CRM: Centro De Giorgi
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Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation

Moduli space of foliations and curves defined by a generic function

speaker: Emmanuel Paul (Université Paul Sabatier, Toulouse (France))

abstract: (common work with Yohann Genzmer) We first describe the moduli space of foliations defined by a germ of holomorphic (or Darboux) function with a generic tangent cone, through normal forms. Then we consider the distribution on this moduli space induced by the classification of singular curves: two points are equivalent if the corresponding foliations define the same singular curve up to conjucacy. We prove that this distribution is completely integrable by rational first integrals: these ones give us a complete system of invariants for plane curves in this generic topological class.

Mon 12 Oct, 16:15 - 17:15, Aula Dini
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