Séminaire GT3
organisé par l'équipe Géométrie
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Sylvain Douteau
Intersection cohomology is a stratified cohomology theory
13 janvier 2025 - 14:00Salle de séminaires IRMA
Objects with singularities are ubiquitous when dealing with manifolds, but are usually tame objects: Pseudo-manifolds which can be equipped with suitable stratifications (à la Whitney or Thom-Mather).
In the 1980, Goresky and MacPherson introduced intersection cohomology. A new invariant, which extends ordinary cohomology and gives pseudo-manifolds the cohomological properties expected of manifolds such as Poincaré duality.
However, by construction, intersection cohomology is not a cohomology theory in the usual sense. It has been an open problem since its introduction to find a context in which intersection cohomology can be interpreted as an actual cohomology theory.
In this talk, I will present such a context inspired by the A^1-homotopy theory of Morel and Voevodsky. This is based on work in progress, joint with David Chataur. -
Fernando Camacho Cadena
Hamiltonian flows and subsurface deformations
3 février 2025 - 14:00Salle de séminaires IRMA
Given a closed compact surface S and a reductive Lie group G, Goldman introduced a symplectic structure on the character variety Hom(pi_1(S),G)//G (the space of representations modulo conjugation). For Teichmüller space, the form coincides with the Weil-Petersson form. The symplectic structure gives rise to Hamiltonian flows associated to functions on character varieties, and therefore gives ways of deforming representations. I will talk about joint work with Anna Wienhard and James Farre, where we focus on a particular type of function on the character variety, whose input includes families of curves on S. The result I will present states that the Hamiltonian flows of such functions are what we call subsurface deformations, which roughly means that the flow is concentrated on a subsurface of S that depends on the curves defining the function. If time permits, I will discuss some applications to Hamiltonian flows of length functions associated to some self intersecting curves.