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Séminaire Géométrie et applications

organisé par l'équipe Géométrie

  • Sergi Burniol-Clotet

    TBA

    12 janvier 2026 - 14:00Salle de séminaires IRMA

    TBA

  • Lamine Messaci

    Superrigidity of Cocycles for Finite-Rank Median Spaces

    26 janvier 2026 - 14:00Salle de séminaires IRMA

    In his foundational work, Margulis demonstrated a superrigidity phenomenon for higher-rank lattices, showing that any “non-elementary” homomorphism from such lattices to a semisimple Lie group extends to the ambient group. Zimmer extended this result to the setting of cocycles, with significant consequences for orbit equivalence rigidity. Since then, many related problems have been explored, extending these ideas to situations where the target group is a more general topological group preserving certain structures. In this talk, we address the case where the target group is the group of isometries of a finite-rank median space, and the source group is a product of locally compact second countable groups. These spaces have attracted interest in geometric group theory due to the unified framework they provide for studying actions on real trees and CAT(0) cube complexes, as well as the characterization they offer of Kazhdan’s property (T).

  • Francesco Cattafi

    An overview on Lie pseudogroups and geometric structures

    26 janvier 2026 - 15:30Salle de séminaires IRMA

    The space of (local) symmetries of a given geometric structure has the natural structure of a Lie (pseudo)group. Conversely, geometric structures admitting a local model can be described via the pseudogroup of symmetries of such local model. The main goal of this talk is to provide several examples and give an intuitive understanding of the slogan above, which can be made precise at various levels of generality (depending on the definition of "geometric structure") and using different tools/methods. Moreover, I will sketch a new framework, which include previous formalisms (e.g. G-structures or Cartan geometries) and allows us to prove integrability theorems. In particular, I will provide intuition on the relevant objects which make this approach work, namely Lie groupoids endowed with a multiplicative "PDE-structure" and their principal actions. Poisson geometry will give us the guiding principles to understand those objects, which are directly inspired from, respectively, symplectic groupoids and principal Hamiltonian bundles. This is based on a forthcoming book written jointly with Luca Accornero, Marius Crainic and María Amelia Salazar.

  • William Sarem

    Entropy, holomorphic convexity, and locally symmetric spaces

    2 février 2026 - 14:00Salle de séminaires IRMA

    Let $X = G/K$ be a Hermitian symmetric space of noncompact type (in rank one, $X$ is the unit ball in $\mathbb{C}^n$ and $G$ is the group $\mathrm{PU}(n,1)$), and let $\Gamma$ be a discrete and torsion-free subgroup of $G$. Can we find criteria on $\Gamma$ implying that the quotient of $X$ by $\Gamma$ is holomorphically convex, or that it contains no compact analytic subvariety of positive dimension? I will present criteria inspired by the work of Dey and Kapovich, which concern the critical exponent of the group (in rank one) or its entropy associated with some linear form (in higher rank). In both cases, the proofs involve Patterson–Sullivan measures, and the ultimate goal is to show that these quotients are Stein manifolds. The results in higher rank come from work in progress, in collaboration with Colin Davalo.