# Lipschitz normal embeddings and determinantal singularities

Date(s) : 19/05/2016   iCal
14 h 00 min - 15 h 00 min

An algebraic singularity {X} has two natural metrics. Both are defined using an embedding to Euclidian space, but are independent of the embedding up to bilipschitz equivalence. The first is the outer metric given by restricting the Euclidian metric to {X}. The other is the inner metric, where the distance between two points is defined as the infimum of the lengths of curves in {X} between the points.
It is clear that the inner distance between two points is equal or larger than their outer distance. The other way is in general not true, and one says that {X} is Lipschitz normally embedded if there exist a constant {K}, such that the inner distance is less than or equal to {K} times the outer distance.
This talk will discuss the case of determinantal singularities. We will show that the model (or generic) determinantal singularity, that is the set of matrices of rank less than a given number, is Lipschitz normally embedded. We will also discuss the case of when a general determinantal singularity is Lipschitz normally embedded.

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