Twentieth Annual Pi Mu Epsilon Lecture

Abstract: In 1984 Alexander Grothendieck circulated his research proposal Equisse d’un Programme which has been called “the best rejected proposal ever”. It showed (among many other things) how one can associate to an algebraic surface (essentially the implicit plot of a polynomial in two variables) a simple combinatorial graph, called a dessin d’enfant (child’s drawing). The study of these objects puts one in a beautiful intersection of the realms of geometry, topology, real and complex analysis, combinatorics, number theory, and abstract algebra. Continuing research in the subject can run quite deep, but the basic ideas are accessible to undergraduates. This introduction to the subject will only require a solid background in high school algebra and maybe a little calculus.