Le séminaire des doctorants se propose de fournir aux doctorants une occasion de s'ouvrir aux autres domaines des mathématiques que le leur. A chaque séance, un intervenant réalise un exposé sur un fait standard de leur domaine d'étude, de niveau adapté à l'ensemble des doctorants.

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Everyday, mathematicians makes numerous choices: how much sugar in a cup of coffee ? which Bourbaki to read next ? which points to select in a infinite product of non-empty sets ? One of these choices in not like the others, it raises a question surrounded by conflict and very intense debate: should coffee be drank with or without sugar ? Answering this question is outside the scope of this talk instead, we tackle the much less controversial question of the axiom of choice. We explain what it is, its place in mathematics and its relation to excluded middle. We also talk about constructivism, what it is and why it is sometimes interesting to not use choice or excluded middle.

The PhD students seminar aims to provide PhD students with an opportunity to explore other areas of mathematics beyond their own. At each session, a speaker gives a presentation on a standard topic in their field of study, at a level suitable for all doctoral students.