Quantum Graph Theory

Vern I. Paulsen
Thu, Mar 9, 2017
PIMS, University of Manitoba
PIMS-UManitoba Distinguished Lecture
Many numerical invariants of a graph, such as the independence number, clique number and chromatic number, have game theoretic descriptions. In these games a referee poses questions to two collaborating non-communicating players and they return answers. Quantum graph theory is concerned with how these graph parameters change when the players are allowed to use the random outcomes of quantum experiments to determine their answers. In this talk I will explain these concepts, focusing on the chromatic number, survey some of what little is known about the quantum chromatic numbers of graphs, explain the connection between these ideas and famous open conjectures of A. Connes and B. Tsirelson, and introduce an algebra affiliated with a graph whose representation theory determines the values of these parameters. Biography: Vern Paulsen is a Professor of Pure Mathematics and the Institute for Quantum Computing at the University of Waterloo. He was a Professor of Mathematics and John and Rebecca Moores Chair at the University of Houston before moving to Waterloo in 2015. His primary research focus is on the theory of operator algebras and their applications in quantum information theory. He is the author of five research monographs and over 100 research articles. He received his PhD from the University of Michigan.