Geometry and Geometric Analysis Working Group

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Some topological isoperimetric problems

Speaker: Fedor Manin, Ohio State University

Location: Warren Weaver Hall 517

Date: Monday, November 12, 2018, 11 a.m.

Synopsis:

I will discuss the following questions (due mostly to Gromov) and some partial answers:

• Given a nullcobordant manifold of (uniformly) bounded geometry and volume \(V\), how does the minimal volume of a nullcobordism of bounded geometry depend on \(V\)?
• Given compact metric spaces \(X\) and \(Y\) and a nullhomotopic \(L\)-Lipschitz map \(f:X \to Y\), how does the minimal Lipschitz constant of a nullhomotopy depend on \(L\)?

Both of these can be seen as a kind of isoperimetric question, and are closely related to each other as well as to more classical notions of isoperimetry.