Time: 9h, Wednesday, June 10, 2020

Location: Room 612, Building A6, Institutte of Mathematics and Google Meet https://meet.google.com/vha-ujbp-kwo

Abstract: Let K be C or R. Two smooth germs f, g : (K^n , 0) ---> K are called bi-Lipschitz right equivalent if there is a germ of bi-Lipschitz homeomorphism h : (K^n, 0) ---> (K^n, 0) such that f = g ◦ h. If h is a germ of a smooth diffeomorphism (rep. a homeomorphism) we say that f and g are smoothly right equivalent (rep. topologically right equivalent). Denote by E^n the space of all smooth function germs at 0 equipped with Whitney topology. A function germ f is called simple with respect to a certain equivalent relation if there is a neighbourhood of f containing only finitely many equivalence classes. Germs not simple are called modal germs. In case of the smooth equivalence, Arnold [1] provided a full classification. It is known that there is no moduli for topological equivalence, i.e. every germs are simple. In [2], Henry-Parusinski found that bi-Lipschitz right equivalence for function germs admits moduli. In this seminar, I would like to talk about our recent result [3] in which we introduce the notion of Lipschitz simple germs and give the full classification. It is surprising that a germ is Lipschitz modal if and only if it deforms to a family of smooth unimodal germs called J_{10} in the Arnold’s list.