# Schedule for: 19w5073 - Topology and Measure in Dynamics and Operator Algebras

Arriving in Banff, Alberta on Sunday, September 8 and departing Friday September 13, 2019

Sunday, September 8 | |
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16:00 - 17:30 | Check-in begins at 16:00 on Sunday and is open 24 hours (Front Desk - Professional Development Centre) |

17:30 - 19:30 |
Dinner ↓ A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |

20:00 - 22:00 | Informal gathering (Corbett Hall Lounge (CH 2110)) |

Monday, September 9 | |
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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) |

08:45 - 09:00 |
Introduction and Welcome by BIRS Staff ↓ A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions. (TCPL 201) |

09:00 - 09:45 |
Gabor Szabo: The stable uniqueness theorem for equivariant Kasparov theory ↓ It can be argued that the Lin-Dadarlat-Eilers stable uniqueness theorem is one of the main driving forces behind several recent landmark results related to the classification program for nuclear C*-algebras. In a nutshell, the theorem strengthens the Cuntz picture of bivariant K-theory, and translates a KK-theoretic assumption into a rather strong statement involving (stable) asymptotic unitary equivalence of *-homomorphisms, which becomes immensely useful for extracting the role of K-theory in classification. In this talk I will present a generalization of the stable uniqueness theorem to the setting of C*-dynamical systems over a given locally compact group. I will also explain why this should be expected to be important in the context of classifying C*-dynamics up to cocycle conjugacy. This is joint work with James Gabe. (TCPL 201) |

09:45 - 10:15 | Coffee Break (TCPL Foyer) |

10:15 - 11:00 | Karen Strung: Constructions in minimal dynamics and applications to the classification of C*-algebras (TCPL 201) |

11:10 - 11:55 |
José Carrión: Classifying *-homomorphisms ↓ We report on a joint project with J. Gabe, C. Schafhauser,
A. Tikuisis, and S. White that develops a new approach to the
classification of C*-algebras and the *-homomorphisms between
them. (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) |

13:00 - 14:00 |
Guided Tour of The Banff Centre ↓ Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus. (Corbett Hall Lounge (CH 2110)) |

14:00 - 14:15 |
Group Photo ↓ Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo! (TCPL 201) |

14:15 - 15:00 |
Zhuang Niu: Comparison radius and mean dimension ↓ Consider a free and minimal topological dynamical system and the corresponding crossed-product C*-algebra. We show that, under an assumption of Rokhlin property and an assumption of Cuntz comparison of open sets, the radius of comparison of the C*-algebra is at most the half of the mean (topological) dimension of the dynamical system. Moreover, still under these two assumptions, if the mean dimension is zero, then the C*-algebra is Jiang-Su stable or finite dimensional. This includes all free and minimal actions by Z^d and some other systems. (TCPL 201) |

15:00 - 15:30 | Coffee Break (TCPL Foyer) |

15:30 - 16:15 |
Volodymyr Nekrashevych: Dynamical asymptotic dimension and hyperbolic dynamics ↓ A group and the corresponding groupoid of germs are naturally
associated with every locally expanding self-covering of a compact
space (such as, for example, hyperbolic complex rational functions
when restricted to their Julia sets). We will show that the dynamical
asymptotic dimension of this groupoid is equal to the topological
(covering) dimension of the space. (In particular, it is finite.) The
K-theory of the corresponding C*-algebras can be explicitly computed
for the case of complex rational functions. Such groupoids are
particular cases of groupoids naturally associated with a Ruelle-Smale
dynamical system. One can show that in this general case the dynamical
asymptotic dimension is also finite, but a more precise statement is
still a conjecture. (TCPL 201) |

16:25 - 17:10 |
Hanfeng Li: Orbit equivalence and entropy ↓ In general orbit equivalence between free measure-preserving actions of
countably infinite groups on standard probability measure spaces may not
preserve entropy. A few years ago Tim Austin showed that integrable orbit
equivalence between actions of finitely generated amenable groups does
preserve entropy. I will introduce a notion of Shannon orbit equivalence,
weaker than integrable orbit equivalence, and a property SC for actions. The
Shannon orbit equivalence between actions of sofic groups with the property
SC preserve the maximal sofic entropy. If a group G has a w-normal subgroup
H such that H is amenable and not locally virtually cyclic, then every
action of G has the property SC. In particular, if two Bernoulli shifts of
such a sofic group are Shannon orbit equivalent, then they are conjugate.
This is joint work with David Kerr. (TCPL 201) |

17:30 - 19:30 |
Dinner ↓ A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |

Tuesday, September 10 | |
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07:00 - 09:00 | Breakfast (Vistas Dining Room) |

09:00 - 09:45 |
Elizabeth Gillaspy: Moves on higher-rank graphs preserving Morita equivalence ↓ Higher-rank graphs (k-graphs) are a combinatorial model for C*-algebras; indeed, much of the structure of k-graph C*-algebras is encoded in the underlying combinatorial data of the k-graph. However, different k-graphs can give rise to isomorphic or Morita equivalent C*-algebras. In this talk, we present several ways to modify the structure of a k-graph which preserve the Morita equivalence class of the associated C*-algebra. Our constructions are inspired by the analogous work for graph C*-algebras of Bates and Pask, as well as by the textile system approach to describing k-graphs. This is joint work with C. Eckhardt, K. Fieldhouse, D. Gent, I. Gonzales, and D. Pask. (TCPL 201) |

09:45 - 10:15 | Coffee Break (TCPL Foyer) |

10:15 - 11:00 |
Samuel Evington: Complemented partitions of unity and uniform property gamma ↓ I will discuss the new concepts of complemented partitions of unity (CPoU) and uniform property gamma, introduced in joint work with Castillejos, Tikuisis, White and Winter. (TCPL 201) |

11:10 - 11:55 |
Hannes Thiel: Rigidity results for $L^p$-operator algebras ↓ An $L^p$-operator algebra is a Banach algebra that admits an isometric representation on some $L^p$-space ($p$ not 2). Given such an algebra $A$, we show that it contains a unique maximal sub-C*-algebra, which we call its C*-core. The C*-core is automatically abelian, and its spectrum is naturally equipped with an inverse semigroup of partial homeomorphisms. We call the associated groupoid of germs the Weyl groupoid of $A$. (TCPL 201) |

11:30 - 13:30 | Lunch (Vistas Dining Room) |

14:00 - 14:45 | Yuhei Suzuki: Non-amenable tight squeezes by Kirchberg algebras (TCPL 201) |

14:45 - 15:15 | Coffee Break (TCPL Foyer) |

15:15 - 16:00 | Matthew Kennedy: Noncommutative Choquet theory and a C*-dynamical characterization of Kazhdan’s property (T) (TCPL 201) |

16:10 - 16:55 |
Mehrdad Kalantar: Representation rigidity of subgroups and ideal structure of C*-algebras of quasi-regular representations ↓ We introduce several equivalence relations on the set of subgroups of a countable group G, defined in terms of the quasi-regular representations, and present some rigidity results in terms of those equivalence relations for certain classes of subgroups. Furthermore, we give some results concerning the ideal structure of the C*-algebras generated by the quasi-regular representations. This is joint work with Bachir Bekka. (TCPL 201) |

17:30 - 19:30 | Dinner (Vistas Dining Room) |

Wednesday, September 11 | |
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07:00 - 09:00 | Breakfast (Vistas Dining Room) |

09:00 - 09:45 | Wilhelm Winter: Nuclear dimension of sub-C*-algebras (TCPL 201) |

09:45 - 10:15 | Coffee Break (TCPL Foyer) |

10:15 - 11:00 | Huaxin Lin: Simple stably projectionless C*-algebras and their invariant (TCPL 201) |

11:10 - 11:55 | Kristin Courtney: Amalgamated products of RFD C*-algebras (TCPL 201) |

11:30 - 13:30 | Lunch (Vistas Dining Room) |

13:30 - 17:30 | Free Afternoon (Banff National Park) |

17:30 - 19:30 | Dinner (Vistas Dining Room) |

Thursday, September 12 | |
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07:00 - 09:00 | Breakfast (Vistas Dining Room) |

09:00 - 09:45 |
Stuart White: Nuclear dimension and $O_\infty$-stability ↓ I’ll discuss developments in computing nuclear dimension in the presence of enough $O_\infty$ stability. (TCPL 201) |

09:45 - 10:15 | Coffee Break (TCPL Foyer) |

10:15 - 11:00 | James Gabe: Classification: purely infinite and stably finite (TCPL 201) |

11:10 - 11:55 |
Jorge Castillejos: Applications of uniform property $\Gamma$ and CPoU ↓ I will discuss applications of complemented partitions of unity and uniform property $\Gamma$ in the Toms-Winter conjecture and the structure theory of uniform tracial completions. (TCPL 201) |

11:30 - 13:30 | Lunch (Vistas Dining Room) |

14:00 - 14:45 | Ilijas Farah: Another look at ultrapowers (TCPL 201) |

14:45 - 15:15 | Coffee Break (TCPL Foyer) |

15:15 - 16:00 |
Charles Starling: Simplicity of algebras associated to non-Hausdorff groupoids ↓ We give conditions on a potentially non-Hausdorff étale groupoid which guarantee that its associated C*-algebra is simple. As a key source of examples, work of Nekrashevych and Exel-Pardo describes a class of C*-algebras arising from the action of a group on a finite alphabet (or more generally, a finite graph). The above authors described these as groupoid C*-algebras and gave conditions which guaranteed their simplicity, usually starting from assumptions which imply the groupoid is Hausdorff. These groupoids need not be Hausdorff, notably for the self-similar action associated to the Grigorchuk group, so it was an open question whether the C*-algebra of the Grigorchuk group action was simple or not. We answer this question in the affirmative. We also discuss simplicity criteria for the associated Steinberg algebras. (TCPL 201) |

17:30 - 19:30 | Dinner (Vistas Dining Room) |

Friday, September 13 | |
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07:00 - 09:00 | Breakfast (Vistas Dining Room) |

09:00 - 09:45 | Rufus Willett: Representation stability and index theory (TCPL 201) |

09:45 - 10:15 | Coffee Break (TCPL Foyer) |

10:15 - 11:00 |
Hung-Chang Liao: Small boundary property, uniform property Gamma, and almost finiteness ↓ The small boundary property for topological dynamical systems was introduced
by Lindenstrauss to construct small entropy factors. A recent work of Kerr
and Szabo showed that this dynamical property is closely related to uniform
property Gamma of the crossed product, hence plays an important role in
classification of crossed products. In this talk we discuss how to
strengthen the connection by considering a relative version of uniform
property Gamma. This is a joint work with Aaron Tikuisis. (TCPL 201) |

11:30 - 12:00 |
Checkout by Noon ↓ 5-day workshop participants are welcome to use BIRS facilities (BIRS Coffee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 12 noon. (Front Desk - Professional Development Centre) |

12:00 - 13:30 | Lunch from 11:30 to 13:30 (Vistas Dining Room) |