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{\Large Department of Mathematics, BGU}

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{\Huge Colloquium}\\[0.2\baselineskip]

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\textbf{On} \emph{Tuesday, December  3, 2024}
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\textbf{At} \emph{14:30 -- 15:30}
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\textbf{In} \emph{Math -101}

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{\large\scshape Dmitry Kerner 
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  (BGU)
}
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will talk about
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{\Large\bfseries How does the germ of a singular space look like?\par}
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\textsc{Abstract:}
Manifolds are locally rectifiable (at each point) to R\^{}n or C\^{}n. The local Geometry, Topology, Algebra of singular spaces is much richer. Such a germ X is homeomorphic to the cone over Link{[}X{]}. In `most cases' this homeomorphism cannot be chosen differentiable. This brings various pathologies.

The Lipschitz equivalence of space-germs has been under investigation in the last 30 years. It excludes various pathologies of homeomorphisms, but is `rough enough' to prevent moduli.

The first natural question is whether/when the homeomorphism X \ensuremath{\sim} Link{[}X{]} can be chosen bi-Lipschitz. The first obstructions to this are fast vanishing cycles on Link{[}X{]}. We detect lots of fast cycles. This gives countable (multi-index) series of `exotic Lipschitz structures' on the germ (R\^{}n,o), all realizable as complex-analytic hypersurface germs.








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