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Stanford University Mathematical Organization (SUMO) Speaker Series

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{\large
{\red  Monday, March 11, 2019

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6-7pm, Arrillaga \textbf{Wellness} Room (Different location!)

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{\large \bf
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Finding Red and Blue progressions, and Relations to Dynamical Systems
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{\bf Prof. Freddie Manners
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Suppose we color the integers $1,\ldots,N$ either red or blue.  Is there a progression of length 10, say $x,x+k,x+2k,\ldots,x+9k,$ which are all the same color?  How big does $N$ need to be to guarantee this?

Now suppose I tell you that at least $1\%$ of the numbers are red.  Is there now necessarily a red progression (if $N$ is big)?

As well as discussing these elementary questions, I hope to explain something about their close relationship to the apparently much more sophisticated world of dynamical systems and ergodic theory.

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