Fall 2020

Remarks on the Discrete Cube

Wednesday, Aug. 19, 2020 10:30 am11:30 am

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Functions on the discrete cube---that is, assigning an outcome to each string of n bits---play a central role in probability theory, analysis, and computer science. The study of Boolean functions is a major research area, which is dominated by beautiful methods coming from Fourier analysis. My aim in these lectures is to draw attention to some much more elementary ideas, using heat flow and simple probabilistic arguments, that make it possible to address some basic questions that appear to be outside the reach of the usual approaches in this area. Fourier analysis will be studiously avoided, and I will aim to introduce all the necessary tools (old and new) in a self-contained manner.