One of the main objectives of the Quantitative Linear Algebra Long Program at IPAM from 2018 was to deepen the link between research communities examining problems in infinite dimensional functional analysis and those working on quantitative finite dimensional ones. The program provided a venue for researchers working in a number of research directions including von Neumann algebras, random matrix theory, ergodic theory, geometric group theory, and spectral graph theory, to name a few.
A goal of this talk it to provide a brief overview of the motivating problems of the QLA Program and the outcomes. Then we will move on to a discussion of quantum graphs, their quantum chromatic numbers, and how this topic fits into the themes of the QLA Program. We will close with recent results for the bounds on quantum chromatic numbers coming from the lexicographical products of quantum graphs. This is work done jointly with A. Meenakshi McNamara.