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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Buildings are simplicial complexes with a number of additional conditions, generalising trees to higher dimensions. They are interesting objects, from the viewpoint of number theory, algebraic geometry, geometric group theory and combinatorics.
I will start by giving motivations for the building axioms by reviewing their “archimedean analogues”, symmetric spaces (no knowledge of Lie groups needed), before giving said definitions as well as examples. There are too many applications of buildings to cover in an hour, we will see how many I can fit in the rest of the time. Among them: decomposition results for algebraic groups, construction of finitely presented simple groups, quasi-isometric rigidity of symmetric spaces, classification of finite simple groups, boundary maps and random walks.

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.