"Geometry and Analysis on Groups" Research Seminar

Time: 2015.11.17, 15:00–17:00
Location: Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock
Title: "Higher-dimensional expansion and topological overlap."
Speaker: Uli Wagner (Institute of Science and Technology Austria)
Abstract: In the first part of the talk, we give an introduction to higher-dimensional expansion properties of cell complexes. A special focus will be on the notion of coboundary expansion (informally: the existence of a linear isoperimetric inequality for the cellular coboundary operator), which was introduced independently by Linial & Meshulam and by Gromov and which generalizes the classical notion of edge expansion of graphs.

In the second part of the talk, we will present a simple proof of Gromov's Topological Overlap Theorem: If $$X$$ is a $$d$$–dimensional complex which is a coboundary expander in dimensions $$1,2,\dots d$$, then for every continuous map $$f\colon\thinspace X\to M$$ into a $$d$$–dimensional PL manifold, there exists an image point $$p\in M$$ that is covered by the $$f$$–images of a constant fraction of the $$d$$–simplices of $$M$$. (Joint work with Dotterrer and Kaufman)