Schedule for: 25w5405 - Operator Systems and their Applications

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Given a classical simple graph $G$, there is a $\{0,1\}$-matrix $A$ which represents which vertices are connected via a directed edge. This matrix gives rise to the Cuntz--Krieger algebra $\mathcal{O}_{A}$ whose algebraic properties reflect combinatorial properties of the graph $G$, and vice versa. This same graph also another structure, called its edge (or graph) correspondence $E_G$, which gives rise to the Cuntz--Pimsner algebra $\mathcal{O}_{E_G}$. When $G$ has no sources (i.e., every vertex in $G$ receives an edge), the Cuntz—Krieger algebra $\mathcal{O}_{A}$ and the Cuntz—Pimsner algebra $\mathcal{O}_{E_G}$ are isomorphic. In joint work with Mitch Hamidi and Brent Nelson, we examine whether or not two analogous $C^*$-algebras associated to a quantum graph $\mathcal{G}$ are isomorphic. Quantum graphs have different (though equivalent) definitions in recent literature. We define them as triples involving a quantum set, which is a C*-algebra equipped with a special type of state, along with a {\em quantum} adjacency matrix, which generalizes the classical $\{0,1\}$-adjacency matrix acting as a linear operator on a commutative C*-algebra. Analogous to the classical setting, we defined in a previous work the graph’s {\em quantum edge correspondence} $E_\mathcal{G}$. In this talk, we will present two results: the Cuntz--Pimsner algebra of the quantum edge correspondence is precisely the {\em local} quantum Cuntz--Krieger algebra for $\mathcal{G}$, i.e., it is a quotient of the (full) quantum Cuntz—Krieger algebra by ``local relations,’’ however, we can construct an example of a quantum graph whose (full) quantum Cuntz--Krieger algebra is not isomorphic to its local counterpart. This example settles an open question raised in the paper which introduced local quantum Cuntz—Krieger algebras.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

5-day workshop participants are welcome to use BIRS facilities (TCPL ) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 11AM.