Apologies for the late notice. This seminar is cancelled.
Thackeray 427
Notes
Neal Bushaw is associate professor in the Department of Mathematics and Applied Mathematics at Virginia Commonwealth University. Prior to his 2017 arrival in Richmond, he was a grade school student in Bremerton Washington, an undergrad in Boulder, a grad student in Bellingham and Memphis, a postdoc in Tempe and Rio de Janeiro, and a frequent guest of Trinity College Cambridge.
His research interests center around “easy problems” — problems that are easy to state and think about, but difficult to solve. Mostly these problems lie within extremal graph theory and combinatorics. He is also interested in expressing this mathematics in diverse ways, exploring its interactions with art and music in recent work. In his spare time, he enjoys listening to / making / thinking about music, doing mathematics in public, and spending time in the outdoors.
Abstract or Additional Information
At each step of the k-neighbor bootstrap percolation process on a graph, every uninfected vertex with at least k infected neighbors becomes infected. An initial set of infected vertices PERCOLATES if eventually every vertex becomes infected. Determining the minimum size of a percolating set under the 2-bootstrap model is a classic combinatorial puzzle -- the slower infection of the 3-bootstrap process seems harder to analyze. Building on the work of Dukes, Noel, and Romer, we determine precisely the minimum size of a percolating in an (m x n) grid. We then consider the same question for toroidal grid graphs.