Title:  The Mathematics of Supersymmetry


Abstract:  In physics, supersymmetry is a pairing between the carriers of mass and energy appearing in theories of subatomic particles. Useful tools when studying supersymmetry mathematically are N-regular, edge N-colored bipartite graphs with signs assigned to the edges and heights assigned to the vertices, subject to certain conditions. Such graphs are known as Adinkras, and have vertices representing the particles in a supersymmetric theory and edges corresponding to the supersymmetry pairings. We will discuss how parts of the structure of an Adinkra can be described using binary linear error-correcting codes, while all of the structure can be captured by a very special case of a geometric construction due to Grothendieck. This talk is designed to be accessible to an undergraduate audience.