# Geometry and Geometric Analysis Working Group

#### 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.