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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.

  • Claire Schnoebelen

    An introduction to Nambu structures

    23 janvier 2025 - 16:30Salle de séminaires IRMA

    Nambu structures on a smooth manifold are a special case of Poisson structures. This notion can be seen as a generalization of symplectic structures on odd-dimensional manifolds. We will present what a Nambu structure is and try to give some elements of comparison between Nambu mechanics and Hamiltonian mechanics.

    References :
    Y. Nambu, Generalized Hamiltonian mechanics, Phys. Rev. D7 (1973), 2405-2412
    L. Takhtajan, On foundation of the generalized Nambu mechanics, Comm. Math. Phys. 160 (1994), 295-315
    J.-P. Dufour, N. T. Zung, Poisson structures and their normal forms, coll. Progress in Mathematics, Birkhauser, 2005

  • Nicolas Stutz

    An introduction to Engel structures with a split through examples

    30 janvier 2025 - 16:30Salle de conférences IRMA

    In this talk, we will discuss Engel structures with a split through three examples. These geometric structures appear on differential manifolds of dimension four as rank-two distributions together with a decomposition into two preferred line fields. We will first consider the configuration space of a car moving in a plane, then we will look at third-order differential equations and finally we will present the geometry of pointed lightlike geodesics in three-dimensional Lorentzian manifolds. This talk is based on the article https://arxiv.org/pdf/1908.01169 by C. D. Hill and P. Nurowski.

  • Vincent Ferrari-Dominguez

    What is entropy ?

    6 février 2025 - 16:30Salle de conférences IRMA

    Entropy is a concept that was first introduced in thermodynamics and later famously used in information theory by Shannon. It then permeated many domains of mathematics, from statistics to dynamical systems. The goal of this seminar is to give some intuitions about this notion and more specifically about the Kolmogorov-Sinai entropy which is an invariant of dynamical systems that quantifies the degree of 'chaos' of a system.

  • Florent Dupont

    Quantum computing and Shor's algorithm

    13 février 2025 - 16:30Salle de conférences IRMA

    The RSA algorithm is one of the oldest widely used public-key encryption algorithm. It relies on the difficulty of factorizing primes, with the best-known classical algorithms performing in sub-exponential time. Shor's algorithm, which relies on the laws of quantum mechanics, drastically reduces this time complexity to polynomial time, making RSA vulnerable if implemented. The goal of this talk is to introduce quantum computing with Shor's algorithm as a guiding example.

  • Louise Martineau

    The ToMATo clustering algorithm for neuronal spike sorting

    27 février 2025 - 16:30Salle de conférences IRMA

    Recording and decoding the activity of multiple neurons is a major subject in contemporary neuroscience. The raw data produced by these recordings are almost systematically a mixture of activities from several neurons. In order to find the number of neurons which contributed to the recording and identify which neuron generated each of the visible spikes, a pre-processing step called spike sorting is required. Spike sorting is nowadays a semi-automatic process that involves many steps. We explain how the ToMATo (Topological Mode Analysis Tool) clustering algorithm, a method that combines graph mode-seeking and persistent homology, can simplify and streamline the usual spike sorting procedure carried out by most neuroscientists.

  • Lauriane Turelier

    Key characteristic of the Landau-Lifschitz-Gilbert equation

    6 mars 2025 - 16:30Salle de conférences IRMA

    The magnetization in a nanowire is described and follows the Landau-Lifshitz-Gilbert equation. As with any PDE, it is useful to know some of its properties. Here, I will give a brief overview of what I know about this equation: the stability of certain solutions, the asymptotic decomposition of solutions, and also a numerical examination of how the solutions behave.