Time：14:00-16:00, Friday, November 17 2023
Venue:E4-233 & ZOOM
ZOOM ID:939 5754 1624
PASSCODE:575859
Speaker：Matteo Ruggiero,Université Paris Cité
Biography:Matteo Ruggiero is maître de conférences at the Université Paris Cité, UFR de Mathématiques, research unit IMJ-PRG, group Géométrie et Dynamique. His interests include (Local and semi-local) dynamics of analytic maps, (non-Kähler) complex geometry and compactification of orbit spaces, birational aspects of singularities of analytic spaces and maps, links with toric, tropical and non-archimedean geometry.
Title：Resolution of vector fields and applications to parabolic dynamics
Abstract:
The local dynamical properties of a high order perturbation of the identity are intimately related to the resolution of singularities of the associated infinitesimal generator.
In particular, Ramis-Sibuya normal forms of resolved infinitesimal generators admitting a separatrix allow to describe the parabolic manifolds asymptotic to such separatrix (by recent works by López-Hernanz, Raissy, Ribón, Sanz-Sánchez, Vivas).
I will present these phenomena via a class of examples in dimension 3, introduced in a joint work with Samuele Mongodi, where all the separatrices lie inside central manifolds of the resolved infinitesimal generator, a behavior in contrast with the situation in dimension 2.
