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Séminaire ART

organisé par l'équipe Algèbre, représentations, topologie

  • Alexander Soibelman

    Quantum integrable systems, noncommutative periods, and normal forms

    11 mars 2025 - 14:00Salle de séminaires IRMA

    Résumé : The quantum normal form of a Hamiltonian, introduced by theoretical physicists developing quantum mechanics in the early 20th century, can be used as an algebraic method of finding the asymptotic expansions of eigenvalues of the Schrödinger operator. In this talk, we will introduce the quantum normal form, then show how it can be reinterpreted in two distinct ways: using formal deformations of variations of Hodge structure and as a noncommutative period associated with the quantization of a complex integrable system. This is joint work with Maxim Kontsevich.

  • Yan Soibelman

    The algebra and geometry of the Riemann-Hilbert correspondence

    11 mars 2025 - 15:15Salle de séminaires IRMA

    Résumé : Riemann-Hilbert correspondence is typically understood as the (derived) equivalence of two categories: the category of (certain) D-modules on a complex manifold X and the category of (certain) constructible sheaves on X. The underlying geometry is the symplectic geometry of the cotangent bundle of X. In 2015 together with Maxim Kontsevich we proposed a vast generalization of the Riemann-Hilbert correspondence in which the cotangent bundle is replaced by an arbitrary complex symplectic manifold. This conjectural generalization is quite natural from the point of view of our program "Holomorphic Floer Theory",since it relates the Fukaya category of the symplectic manifold with the category of holonomic modules over its deformation quantization algebra. Our proposal is related to interesting questions of representation theory, Donaldson-Thomas invariants, periodic monopoles, etc. I am going to review algebraic and geometric structures involved in our generalized Riemann-Hilbert correspondence, illustrate it in several examples and discuss some open questions.

  • Benjamin Dequêne

    tba

    18 mars 2025 - 14:00Salle de séminaires IRMA

  • Victor Carmona

    Enveloping operads; one construction to rule them all

    25 mars 2025 - 14:00Salle de séminaires IRMA

    Résumé : Enveloping algebras have been the focus of numerous studies and a possible reason for that is their appearance in different fields of mathematics and mathematical physics. In many of those cases, the universal enveloping algebra construction is restricted to Lie-algebras, but enveloping algebras are a general device that can be considered for a quite broad notion of algebra. Furthermore, enveloping algebras are just the unary part of a more general construction, enveloping operads. While this operadic enhancement has been of crucial importance in work of Berger-Moerdijk, Fresse, Harper, Muro, Pavlov-Scholbach, White-Yau, etc, it has not been given the attention that it deserves. It is curious that a quick search of “universal enveloping algebra” in Mathscinet gives back around 5000 matches, whereas searching “enveloping operad” just gives 52 matches. In this talk, based on arXiv:2407.18190, we are going to discuss all these notions and various applications of enveloping operads that will hopefully convince the audience about the potential of these objects.

  • Joakim Færgeman

    tba

    8 avril 2025 - 14:00Salle de séminaires IRMA

  • Adrien Laurent

    à preciser

    8 avril 2025 - 15:15Salle de séminaires IRMA

  • Anna-Laura Sattelberger

    à preciser

    22 avril 2025 - 14:00Salle de séminaires IRMA

  • Dmitry Rumynin

    à preciser

    27 mai 2025 - 14:00Salle de séminaires IRMA