manin obstruction. In this talk, I aim to explain what the local-global principle and the Brauer-Manin obstruction are, and to overview the tools involved in their study for homogeneous spaces.