Speaker: Lara Ismert, UNM

Title: Quantum graphs and associated C*-algebras

Abstract: Given a compact Hausdorff space X, the algebra of continuous functions C(X) equipped with point wise operations, an involution by complex conjugation, and the supremum norm defines a C*-algebra. The Banach Stone theorem states that two compact Hausdorff spaces X and Y are homeomorphic if and only if their respective C*-algebras C(X) and C(Y) are isomorphic. Thus, C*-algebras provide a natural tool to study topological spaces and dynamics. We introduce the notion of a quantum graph as a generalization of a classical simple graph and also as a generalization of a classical relation on a finite set using this notion of duality for topological spaces. We introduce the notion of a quantum edge correspondence for a quantum graph and an associated C*-algebra for the Fock space of that correspondence, and, time permitting, characterize this associated C*-algebra for nice examples of quantum graphs.