Título del evento: "Real and Complex Dynamical Systems" on the occasion of Prof. Yulij Ilyashenko's 75-th birthday

Lugar: Moscú, Rusia

Fechas: del 26 al 30 de Noviembre de 2018

Participación del equipo: 

Laura Ortiz Bobadilla

Conferencia plenaria: Analytic invariants of germs of curves and foliations in (C^2 , 0)

Resumen:  This talk deals with two geometric objects: on one side, the germs of analytic curves in (C^2 , 0) and their analytic moduli, and on the other, the analytic functional invariants of germs of holomorphic dicritic foliations in (C^2 , 0). We prove that any analytic class of germs of singular curves in (C^2 , 0) having n+1 pairwise transversal smooth branches can be realized in an appropriate dicritic foliation with prescribed collection of involutions. This collection of involutions is related to the tangency points with the exceptional divisor of the corresponding dicritic foliation; we recall that the involutions (with fixed parametrization) of a generic dicritic foliation is one of the, so called, Thom’s invariants (the functional one) of analytic classification of generic dicritic foliations. The purpose of this talk is to talk about a recent work with Jessica Jaurez [1], and to give as well an overview of results previously obtained in joint works with Ernesto Rosales and Sergei Voronin [2, 3]. All together they constitute some steps towards the thorough understanding of the geometry of the finite parametric (analytic) invariants of singular curves and singular foliations (work in progress).

Beatriz Molina Samper

Presentación de póster: Invariant surfaces for Toric type foliations in dimension 3.