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Séminaire GT3

organisé par l'équipe Géométrie

  • 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.

  • Ken'ichi Ohshika

    Les dimensions des faces de la sphère unité de l’espace tangent de l’espace de Teichmüller

    10 mars 2025 - 14:00Salle de séminaires IRMA

    Je vais donner une expression d’une face de la sphère unité de l’espace tangent de l’espace de Teichmüller par rapport la norme de Thurston en utilisant des vecteurs d’étirement, et expliquer comment on peut estimer la dimension de la face. C’est un travail en progrès.

  • Sumio Yamada

    Cross Ratio, Green's functions and Riemann surfaces

    24 mars 2025 - 11:30Salle de conférences IRMA

    Abstract: Given an ordered pair of points on a Riemann surface, there exists a unique Green's function with the given points being the two poles. Such a Green's function can be described as the real part of the cross ratio when the Riemann surface is the sphere. We consider the question of the existence of complex automorphisms of hyperelliptic Riemann surfaces, and formulate it by utilizing the behavior of Green's functions on the sphere. This is a ongoing project with Norbert A'Campo and Athanase Papadopoulos.

  • Norbert A'campo

    Structures combinatoires et géométriques sur la fibre de Milnor d'une singularité d'une courbe plane

    24 mars 2025 - 14:00Salle de séminaires IRMA

    Résumé: Je vais exposer un travail en cours, commun avec Pablo Portilla Cuadrado. Un théorème récent de Pablo Portilla Cuadrado et Nick Salter permet d'équiper la fibre de Milnor d'une singularité d'une courbe plane de structures additionnelles : une métriqueEuclidienne, une structure de surface de translation, une décomposition en hexagones par des des acrs spéciaux

  • Ingrid Irmer

    The Thurston spine and critical points of the systole function on Teichm\"uller space

    14 avril 2025 - 14:00Salle de séminaires IRMA

    Abstract - Thurston defined a mapping class group-equivariant spine for Teichm\"uller space; the ``Thurston spine''. This spine is a CW complex, consisting of the points in Teichm\"uller space at which the set of shortest geodesics - the systoles - cut the surface into polygons. The systole function is a map from Teichm\"uller space to $\mathbb{R}_{+}$ whose value at any point is given by the length of the systoles. It is known that the systole function is a topological Morse function on Teichm\"uller space, whose critical points are contained in the Thurston spine. This talk surveys what the systole function tells us about the Thurston spine.

  • Stavros Garoufalidis

    From Bill Thurston to Maxim Kontsevich and Peter Scholze

    14 avril 2025 - 15:30Salle de séminaires IRMA

    Abstract: We will attempt to explain, in broad strokes, how Thurston's ideas on constructing hyperbolic metrics on 3-manifolds lead to quantum topology of complex Chern-Simons theory and to canonical q-deformations of arithmetic and motivic interest. Joint work with Peter Scholze, Campbell Wheeler and Don Zagier.