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Organizers Michael Brannan Matthew Kennedy Nico Spronk Kateryna Tatarko Andy Zucker |
| Date | Speaker, Title and Abstract |
|---|---|
| February 27 | Pavlos Kalantzopoulos, UC Irvine . |
January 23 | Daniel Gromada, Czech Technical University /b> . |
December 12 | Ryoya Arimoto, Kyoto University Simplicity of crossed products of the actions of totally disconnected locally compact groups on their boundaries Results of Archbold and Spielberg, and Kalantar and Kennedy assert that a discrete group admits a topologically free boundary if and only if the reduced crossed product of continuous functions on its Furstenberg boundary by the group is simple. In this talk, I will show a similar result for totally disconnected locally compact groups. |
November 14 | Astrid an Huef, Victoria University of Wellington Nuclear dimension of $C^*$-algebras of groupoids. Let $G$ be a locally compact, Hausdorff groupoid. Guentner, Willet and Yu defined a notion of dynamic asymptotic dimension (dad) for \'etale groupoids, and used it to find a bound on the nuclear dimension of $C^*$-algebras of principal groupoids with finite dad. To have finite dad, a groupoid must have locally finite isotropy subgroups which rules out, for example, the graph groupoids and twists of \'etale groupoids by trivial circle bundles. I will discuss how the techniques of Guentner, Willett and Yu can be adjusted to include some groupoids with large isotropy subgroups, including an applications to $C*$-algebras of directed graphs that are AF-embeddable. This is joint work with Dana Williams. |
November 13 ***Special Day*** 4:00PM, in MC 4042. ** | Yasuyuki Kawahigashi, University of Tokyo Subfactors, quantum 6j-symbols and alpha-induction Tensor categories have found many applications in physics and mathematics, particularly quantum field theory and condensed matter physics in recent years, as a new type of symmetry generalizing a classical notion of a group. Operator algebras give useful and efficient tools to study tensor categories. A fusion category, a tensor category with certain finiteness condition, is characterized by a finite set of complex numbers satisfying certain compatibility condition, called quantum 6j-symbols. Its variant, called bi-unitary connections, has played an important role in the Jones theory of subfactors in operator algebras. We have a tensor functor called alpha-induction for a braided fusion category, as a quantum version of a classical machinery of an induced representation for a subgroup. We describe alpha-induction in the framework of quantum 6j-symbols from a viewpoint of being of a canonical form. |
October 31 | Camila Sehnem, University of Waterloo A characterization of primality for reduced crossed products In this talk I will discuss ideal structure of reduced crossed products by actions of discrete groups on noncommutative C*-algebras. I will report on joint work with M. Kennedy and L. Kroell, in which we give a characterization of primality for reduced crossed products by arbitrary actions. For a class of groups containing finitely generated groups of polynomial growth, we show that the ideal intersection property together with primality of the action is equivalent to primality of the crossed product. This extends previous results of Geffen and Ursu and of Echterhoff in the setting of minimal actions. |
October 24 | Matthew Wiersma, University of Winnipeg Entropies and Poisson boundaries of random walks on groups with rapid decay Let $G$ be a countable group and $\mu$ a probability measure on $G$. The Avez entropy of $\mu$ provides a way of quantifying the randomness of the random walk on $G$ associated with $\mu$. We build a new framework to compute asymptotic quantities associated with the $\mu$-random walk on $G$, using constructions that arise from harmonic analysis on groups. We introduce the notion of \emph{convolution entropy} and show that, under mild assumptions on $\mu$, it coincides with the Avez entropy of $\mu$ when $G$ has the rapid decay property. Subsequently, we apply our results to stationary dynamical systems consisting of an action of a group with the rapid decay property on a probability space, and give several characterizations for when the Avez entropy coincides with the Furstenberg entropy of the stationary space. This leads to a characterization of Zimmer amenability for stationary dynamical systems whenever the acting group has the property of rapid decay. This talk is based on joint work with B. Anderson-Sackaney, T. de Laat and E. Samei. |
October 17 | Pawel Sarkowicz, University of Waterloo Universal covering groups of unitary groups We will discuss a notion from algebraic topology, that of "universal covering groups", but with the goal of further understanding unitary groups of C*-algebras. In this talk, we give a basic run down of universal covering groups and discuss what they are for unitary groups of von Neumann factors, answering a question of de la Harpe and McDuff regarding the algebraic perfectness of the universal covering group in the II1 case. One of the keys in understanding the II1 setting is being able to utilize the pairing between K_0 and traces, viewing K_0 as loops in the unitary group (up to homotopy) and the pairing as path-integration against a trace. Time permitting, we will discuss some homological implications for unitary groups of general C*-algebras. |
October 10 | Adina Goldberg, University of Waterloo Synchronous Quantum Games We recast nonlocal games using string diagrams, allowing for a natural extension to quantum games (with bipartite question and answer states). We define strategies in this setting and show that synchronous quantum games require synchronized players to win. We give examples of some quantum games on quantum graphs and see that these require quantum homo/isomorphisms to win. (The talk is based on a preprint ``Quantum games and synchronicity'' (https://arxiv.org/abs/2408.15444). This work is inspired by Musto, Reutter, and Verdon's paper ``A compositional approach to quantum functions'', and relies heavily on the reference ``Categories for Quantum Theory'' by Heunen and Vicary for string diagrams in quantum information.) |
October 3 | Matjaž Omladič, University of Ljubljana The Solution to the Loewy-Radwan Conjecture A seminal result of Gerstenhaber gives the maximal dimension of a linear space of nilpotent matrices. It also exhibits the structure of such a space when the maximal dimension is attained. Extensions of this result in the direction of linear spaces of matrices with a bounded number of eigenvalues started 30 years ago in Ljubljana with a joint paper of mine with Peter Šemrl. The problem was proposed in perhaps the most general way by Professor Loewy and his student Radwan 25 years ago- By solving their conjecture in the positive jointly with Klemen Šivic, the problem ends its short but exciting life in Ljubljana again. We give the dimension of a maximal vector space of n×n matrices with no more than k < n eigenvalues. We also exhibit the structure of the spaces for which this dimension is attained. There is a surprising hidden connection of this solution to Waterloo to be revealed in the talk. |
September 26 | August 29 ***MC5403 from 2-3 pm | Mathias Sonnleitner, University of Passau Covering completely symmetric convex bodies A completely symmetric convex body is invariant under reflections or permutations of coordinates. We can bound its metric entropy numbers and consequently its mean width using sparse approximation. We provide an extension to quasi-convex bodies and present an application to unit balls of Lorentz spaces, where we can provide a complete picture of the rich behavior of entropy numbers. These spaces are compatible with sparse approximation and arise from interpolation of Lebesgue sequence spaces, for which a similar result is by now classical. Based on joint work with J. Prochno and J. Vybiral. |
June 3 | Manuel Fernandez, Georgia Tech On the $\ell_0$-Isoperimetry of Measurable Sets Gibbs-sampling, also known as coordinate hit-and-run (CHAR), is a random walk used to sample points uniformly from convex bodies. Its transition rule is simple: Given the current point p, pick a random coordinate i and resample the i'th coordinate of p according to the distribution induced by fixing all other coordinates. Despite its use in practice, strong theoretical guarantees regarding the mixing time of CHAR for sampling from convex bodies were only recently shown in works of Laddha and Vempala, Narayanan and Srivastava, and Narayanam, Rajaraman and Srivastava. In the work of Laddha and Vempala, as part of their proof strategy, the authors introduced the notion of the $\ell_0$ isoperimetric coefficient of a measurable set and provided a lower bound for the quantity in the case of axis-aligned cubes. In this talk we will present some new results regarding the $\ell_0$ isoperimetric coefficient of measurable sets. In particular we pin down the exact order of magnitude of the $\ell_0$ isoperimetric coefficient of axis-aligned cubes and present a general upper bound of the $\ell_0$ isoperimetric coefficient for any measurable set. As an application, we will mention how the results give a moderate improvement in the mixing time of CHAR. |
May 9 ***4:30PM-5:20PM in MC 5417 | Sascha Troscheit, University of Oulu Dynamical Self-similar Covering Sets A classical problem in dynamical systems is known as the shrinking target problem: given a sequence of 'target' subsets A_n \subset X and a dynamic T: X \to X we ask how 'large' the set of all points R \subset X is whose n-th iterate hits the target, T^n (x) \in A_n, infinitely often. Much progress has been made on understanding this type of 'recurrent' set and I will highlight some recent results on this and the related 'dynamical covering problem' which is a dynamical generalisation of the Dvoretzky covering problem. The talk is based on joint results with Balázs Bárány, and Henna Koivusalo and Balázs Bárány. |
May 9 ***3:30PM-4:20PM in MC 5417 | Alex Chirvasitu, University at Buffalo Strange manifolds, small cohomotopy and Baire classes Pr¨ufer surfaces are non-metrizable separable 2-manifolds originally defined by Calabi and Rosenlicht by doubling the upper half-plane along a continuum’s worth of real-line boundary components. The construction and variations on it have since been studied by Gabard, Baillif and many others for the purpose of probing the pathologies of non-paracompact manifolds. The fundamental groups of such surfaces and higher-dimensional cousins are known to be (essentially) free on the sets S of connected boundary components, so their first cohomotopy groups (i.e. sets of homotopy classes of continuous maps to rather than from the circle) are identifiable with maps from S to the integers. Which functions S → Z arise in this manner is a natural question, with (perhaps) a surprising answer. The goal will be to discuss that problem, but the manifolds themselves might provide some entertainment value on their own. |