|
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 12 | Bradd Hart, McMaster University
|
| November 5 | Alec Gow, University of Waterloo |
| October 29 | Thomas Bray, University of Waterloo |
| 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. |