Claudia Lückert

Wilhelm Killing Kolloquium: Prof. Dr. Anne Pichon (Aix Marseille University): How looks a singular space in a small neighbourhood of a 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 22.09.2023 von Claudia Lückert
Geändert am 15.12.2023 von Claudia Lückert
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Kolloquium Wilhelm Killing
Vorträge des SFB 1442