Short Paths in the Sierpinski 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 [above? below?].  Along the way, we’ll highlight some recent research results in this area and discuss several open problems that are ripe for exploration. This talk, which assumes no mathematical background and will be filled with pictures, is based on joint work with Ethan Berkove and several students.