Samuel Clearman, Rutgers Experimental Mathematics Seminar, February 26, 2015
See part 2 at vimeo.com/123640111
Abstract: Matrix immanants are a family of functions on matrices which generalize the permanent and determinant. They have a q-analog called a quantum immanant. We give a combinatorial method for evaluating these immanants on certain matrices, which arise as a q-analog of the path matrix of a planar network. We apply these techniques to the representation theory of certain algebras, and discuss connections to chromatic symmetric functions.