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# Dominic Dotterrer : Algorithms for the isoperimetric problem in high dimensional cubes

Thinking of high dimensional cubes as large cellular complexes, we pose the question of finding for each cellular cycle, a small cellular chain which bounds it. We will describe an algorithm which solves this problem. The algorithm is based on a trichotomy which describes the different ways cycles can sit in a cube. We will give examples of large topological spheres which are cellularly embedded in the cubes in a purely combinatorial way. These cycles will show that the exponent obtained by our algorithm is sharp.

**Category**: Geometry and Topology**Duration**: 01:34:53**Date**: February 26, 2013 at 4:25 PM**Views**: 133-
**Tags:**seminar, Geometry/topology Seminar

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