Séminaires : Séminaire sur les Singularités

Equipe(s) : gd,
Responsables :André BELOTTO, Hussein MOURTADA, Matteo RUGGIERO, Bernard TEISSIER
Email des responsables : hussein.mourtada@imj-prg.fr
Salle : salle 2015
Adresse :Sophie Germain

Archive avant 2015

Hébergé par le projet Géométrie et Dynamique de l’IMJ-PRG



Orateur(s) Hasti Mohadeseh Vakili - Université de Grenoble,
Titre Singularities of linear families of symmetric matrices
Horaire10:30 à 12:30
Diffusion Link: https://u-paris.zoom.us/j/81523852196?pwd=ZHRadUNrbFZZYVZibkY5UkRrUS82QT09 Meeting ID: 815 2385 2196 Passcode: 271828
RésumeIn this work, we study the regularities of eigenvalues and eigenvectors of k-parameter linear families of real symmetric matrices A(t), t ∈ R^k, following, among others, works of Rellich (1937) and Kurdyka-Paunescu (2008). We introduce the monodromy of A(t), which is the action of the first homotopy group of regular parameters on the spectrum of A(t), and the related antipodal monodromy. We first characterize all possible monodromies, and in particular, realize any permutation as the antipodal monodromy of a 2-family. We then study the analytic reductions of A(t) , and prove that the existence of a non trivial antipodal monodromy is the only obstruction to get full diagonalization of A(t) . Finally, we study the couples eigenvalues/eigenvectors for 2-families in Sym_3(R), and prove that those families are classified by the given of one couple of type of cubic curves of P^2 among nine possibilities.
Sallesalle 2015
AdresseSophie Germain