Presented by: 
Jorgen Rasmussen (UQ)
Date: 
Mon 28 Oct, 2:00 pm - 2:45 pm
Venue: 
Otto Hirschfeld Building 81-214
Planar algebras have found applications in the description of lattice models in statistical mechanics with non-local degrees of freedom. Of particular importance are the diagrammatic objects known as transfer tangles since certain representations thereof correspond to lattice model transfer matrices. Working in the planar Temperley-Lieb algebra, we discuss how the corresponding transfer tangles satisfy various functional relations. We also indicate how such relations can be used to solve the associated lattice models exactly and illustrate this in the case of critical dense polymers.