We are pleased to announce that the 7th annual workshop on Operator Algebras and their Applications will be held at the School of Mathematics of Institute for Research in Fundamental Sciences (IPM) on January 6-9, 2020. These workshops intend to bring home new advances in modern analysis and give graduate students and young researchers an opportunity to meet well-known researchers in the field of operator algebras. This year, the workshop will focus on recent developments on Dynamical Systems, Ergodic Theory, and Operator Algebras. It will consist lectures, invited talks and a limited number of contributed talks. As in the previous years, there will be a 1-day pre-workshop mini courses delivered by local speakers which is aiming for students or non-experts.
We look forward to welcoming you in Tehran and meeting you at IPM.

#### Organizers

• Massoud Amini (IPM and Tarbiat Modares University, Iran)
• Mehrdad Kalantar (University of Houston, USA)
• Fatemeh Khosravi (IPM, Iran)

• #### Important Dates

Registration and accommodation request: December 7, 2019 (Azar 16, 1398)
To pay registration and accommodation fees: December 14, 2019 (Azar 23, 1398)

#### Previous workshops

• January 2014: Quantum Groups and Harmonic Analysis
• January 2015: Actions and Crossed Products
• January 2016: $\text{C}^*$-Dynamics
• December 2016: Classification of $\text{C}^*$-algebras
• January 2017: Approximation Properties,
• February 2018: Coarse Geometry
• January 2019: Quantum Groups

• # Program

## Invited Speakers

Abstract: TBA
Abstract: One of the definitions of property (T) is that a group G has (T) if every unitary representation of G that weakly contains the trivial representation actually contains it strongly. This automatically generalizes into two different directions: One is a quantitative version of that statement saying that almost invariant vectors are close to invariant vectors. The second is the Wang's theorem which allows us to substitute any finite-dimensional irreducible representation for the trivial representation from the original definition. We unify these two generalizations by proving a quantitative version of the Wang's theorem. We provide several applications of that result. One of them concerns description of 'generic unitary representations', i.e. unitary representations whose unitary equivalence class is generic in the sense of Baire category. This is based on joint work with Maciej Malicki and Alain Valette.
Abstract: Strongly self-absorbing C*-algebras are playing a central role in the classification program of C*-algebras. Recently, studying strongly self-absorbing dynamical systems has been initiated by Gabor Szabo. It is tempting to generalize the results concerning strongly self-absorbing C*-algebras to a dynamical set up. In this direction, we study equivariant C(X)-algebras whose all fibers absorb some strongly self-absorbing dynamical system. We generalize a result by Hirshberg, Rordam and Winter on C(X)-algebras whose all fibers absorb some fixed strongly self-absorbing C*-algebras. In this talk, I will discuss some technical difficulties in generalizing the results on strongly self-absorbing C*-algebras to the dynamical systems setting; in particular, in our work on equivariant C(X)-algebras. This is joint work with Eusebio Gardella and Klaus Thomsen.
Abstract: Tracial $\mathcal{Z}$-absorption was defined by Hirshberg and Orovitz in 2013 to be a local version of $\mathcal{Z}$-absorption. The two notions are not equivalent in general, but coincide for simple, unital, separable, nuclear algebras. We give a distinguishing example which is purely infinite. A stably finite example was given by Niu and Wang. We define a suitable notion of tracial $\mathcal{Z}$-absorption for simple nonunital C*-algebras and we prove its permanence properties. We study integer actions and finite group actions with the weak tracial Rokhlin property on these algebras. Then we obtain crossed productswhich are simple and tracially $\mathcal{Z}$-absorbing. The talk is based on a joint work with M. Amini, S. Jamali, and N. C. Phillips.
Abstract: TBA
Abstract: Multipliers of a discrete group can be used to characterise approximation properties of the associated reduced group C*-algebra. These techniques have proved influential in the theory of approximation properties of C*-algebras: they have shed new light on some C*-algebra properties and motivated the introduction and study of others. I will begin by introducing multipliers defined on a group, and describe how they can be used to characterise approximation properties of the reduced group C*-algebra. I will then discuss some of the difficulties one encounters in trying to describe approximation properties of the reduced crossed product C*-algebra associated to a group action. To get around these difficulties I will introduce multipliers of group actions, which generalize multipliers of groups, and explain how these allow us to characterise approximation properties of reduced crossed products, as well as give new proofs of existing results on such properties.
Abstract: TBA
Abstract: Let $\Gamma$ be a countable discrete group. A $\Gamma$-boundary in the sense of Furstenberg is a minimal strongly proximal $\Gamma$-space. In 2014 Kalantar and Kennedy proved that the spectrum of $\Gamma$-injective envelope of complex numbers $\mathrm{I}_{\Gamma}(\mathbb{C})$, is identified with the universal $\Gamma$-boundary. Generalizing this, we show that the spectrum of $\mathrm{I}_{\Gamma}(C(X))$ when $X$ is a minimal $\Gamma$-space, is the universal minimal strongly proximal extension of $X$ in the sense of Glasner. This helps us to characterize the notion of $(\Gamma, X)$-boundary when $X$ is minimal and finite. As an application, we answer a problem of Hadwin and Paulsen in negative and find necessary and sufficient conditions for the corresponding reduced crossed product to be exact.
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# Registration

To register for the workshop, please fill out the Registration Form.

#### Registration fee for the workshop:

1) Registration fee for Iranian participants:

2) Registration fees for international participants:
The registration fee is 250 Euro for faculties and postdocs and 150 Euro for students. The registration fee for international participants will be due in cash at the time of registration on the first day of the meeting. Please note that standard credit cards; e.g., Visa, Master or AmEXP, cannot be used in Iran.

Registration fee includes: Participation in the workshop, documentation package, lunches and coffee breaks during the meeting.

Residence fee at IPM guest house is 40 Euro per night.