Short Paths in the Sierpiński Carpet and Other Fractals

In this talk we’ll try to determine the shortest paths between any two points in the Sierpiński carpet and in related fractals, including the 3-dimensional Menger sponge, which has an approximation shown in green.  Along the way, we’ll highlight recent research results in this area and discuss several open problems that are ripe for exploration.  This talk is based on joint work with Ethan Berkove and several undergraduate students.