November 22,  2024

on-line on zoom

• 10:00 - 10:50 Anne Pichon (Universite d'Aix-Marseille) Logarithmic links of complex germs and Lipschitz geometry

  Abstract: I will present a joint work with Lorenzo Fantini and Walter Neumann which gives new tools to encode the Lipschitz classifications of complex germs. I will define what we call the logarithmic link of the singularity and ultrametrics on it, which provide a canonical geometric model.

• 11:00 - 11:50 Dmitry Kerner (Ben-Gurion University of the Negev) Fast cycles and where to find them
  

  Abstract:  Take an analytic germ \((X,0)\) in \((\mathbb{C}^N,0)\), and its link \(Link_r[X]\). When \(r\to 0\), the link contracts to the origin, and "at most points" this contraction occurs at the linear rate. But "in most cases" \(Link[X]\) contains cycles with higher vanishing rates. These fast cycles can be of zero homology class inside \(Link[X]\), but they cannot be "shrunk" in a Lipschitz way.
  
  Fast cycles are preserved under the ambient Lipschitz equivalence. In fact, their homotopy types and vanishing rates depend only on the inner-Lipschitz type of \(X\). Hence these are important "almost topological" invariants of the germ.
  
  I will show how to detect the fast cycles on perturbations of weighted-homogeneous complete intersections, and on surface germs (with arbitrary singularities).
  As a simple application we get plenty of exotic Lipschitz structures. E.g. Brieskorn-Pham germs are often topological manifolds (their links being topological spheres). But most of them have (pairwise) distinct inner Lipschitz types.
  
  Joint work with Rodrigo Mendes.