April 12,  2024

on-line on zoom

• 10:00 - 10:50 Dmitry Kerner (Ben-Gurion University of the Negev) Which germs are inner-metrically conical? (And how to detect fast vanishing cycles?).

  Abstract:  Let \(X\) be a complex-analytic germ. It is (non-embedded) homeomorphic to the cone over \(Link[X]\). The germ \(X\) is called "inner metrically conical" (IMC) when this homeomorphism can be chosen bi-Lipschitz. IMC's are the simplest germs from the metric point of view. "Most germs" are not IMC.
   The first obstruction to the IMC-property are "fast vanishing cycles". These are topologically non-trivial subsets of \(Link[X]\) that vanish faster than linearly, as \(Link[X]\) shrinks to the origin.
  
  I will speak about (perturbations of) weighted-homogeneous germs and about surface-germs. In these cases we get simple criteria to detect/forbid the fast cycles. In particular, already among normal surface germs one gets large ("unclassifiable") collection of IMC's.
  (Joint work with Rodrigo Mendes Pereira)

   

• 11:00-11:50 Patrick Popescu-Pampu (Université de Lille) Combinatorics of real analytic morsifications

  Abstract: I will present a work done in collaboration with A. Bodin, E. García Barroso and M.-Ş. Sorea. We study a large class of morsifications of germs of univariate real analytic functions. We characterize the combinatorial types of the associated Morse functions in terms of a contact tree built from the real Newton-Puiseux roots of the polar curve of the morsification.