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Séminaire de Théorie Algorithmique des Nombres

Responsables : Xavier Caruso et Aurel Page

Page du séminaire

  • Le 26 janvier 2021 à 10:00
  • Online
    Mercedes Haiech (Université Rennes 1)
    The Fundamental Theorem of Tropical Partial Differential Algebraic \nGeometry

    Given a partial differential equation (PDE), its solutions can be difficult, if not impossible, to describe. The purpose of the Fundamental theorem of tropical (partial) differential algebraic geometry is to extract from the equations certain properties of the solutions. More precisely, this theorem proves that the support of the solutions in $k[[t_1, cdots, t_m]]$ (with $k$ a field of characteristic zero) can be obtained by solving a so-called tropicalized differential system.

  • Le 2 février 2021 à 10:00
  • Online
    Bogdan Dina (Ulm University)


  • Le 16 mars 2021 à 10:00
  • Online
    Vincent Neiger (Université de Limoges)
    Deterministic computation of the characteristic polynomial in the time\nof matrix multiplication

    This talk describes joint work with Clément Pernet on an algorithm which computes the characteristic polynomial of a matrix over a field within the same asymptotic complexity, up to constant factors, as the multiplication of two square matrices. Previously, this was only achieved by resorting to genericity assumptions or randomization techniques, while the best known complexity bound with a general deterministic algorithm was obtained by Keller-Gehrig in 1985 and involves logarithmic factors. The new algorithm computes more generally the determinant of a univariate polynomial matrix in reduced form.

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