The plan is to describe the proof of Reifenberg's topological
disk theorem, hoping that it will be new to a good part of the audience.
I'll also say why minor variants of the algorithm could lead to slightly
different results, and for instance give pieces of bilipschitz images of $R^d$
in $E$ when $E$ is Ahlfors-regular and Reifenberg-flat. This is joint work
with T. Toro. We did not check everything yet, so if something fails,
I'll talk about regularity for soap bubbles instead.
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