Claudia Lückert

Wilhelm Killing Kolloquium: Prof. Dr. Anne Pichon (Aix Marseille University): How looks a singular space in a small neighbourhood of point?

Thursday, 11.01.2024 14:15 im Raum M5

Mathematik und Informatik

Consider a subspace X of Rn defined by polynomial equations. Suppose we fix a point p on X. When the implicit function theorem applies at p, the answer to the question in the title becomes clear! However, what happens when p is singular? A classical result ensures that X is locally topologically conical: for every sufficiently small ε > 0, the intersection of X with the ball of radius ε around p is homeomorphic to the cone formed over the intersection of X with the boundary sphere. Nevertheless, X is generally not metrically conical: there are parts of it which shrink faster than linearly when ε tends to 0. A natural problem is then to build classifications of the germs up to local bi-Lipschitz homeomorphism. I will give an introductive talk on this very active topic at the crossing point between metric topology and algebraic geometry.

Angelegt am Friday, 22.09.2023 10:57 von Claudia Lückert
Geändert am Thursday, 23.11.2023 18:26 von Claudia Lückert
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Vorträge des SFB 1442
Kolloquium Wilhelm Killing