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.