# 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