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Séminaire Analyse

organisé par l'équipe Analyse

  • Gaetan Leclerc

    Fourier dimension an dynamical fractals

    16 mai 2024 - 11:00Salle de conférences IRMA

    Abstract: Consider the triadic Cantor set equipped with the Cantor law. It happens that its cumulative distribution function, the devil’s staircase, is Hölder regular, and its best exponent of regularity is ln(2)/ ln(3), which is exactly the Hausdorff dimension of the Cantor set. Moreover, one can show that the Fourier transform of the Cantor law decay like |ξ|^{− ln 2/ ln 3} “on average”. This is no coincidence, and hint for a deeper link between Fractal Geometry and Fourier Analysis. In this talk we will detail and explore this link through the notion of Fourier Dimension. We will introduce the Fourier dimension, compute it on some easy examples, quote some natural questions that arise, and then discuss a (partial) state of the art on the topic.

  • Yohann Genzmer

    TBA

    30 mai 2024 - 11:00Salle de conférences IRMA

  • Michele Ancona

    TBA

    27 juin 2024 - 11:00Salle de conférences IRMA