Contributed talk, ASU \(C^*\) Seminar, Tempe
There is a certain class of ordinal graphs whose \(C^*\)-algebras are always Cuntz-Pimsner algebras in a natural way. In these examples, homomorphisms from algebras of distinguished subcategories into the ordinal graph algebra are injective. We will discuss this construction and some of the interesting details of the proof that these algebras are Cuntz-Pimsner algebras.
Lecture, GOALS 2025, Virtual
I lectured on universal \(C^*\)-algebras and graph \(C^*\)-algebras. Here is a recording. I learned from last time not to trust zoom, and I used my own recording software this time.
Lecture, GOALS 2025, Virtual
I lectured on ideals and approximate units in \(C^*\)-algebras for GOALS 2025, which was held virtually. Here is a recording. Unfortunately zoom decided to cover half of the screen with the participants.
Contributed Talk, COSY 2025, Waterloo, Ontario, Canada
We introduce a class of left-cancellative categories which generalizes the category of paths of a directed graph by allowing paths to have ordinal length. We use generators and relations to study the Cuntz-Krieger algebra defined by Spielberg. For each ordinal we construct an associated \(C^*\)-correspondence. Then we apply Eryüzlü and Tomforde’s condition (S) and obtain a Cuntz-Krieger uniqueness theorem for ordinal graphs.
Contributed Lightning Talk, COMPhY 2025, Waterloo, Ontario, Canada
We introduce a class of left-cancellative categories which generalizes the category of paths of a directed graph by allowing paths to have ordinal length. We use generators and relations to study the Cuntz-Krieger algebra defined by Spielberg. For each ordinal we construct an associated \(C^*\)-correspondence. Then we apply Eryüzlü and Tomforde’s condition (S) and obtain a Cuntz-Krieger uniqueness theorem for ordinal graphs.
Invited Talk, MAA Rocky Mountain Section 2025 Meeting, Boulder, Colorado, USA
We introduce a class of left-cancellative categories which generalizes the category of paths of a directed graph by allowing paths to have ordinal length. We use generators and relations to study the Cuntz-Krieger algebra defined by Spielberg. For each ordinal we construct an associated \(C^*\)-correspondence. Then we apply Eryüzlü and Tomforde’s condition (S) and obtain a Cuntz-Krieger uniqueness theorem for ordinal graphs.
Invited Talk, IMPAN North Atlantic Noncommutative Geometry Seminar, Virtual
We introduce a class of left-cancellative categories which generalizes the category of paths of a directed graph by allowing paths to have ordinal length. We use generators and relations to study the Cuntz-Krieger algebra defined by Spielberg. For each ordinal we construct an associated \(C^*\)-correspondence. Then we apply Eryüzlü and Tomforde’s condition (S) and obtain a Cuntz-Krieger uniqueness theorem for ordinal graphs.
Contributed Talk, ASU,Embry-Riddle \(C^*\) Seminar, Tempe, AZ, USA
We introduce a class of left-cancellative categories which generalizes the category of paths of a directed graph by allowing paths to have ordinal length. We use generators and relations to study the Cuntz-Krieger algebra defined by Spielberg. For each ordinal we construct an associated \(C^*\)-correspondence. Then we apply Eryüzlü and Tomforde’s condition (S) and obtain a Cuntz-Krieger uniqueness theorem for ordinal graphs.
Contributed Talk, GOALS seminar, Virtual
We introduce a class of left-cancellative categories which generalizes the category of paths of a directed graph by allowing paths to have ordinal length. We use generators and relations to study the Cuntz-Krieger algebra defined by Spielberg. For each ordinal we construct an associated \(C^*\)-correspondence. Then we apply Eryüzlü and Tomforde’s condition (S) and obtain a Cuntz-Krieger uniqueness theorem for ordinal graphs.
Contributed Talk, ASU,Embry-Riddle \(C^*\) Seminar, Tempe, AZ, USA
We introduce a class of left-cancellative small categories for which there is a Cuntz-Krieger uniqueness theorem. The categories arise naturally as a generalization of directed graphs for which paths are allowed to have lengths which are ordinals. We will describe a collection of \(C^*\)-correspondences which generalize the usual correspondence for a directed graph. Under suitable conditions, these correspondences satisfy condition (S) of Eryüzlü and Tomforde, and we describe how a transfinite induction argument yields the uniqueness theorem.
Contributed Talk, GPOTS 2024, University of Nebraska-Lincoln, Lincoln, NE, USA
Topological quivers are a somewhat natural generalization of topological graphs, where we insist that edge space is additionally endowed with a family of Radon measures, indexed by the vertex space, satisfying some regularity conditions. In this series of talks, we aim to present the needed background material to understand what a topological quiver \(C^*\)-algebra is, as well as discuss some results we hope to generalize from Deaconu, Kumjian and Quigg in the topological graph setting. One of these main results being that a locally compact group acting freely and properly on a topological quiver induces a Morita equivalence between the reduced crossed product of the quiver \(C^*\)-algebra and the \(C^*\)-algebra of the corresponding ‘quotient quiver’.
Contributed Talk, ASU,Embry-Riddle \(C^*\) Seminar, Tempe, AZ, USA
In this talk we introduce Quantum mechanics from first principles. We illustrate how Stone’s theorem and the Stone-von Neumann theorem bridge the gap between the canonical commutation relations for unbounded operators and the Weyl relations for unitary groups. Time permitting, we’ll recast the Stone-von Neumann theorem in terms of \(C^*\) crossed products and discuss how this motivates natural generalizations of the Stone-von Neumann theorem.
Contributed Talk, ASU,Embry-Riddle \(C^*\) Seminar, Tempe, AZ, USA
Topological quivers are a somewhat natural generalization of topological graphs, where we insist that edge space is additionally endowed with a family of Radon measures, indexed by the vertex space, satisfying some regularity conditions. In this series of talks, we aim to present the needed background material to understand what a topological quiver \(C^*\)-algebra is, as well as discuss some results we hope to generalize from Deaconu, Kumjian and Quigg in the topological graph setting. One of these main results being that a locally compact group acting freely and properly on a topological quiver induces a Morita equivalence between the reduced crossed product of the quiver \(C^*\)-algebra and the \(C^*\)-algebra of the corresponding ‘quotient quiver’.