An introduction to quantum graphs and quantum Cuntz—Krieger algebras (or, slap `Quantum' in front)

A finite simple graph can be described through the lens of a vertex set V paired with a set of edges, E, that's a subset of VxV, or as a square matrix with entries in {0,1}. In the first talk, we will introduce quantum graphs and discuss how they generalize classical graphs. We will see some canonical examples (quantum complete and quantum trivial graphs), and discuss a notion of "quantum edges" that gives rise to a neat Cuntz-Pimsner algebra.

In the second talk, we will relate this Cuntz-Pimsner algebra to the quantum Cuntz-Krieger algebra associated to a quantum graph's quantum adjacency matrix. Basic definitions of Cuntz-Pimsner algebras and Cuntz-Krieger algebras will be provided, so come hungry!

Bio
https://faculty.erau.edu/Lara.Ismert