Mathematics Colloquium

Upcoming Colloquium

Quantum graphs and associated C*-algebras
Dr. Lara Ismert, University of New Mexico

September 25, 2026
12:00pm-1:00pm via Zoom

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Meeting ID: 885 2240 9302

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Abstract

Given a compact Hausdorff space X, the algebra of continuous functions C(X) equipped with pointwise 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 quantum graphs as a generalization of classical simple graphs 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. Time permitting, we characterize this associated C*-algebra for some nice examples of quantum graphs.

Biosketch

Dr. Lara Ismert is a Research Assistant Professor in the Department of Mathematics & Statistics at the University of New Mexico. Her position is primarily supported by Terry Loring's ARL grant "Quantifiable Topological Protection For Quantum Materials". Their work focuses on signatures of topological insulators via C*-algebraic K-theory and joint spectrum techniques for noncommuting tuples of operators.

She is also sole PI for NSF DMS-2603107, "KMS States of Quantum Cuntz–Krieger algebras."