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Organizers Michael Brannan Matthew Kennedy Jesse Peterson Nico Spronk Kateryna Tatarko Andy Zucker |
| Date | Speaker, Title and Abstract |
|---|---|
| November 26 | Nathan Pagliaroli, University of Waterloo |
| November 19 | Kyle Roy, Kent State University |
| November 12 | Bradd Hart, McMaster University
Ultraproducts and the model theory of operator algebras. W*-probability spaces: a case study Ultraproducts are familiar tools in operator algebras, but they can also guide the model theory of operator algebras. I want to highlight the exploratory role that ultraproducts play in this endeavour. The main example is W*-probability spaces: von Neumann algebras equipped with faithful normal states. I will explain how capturing totally bounded elements yields an axiomatization for this class whose model-theoretic ultraproduct agrees with the Ocneanu ultraproduct. No background in model theory will be assumed. This is joint work with Hiroshi Ando, Jananan Arulseelan, Isaac Goldbring, and Thomas Sinclair. |
| November 5 | Alec Gow, University of Waterloo Property (SP) and Inclusions of C*-algebras A C*-algebra is said to have Property (SP) if each of its hereditary subalgebras contains a nonzero projection. This property is closely related to, though weaker than, the more familiar notion of real rank zero. Motivated by recent work of Gabe and Neagu (2025) on inclusions of real rank zero, we introduce a corresponding notion of Property (SP) for inclusions of C*-algebras and begin its systematic study. Extending classical work of Osaka (2001), we also show that Property (SP) for C*-algebras is preserved under a large class of quantum symmetries. Talk is based on joint work with Roberto Hernández Palomares (arXiv:2608.30057). |
| October 29 | Thomas Bray, University of Waterloo Simplicity of reduced crossed products. Determining when a crossed product is simple is a fundamental question at the intersection of operator algebras and dynamics. Recently, in joint work with Matthew Kennedy, we established a new characterization of simplicity of reduced crossed products of commutative C*-algebras by countable groups, answering a problem of Ozawa. In this talk I will give a tour through some of the motivation and important developments in C*-simplicity and topological dynamics that build up to this characterization, and finish by explaining some of the new ideas that were used in our proof. |
| October 22 | Lucas Hall, University of Haifa The Covariant Stone-von Neumann Theorem for Locally Compact Quantum Groups We analyze representations of locally compact quantum groups over Hilbert modules, which recovers the classical result for the action of the real line on itself. On one hand, for suitable Modules any covariant representation is a multiple of a specified fundamental one; on the other, whenever a covariant representation enjoys the multiplicity property, the spectrum of the double crossed product has only one point. |
| October 15 | No Speaker Reading Week |
| **Tuesday** October 6, MC 5403 | David Jekel, University of Ottawa Optimal transport in the free and quantum settings We discuss several noncommutative generalizations of the classical Wasserstein distance of two probability measures on $\mathbb{R}^d$, or more general metric spaces, which measures the minimal $L^2$ distance of two random variables with the given distributions. The first motivation comes from free probability theory, where ideas from optimal transport theory have been used to show isomorphism of von Neumann algebras and appear in functional inequalities with free entropy, as well as providing a general notion of "perturbing generators" of a von Neumann algebra. The second motivation comes from quantum information theory, where optimal transport theory provides a way to assign distances for states on a von Neumann algebra. As we will see, Duvenhage's version of quadratic Wasserstein distance relates quite closely to the Biane and Voiculescu's free Wasserstein distance. We discuss these distances in a common framework and demonstrate several properties that make the noncommutative setting more challenging, including non-separability of the Wasserstein space, and a stark difference between the Wasserstein and weak-* topologies on certain state spaces. |