Graduate Seminar: Making Physical Models of Maps on Surfaces

Abstract

Given a map of countries, cartographers color the map so that bordering countries are colored differently. A classic problem in graph theory asks for the minimum number of colors needed for any map. For maps drawn on the plane or the sphere, this is the well-known Four Color Theorem, but there is also a generalization to arbitrary closed surfaces, like the torus or the Klein bottle. Recently, mathematical artists have been interested in making physical models of those maps that need the most number of colors. In this talk, I will discuss the various approaches people have taken for making these models. In particular, I will cover my own attempts using a 3D printer, and the challenges and workarounds I found while making my "Neighborly Nine" sculpture.

Biography of Speaker

Timothy Sun is an Assistant Professor in the Computer Science department at SFSU. His research is primarily in topological graph theory, but he sometimes dabbles in computer science education and recreational mathematics."