We study the scaling limit of the dimer model on ‘critical’ graphs. We establish a connection between the dimer model and the free Dirac Fermion quantum field theory in various ways by studying them in a background ‘gauge field’. We speculate on how to leverage the fundamental nature of the Dirac Fermion in 2D CFT to study general CFTs from the dimer point-of-view.
Vaughan Jones showed how to associate links in the $3$-sphere to elements of Thompson’s group $F$ and proved that $F$ gives rise to all link types. This talk will discuss two recent extensions of Jones’ work– the first is a method of building annular links from Thompson’s group $T$, which contains $F$ as a subgroup, and the second is a method of building $(n,n)$-tangles from $F$ . Annular links from $T$ arise from Jones’s unitary representations of the Thompson groups, and tangles from $F$ give rise to an action of $F$ on Khovanov’s chain complexes. This talk includes joint work with Slava Krushkal and Yangxiao Luo