The Hallway Probelm

This talk will be given by Jason Siefken!

The hallway problem considers adjacent parallel hallways of unit width each with a single doorway (aligned with integer lattice points) of unit width. It then asks: what are the properties of lines that pass through each doorway? Configurations of doorways closely correspond to Sturmian words, and so properties of these configurations may be lifted to properties of Sturmian words. This talk will explore lines of sight, lines that pass through each doorway, for both the case for both a finite number of parallel hallways and an infinite number, and their consequences for Sturmian words. We then produce a metric on configurations with an infinite number of hallways that preserves the property of admitting a line of sight under limits.

Refreshments will be served at 4:30pm in the graduate lounge on the 6th floor of Bahen.

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