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Séminaire Doctorants

organisé par l'équipe DOCT

  • Anna Marduel

    An introduction to barcodes

    9 janvier 2025 - 16:30Salle de conférences IRMA

    Barcodes are simple combinatorial objects that detect topological features. They first appeared as a tool for topological data analysis and have found new applications in Morse and Floer theories. We will use examples to illustrate the information they can provide (particularly quantitative information) and set out the basic definitions. This presentation is based on "Topological Persistence in Geometry and Analysis" by Polterovich, Rosen, Samvelyan, and Zhang.

  • Arthur Douay

    Drawing the p-adic unit disc

    16 janvier 2025 - 16:30Salle de conférences IRMA

    In algebraic geometry, we study geometric objects given by zeros of polynomial equations. However, in this context, we only have a very coarse topology, and we are jealous of the powerful tools of real analysis. A common object in algebraic geometry, the field of p-adic numbers, has both an arithmetic and analytic nature. One might then be tempted to try and develop a theory of p-adic analytic geometry. I will go through the various constructions of p-adic analytic geometry theories (from Tate’s rigid geometry to Huber’s adic spaces) and give motivations for these theories through the example of the p-adic unit disc.