It is a great pleasure to announce the 9th Workshop on Operator Algebras and Their Applications in the Institute for Research in Fundamental Sciences (IPM). The lectures are delivered via 'zoom' and we encourage the participants to download the app in advance. The event is also posted on:
- https://www.ams.org/meetings/calendar/mathcal

No formal registration is needed, and to be added to the mailing list you may send your name and affiliation to Massoud Amini (mamini@ipm.ir).

#### Organizers:

• Massoud Amini (Tarbiat Modares University and IPM)
• Mehrdad Kalantar (University of Houston)

#### Local Organizers:

• Nasser Golestani (Tarbiat Modares University and IPM)

#### Joining info:

The lectures are delivered via 'zoom' and the link and password to enter the sessions are sent to participants by email. We encourage the participants to download the app in advance.

#### 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
• January 2020: Dynamical Systems, Ergodic Theory, and Operator Algebras
• September-October 2020: The First WSU-IPM Joint Workshop on Operator Algebras
• February 2021: the 8th Workshop on Operator Algebras and their Applications
• # Workshop (February 7-9, 2022)

## Invited Speakers

Abstract:
The notion of amenability of a locally compact group was generalized to certain operator algebraic settings by Anantharaman-Delaroche in the late 70s. We will review the history and triumphs of amenability in W*- and C*-dynamical systems, and then describe recent progress in the understanding of the various competing notions of amenability from the work of Buss/Echterhoff/Willett, Ozawa/Suzuki, and our joint work with Jason Crann.

Abstract:
I will discuss a way to study von Neumann algebras via quantifying ''how many'' finite-dimensional approximations they have. This line of study goes back in the 90's with work of Voiculescu, who used it to solve many long-standing open problems. My first lecture will start with a brief overview of this area of operator algebras. I will then transition to some recent developments, highlighting connections to random matrices as well as group theory.

Abstract:
Abstract of the 1st lecture:
Recently, Davidson and I introduced a new framework for noncommutative convexity and noncommutative function theory, along with a corresponding noncommutative Choquet theory that generalizes much of classical Choquet theory. A key point is that the category of compact noncommutative sets is dual to the category of operator systems. In recent work with Kim and Manor, we extended this duality to the category of (potentially) non-unital operator systems in the sense of Werner and Connes-van Suijlekom. I will motivate and discuss these developments, as well as some applications to C*-algebras and noncommutative dynamics.

Abstract of the 2nd lecture:
I will discuss new descriptions of some universal flows associated to a discrete group, obtained using what we view as a kind of ''topological Furstenberg correspondence.''The descriptions are algebraic and relatively concrete, involving subsets of the group satisfying a higher order notion of syndeticity. We utilize them to establish new necessary and sufficient conditions for strong amenability and amenability. Throughout, I will discuss connections to operator algebras. This is joint work with Sven Raum and Guy Salomon.

Abstract:
We will present applications of boundary actions to the investigation of the ideal and tracial structure of C*-algebras generated by unitary representations. In particular, for quasi-regular representations associated to stabilizers of boundary actions we have a complete understanding of the trace space of such C*-algebras and when they are simple. We will also present some examples coming from Thompson's groups and topological full groups which do not fit yet in the general theory.

Abstract:
We define an invariant for an inclusion of operator systems based on Pimsner and Popa's formulation for the Jones index of a subfactor. We will discuss how this index is connected with certain invariants studied in quantum information theory. This is joint work with Roy Araiza and Colton Griffin.

Abstract:
A well-popularized problem in C*-algebra theory is the classification of C*-algebras up to isomorphism. Through an intertwining argument, this is generally achieved through understanding and classifying *-homomorphisms between C*-algebras - a problem that is also natural in its own right. In joint work with J. Carrión, J. Gabe, C. Schafhauser, and S. White, we have classified *-homomorphisms using minimal (and abstract) hypotheses on the domain A and codomain B: A can be any separable exact C*-algebra satisfying the UCT, and B can be any separably Z-stable C*-algebra with compact tracial state space and strict comparison with strict comparison with respect to traces. I will discuss this result in the context of classification of C*-algebras, and some of the key ideas in our approach.

## Workshop Schedule

The pdf file of the schedule of the talks is available here.

## Abstracts of the Workshop

You can see the abstracts of the workshop here.

## List of Participants

The list of participants is avaiable here.

## Mini-Course

A series mini-course for supporting the workshop will be held on February 5 and 6, 2022 (Bahman 16 and 17, 1400)
Lectures are in English and international participants are welcome to join.

## Speakers

• Jorge Castillejos (Instituto de Ciencias Matemáticas, Madrid)
• Alexander Frei (University of Copenhagen)
• Nasser Golestani (Tarbiat Modares University and IPM)
• Zahra Naghavi (IPM)
• Mohammad Shavandi (Tarbiat Modares University)
• Carlos Vargas (Guanajuato)

## Mini-course Schedule

You can see the program of the mini-course here.

## Abstracts (Mini-course)

You can see the abstracts of the lectures in the mini-course here.

## Registration

No formal registration is needed, and to be added to the mailing list you may send your name and affiliation to Massoud Amini via mamini@ipm.ir.

### IPMInstitute for Research in Fundamental Sciences

Niavaran

P.O. Box 19395-5746, Tehran - Iran

• Tel: +98 21 222 90 928, Fax: +98 21 222 90 648
• mamini@ipm.ir
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