May 17,  2024

on-line on zoom

• 10:00 - 10:50 Lorenzo Fantini  (École Polytechnique, Paris)  Lipschitz geometry of complex surfaces

  Abstract:  Lipschitz geometry is a branch of singularity theory that studies a complex analytic germ \((X, 0)\) in \((\mathbb{C}^n, 0)\) by equipping it with either one of two metrics: its outer metric, induced by the euclidean metric of the ambient space, and its inner metric, given by measuring the length of arcs on \((X, 0)\). Whenever those two metrics are equivalent up to a bi-Lipschitz homeomorphism, the germ is said to be Lipschitz normally embedded (LNE). I will give an overview of several results obtained together with André Belotto, András Némethi, and Anne Pichon on the Lipschitz geometry of surfaces, and more precisely on their inner metric structure, properties of LNE surfaces, and the so-called problem of polar exploration, which is the quest of determining the generic polar curves of a complex surface from its topology.