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Séminaire ART

organisé par l'équipe Algèbre, représentations, topologie

  • Julia Schneider

    Which Cremona groups are generated by involutions?

    3 mars 2026 - 14:00Salle de séminaires IRMA

    Résumé : The Cremona group of rank N over a field K is the group of birational transformations of the N-dimensional projective space over K. A classical theorem by Noether and Castelnuovo states that the Cremona group of rank 2 over the complex numbers is generated by the birational involution sending (x,y) onto (1/x,1/y) and PGL(3). In particular, it is generated by involutions. Over non-algebraically closed fields, and even more so in higher dimensions, generators are more difficult to describe. The group theoretic properties of Cremona groups often depend on the rank and on the field. In this talk, I will tell the story about two theorems: A) The Cremona group of rank 2 over any perfect field is generated by involutions [joint with S. Lamy]. B) The Cremona group of rank at least 4 over the complex numbers admits the free group over an uncountable set as a quotient [joint with J. Blanc and E. Yasinsky]. Both of these theorems rely on the Sarkisov program, which gives an interesting set of generators not of the Cremona group but of a larger groupoid.

  • Caroline Lassueur

    Des tables de caractères des modules de p-permutation

    3 mars 2026 - 14:00Salle de séminaires IRMA

    Le but de cet exposé est de présenter certains résultats récents obtenus en vue du calcul des tables de caractères des modules de p-permutation de "petits" groupes finis et de la création d'une base de données de telles tables. On passera aussi en revue l'importance de telles classifications dans le contexte des équivalences de blocs d'algèbres de groupes finis.

  • Bérénice Delcroix-Oger

    à preciser

    10 mars 2026 - 14:00Salle de séminaires IRMA

  • Yann Palu

    TBA

    17 mars 2026 - 14:00Salle de séminaires IRMA

  • Anna-Laura Sattelberger

    Border Bases in the Rational Weyl Algebra

    24 mars 2026 - 14:00Salle de séminaires IRMA

    Résumé : Border bases are a generalization of Gröbner bases for zero-dimensional ideals in polynomial rings. In recent work with Carlos Rodriguez (https://arxiv.org/abs/2510.23411), we introduced border bases for a non-commutative ring of linear differential operators, namely the rational Weyl algebra. We elaborate on their properties and present algorithms to compute with them. We apply this theory to represent integrable connections as cyclic D-modules explicitly. As an application, we visit computations with linear PDEs behind integrals in theoretical physics. We also address the classification of particular D-ideals of a fixed holonomic rank, namely the case of linear PDEs with constant coefficients as well as Frobenius ideals. Our approach rests on the theory of Hilbert schemes of points in affine space.

  • Francesco Sala

    tba

    19 mai 2026 - 14:00Salle de séminaires IRMA

  • Chris Bowman

    tba

    26 mai 2026 - 14:00Salle de séminaires IRMA