Percolation phenomena: a broad-brush introduction with some recent applications to porous media, liquid water, and city growth

This brief overview is designed to introduce some of the advances that have occurred in our understanding of percolation phenomena. We organize our presentation around three simple questions: (i) What are percolation phenomena? (ii) Why do we care? (iii) What do we actually do? To answer the third question, we will briefly review some recent applications of percolation that have been the subject of research in the Boston University group.