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Séminaire GT3

organisé par l'équipe Géométrie

  • 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.