Thursday, September 26 |
07:00 - 08:45 |
Breakfast ↓ Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
09:00 - 09:50 |
Denis Osin: Classifying group actions on hyperbolic spaces ↓ Studying groups via their actions on Gromov hyperbolic spaces has been a recurrent theme in geometric group theory over the past three decades. Of particular interest in this approach are actions of general type, i.e., non-elementary actions without fixed points at infinity. For a given group G, it is natural to ask whether it is possible to classify all general type actions of G on hyperbolic spaces. In a joint paper with K. Oyakawa, we propose a formalization of this question based on the complexity theory of Borel equivalence relations. Our main result is the following dichotomy: for every countable group G, general type actions of G on hyperbolic spaces can either be classified by an explicit invariant ranging in the infinite-dimensional projective space or are unclassifiable by countable structures. Special linear groups over countable fields provide examples satisfying the former alternative, while every non-elementary hyperbolic group satisfies the latter. (TCPL 201) |
10:00 - 10:30 |
Coffee Break (TCPL Foyer) |
10:30 - 11:20 |
Shirly Geffen: Essential freeness, allostery, and classifiability of crossed product C*-algebras. ↓ We will explore the notion of almost finiteness, as introduced by Kerr, in the setting of essentially free actions. This notion is one of the main tools in establishing classifiability of crossed product C*-algebras of actions of countable amenable groups on compact, metrizable spaces. Very recently, Joseph produced the first examples of minimal actions of amenable groups which are topologically free and not essentially free. While our general machinery does not give any information for his examples, as those are not almost finite,we develop ad-hoc methods to show that his actions have classifiable crossed products. This is joint work with Eusebio Gardella, Rafaela Gesing, Grigoris Kopsacheilis, and Petr Naryshkin. (TCPL 201) |
11:30 - 13:00 |
Lunch ↓ Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
13:30 - 14:20 |
Karen Strung: C*-algebras associated to homeomorphisms and vector bundles ↓ Let X be an infinite compact metric space and \alpha : X \to X a homeomorphism. A classic construction in C*-algebras gives us the crossed product of C(X) by the integers. Adding in additional data allows us to construct more C*-algebras: Given a closed subspace Y \subset X, we can construct a so-called orbit-breaking groupoid and its groupoid C*-algebra. Given a vector bundle V over X, we can construct a C*-correspondence and its Cuntz–Pimnser algebra, and if we include both Y and V, we can build an orbit-breaking C*-correspondence and its Cuntz–Pimsner algebra. In the case the V is a line bundle, these Cuntz–Pimnser algebras can be viewed as twisted groupoid C*-algebras over the transformation groupoid and orbit-breaking groupoid, respectively. In this talk I will discuss the relationship between these C*-algebras. In particular I will talk about properties––such as simplicity, Jiang–Su stability and stable rank—are shared by all four, and how they differ. This is based on ongoing joint works with Forough and Jeong. (TCPL 201) |
14:30 - 14:35 |
Emilie Elkiær: Rigidity for groups and algebras acting on Banach spaces ↓ Property (TE) is a rigidity property concerning how a group may act on Banach spaces belonging to a class, E. I will define Property (TE), a weaker relative of it, and their generalization to Banach algebras, and give an overview of how these notions of rigidity are related. (TCPL 201) |
14:35 - 14:40 |
David Gao: Constructing II_1 factors with one unitary conjugacy orbits and certain properties of these factors. ↓ We will construct (nonseparable) II_1 factors with the property that all their Haar unitaries are conjugated to each other by unitaries, and which are not the classical examples of ultraproduct II_1 factors. These factors may be assumed to have certain additional properties, for example being existentially closed. We will observe some consequences of this unique unitary conjugacy orbit property, some of which follow from earlier works of Popa. A new observation that these factors cannot be group algebras of groups with a certain conjugation property on group elements will also be made. This is joint work with Srivatsav Kunnawalkam Elayavalli, Gregory Patchell, and Hui Tan. (TCPL 201) |
14:40 - 14:45 |
Ryoya Arimoto: 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. (TCPL 201) |
14:45 - 14:50 |
Juan Felipe Ariza Mejia: Rigidity for W^*-McDuff groups ↓ In the past two decades there has been major progress in producing W^*-superrigid groups (groups G that can be completely recovered from the group von Neumann algebra \mathcal{L}(G)). On the other hand, there are many classes of groups that were already known to not be W^*-superrigid. In particular, if \mathcal{L}(G) is a McDuff factor, then G cannot be W^*-superrigid as \mathcal{L}(G) \cong \mathcal{L}(G\times A) for any icc amenable group A. In our work, we introduce the first examples of groups whose lack of W^*-superrigidity can be completely characterized. Specifically, we introduce the notion of, and construct, groups that are McDuff W^*-superrigid, that is groups G such that if \mathcal{L}(G) = \mathcal{L}(H) (for an arbitrary group H), then we must have H = G \times A for some icc amenable group A. We do this by combining geometric group theory methods to construct wreath-like product groups with a 2-cocycle with uniformly bounded support, and deformation/rigidity methods (via the interplay of two types of deformations) to prove these groups possess the infinite product rigidity property. This is ongoing work with Ionu\c{t} Chifan, Denis Osin and Bin Sun. (TCPL 201) |
14:50 - 14:55 |
Alon Dogon: Relating Hilbert--Schmidt stability and character rigidity of lattices in products. ↓ We will present some ideas from an ongoing joint work with Itamar Vigdorovich. These arise in an attempt to find new spectral gap properties of higher rank lattices without property (T) in order to complete the missing "property (T) half" of character rigidity. Somewhat surprisingly, we show that character rigidity is equivalent to a weak form of Hilbert--Schmidt stability for such groups. (TCPL 201) |
14:55 - 15:00 |
Koichi Oyakawa: Geometry and dynamics of the extension graph of graph product of groups ↓ In this talk, I will introduce a graph for graph product of groups, which I call the extension graph. This new object enables us to exploit the geometry of a defining graph to study properties of graph product of groups beyond the case of finite defining graphs. As an application in operator algebras, I present strong solidity and relative bi-exactness of graph product of finite groups whose defining graph is hyperbolic. (TCPL 201) |
15:00 - 15:30 |
Coffee Break (TCPL Foyer) |
15:30 - 16:20 |
Yuhei Suzuki: Crossed product splitting of intermediate operator algebras via 2-cocycles ↓ We give a new complete description theorem of the intermediate operator algebras, which unifies the discrete Galois correspondence results and the crossed product splitting results, and involves 2-cocycles. As an application, we obtain a Galois’s type result for Bisch--Haagerup type inclusions arising from isometrically shift-absorbing actions of compact-by-discrete groups. Based on my preprint arxiv:2406.00304 (TCPL 201) |
16:30 - 17:20 |
William Slofstra: Positivity is undecidable in products of free algebras ↓ For free *-algebras, free group algebras, and related algebras, it is possible to decide if an element is positive (in all representations) using results of Helton, Bakonyi-Timotin, Helton-McCullough, and others. In this talk, I'll discuss joint work with Arthur Mehta and Yuming Zhao showing that this problem becomes undecidable for tensor products of this algebras. I'll also discuss how results of this type could be aided by having a Higman embedding theorem for algebras with states, as well as work in progress on this question. (TCPL 201) |
17:30 - 19:30 |
Dinner ↓ A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building. (Vistas Dining Room) |