Associate Professor at IMECC UNICAMP, Campinas, Brazil. Research interests: Dynamical systems, PDEs, and symplectic geometry. (Source: Lattes Curriculum)
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Consider a closed Riemann surface. Our ultimate goal is to construct Morse homology groups associated to the length functional L on the space C of unparametrized immersed loops. Namely, equivalence classes under reparametrization of parametrized immersed loops. The Morse chain groups are generated by the critical points of L - the periodic geodesics of the Riemann surface - and graded by …
Consider the infinite dimensional hyperbolic dynamical system given by the heat (semi-)flow on the loop space of a closed Riemannian manifold (in the presence of a generic perturbation). The recently discovered *backward* lambda-Lemma is expected to be the key substitute for the non-existing backward flow. The lack of a backward flow caused the field to dry out in the mid 80s after those …
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