[PAST EVENT] Mathematics Colloquium: Neal Bushaw (Virginia Commonwealth University)
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- Open to the public
Title: Bootstrap Percolation on Polygonal Tilings of the Plane
Abstract: We consider bootstrap percolation in tilings of the plane by regular polygons. First, we determine the percolation threshold for each of the infinite Archimedean lattices. More generally, let T denote the set of plane tilings t by regular polygons such that if t contains one instance of a vertex type, then t contains infinitely many instances of that type. We show that no tiling in T has threshold 4 or more. This material is self-contained, and requires no particular background. We'll share many open problems, as well as the intuition behind these results.