Undergraduate Math Club Seminar

The simply laced Dynkin diagrams - the graphs A_n, D_n, E_6, E_7, and E_8 - are surprisingly ubiquitous throughout mathematics. In this talk, we'll give a simple combinatorial characterization of these graphs, and then mention several natural classification problems whose solutions are given by the Dynkin diagrams. Finally, we'll discuss how certain small-n coincidences in the Dynkin diagrams relate to other exceptional objects, including the non-simplicity of the alternating group Alt_4, the fact that one can draw a tetrahedron with integer vertex coordinates, and the existence of the quaternions and octonions.