# Noon lecture

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On 16.12.2010 at 12:20 in S11, there is the following noon lecture:

# Spirals

## Eric Sedgwick

## Abstract

This is joint work with Jan Kyncl, Marcus Schaefer, Daniel Stefankovic.

In a surface, draw a pair of curves with a large number of intersections. Must the drawing contain any particular sub--structures? A spiral is especially desirable because it can be used to simplify drawings in a number of contexts (string graphs, quadratic word equations).

However, we show that for every n there is a pair of curves in the plane with n intersections, but that do not form a spiral. This proof utilizes train tracks, a topological tool that provides a compressed representation for densely packed curves.

list of noon lectures ( 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | future lectures)

Webmaster: kamweb.mff.cuni.cz Modified: 19. 10. 2010