Title: Deterministic percolation from random initial seeds
Speaker: David Sivakoff, The Ohio State University, Mathematics and Statistics
Seminar Type: Topology, Geometry and Data Seminar
Abstract: I will discuss background and some recent work on two percolation models: bootstrap percolation and jigsaw percolation. Bootstrap percolation is a simple growth model developed in 1979 by Chalupa, Leath and Reich to understand nucleation and metastability in physical processes such as crack formations, clustering, and alignment of magnetic spins. In this model, each vertex of a graph is either open or closed. Open vertices remain open forever, and closed vertices become open if at least a fixed threshold number of their graph neighbors are open. The questionis, given an initial state, does the entire graph eventually become open? Jigsaw percolation is a novel model intended to study how individuals in a social network might collaboratively solve a puzzle. The model may be viewed as an edge-based version of bootstrap percolation, which I will formally define in my talk.
