Geometry of finite graphs and QFT axiomatization of Hopf algebras

GAP Seminar

Meeting Details

For more information about this meeting, contact Amy Hanley, Ping Xu, Eyal Subag, Nigel Higson, Mathieu Stiénon.

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

Date: 03/28/2017

Time: 2:35pm - 3:30pm