Ottawa

The elliptic Hall algebra has appeared in many different contexts in representation theory and geometry under different names.  We will explain how this algebra is categorified by the quantum Heisenberg category.  This diagrammatic category is modelled on affine Hecke algebras and can be viewed as a deformation of the framed HOMFLYPT skein category underpinning the HOMFLYPT link invariant.  Using the categorification of the elliptic Hall algebra, one can construct large families of representations for this algebra.

I will introduce product structure theory of graphs and show how families of graphs that have such a structure admit short adjacency labeling scheme and small induced universal graphs. Time permitting, I will talk about another recent application of product structure theory, namely vertex ranking (coloring).