Two shorter talks
by Alex Lee / Nick Beaton
First Talk (Alex):
There is a correspondence due to Bonnet and Eynard between the q-state Potts and O(n) loop models defined on random lattices via matrix integrals. The correspondence is known to hold to lowest order, that is for the models defined on disks, and is one of the few ways to obtain information about the Potts model on random lattices. Beyond planar order little is known. In this talk I will describe our current work aiming to extend this correspondence to surfaces of arbitrary Euler characteristic, starting with cylinders. This would allow for an understanding of the random lattice Potts model on more complex surfaces and should also provide a further test for what are thought to be certain universality aspects of the Eynard-Orantin recursion.
2nd Talk (Nick):
Self-avoiding walks have long been considered as an idealised model of polymers, and can be used to study phenomena like polymer collapse and adsorption. Thus far the only models which have been solved exactly, such as Dyck paths and partially directed walks, have a directedness constraint. I'll introduce a new model which is not restricted in this way.
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