2012 Section Meeting

Invited talks

Erica Flapan, Pomona College

Topological Symmetry Groups

Abstract: Chemists have defined the point group of a molecule as the group of rigid symmetries of its molecular graph in R3. While this group is useful for analyzing the symmetries of rigid molecules, it does not include all of the symmetries of molecules which are flexible or can rotate around one or more bonds. To study the symmetries of such molecules, we define the topological symmetry group of a graph embedded in R3 to be the subgroup of the automorphism group of the abstract graph that is induced by homeomorphisms of R3. This group gives us a way to understand not only the symmetries of non-rigid molecular graphs, but the symmetries of any graph embedded in R3. The study of such symmetries is a natural extension of the study of symmetries of knots. In this talk we will present results about the topological symmetry group and how it can play a role in analyzing the symmetries of non-rigid molecules.

James Tanton, St. Mark's School

A Dozen Fibonacci Surprises

Abstract: The Fibonacci numbers 1,1,2,3,5,8,13,... have been studied and probed and generalized and analyzed in most every possible way for centuries (well, for 810 years to be precise; well, ... longer actually if you read Sanskrit) and one might think there is little more to say about them. Let me surprise you then, a dozen times over no less!

Paul Zorn, St. Olaf College

Revisiting Familiar Places: What I Learned at the Magazine

Abstract: Among the perks of editing Mathematics Magazine for me was to learn a lot of mathematics. Much of it was new to me, but could there possibly be anything new to learn about cubic polynomials? Countable sets? Equilateral triangles? Bijective functions? The short answer is yes. The Magazine and other MAA journals are rich sources of novel --- and often surprising --- views of supposedly familiar, thoroughly understood, topics from undergraduate mathematics. I'll give some examples that worked for me. That such examples exist derives not only from the speaker's ignorance but also from the depth and richness of our subject.