Geometry of finite graphs and QFT axiomatization of Hopf algebras
Speaker: Adrian Ocneanu, Penn State
Abstract: We show that the axioms of a Hopf algebra are the properties of a square handkerchief, pulled from a hat, read with QFT. The axioms are described in a manner similar to finite element methods. We then construct from scratch, in an explicit, elementary way, a class of examples. A finite graph has, besides its usual symmetries, also quantum symmetries. These are related to its geometry, when a finite graph is viewed as a manifold with a parallel transport connection, using statistical mechanics. Thus the exceptional E_6, E_7 and E_8 have 12, 17 and respectively 32 quantum symmetries. These symmetries form a Hopf algebra of a new multiplicative quiver theory. They yield modular invariants related to number theory, first found by physicists.
Room Reservation Information
Room Number: 104 Osmond Building
Time: 2:35pm - 3:30pm