# Masterclass on Classification, STructure, Amenability and Regularity

The masterclass will run from Monday 25 August to Friday 29 August in room 515 of the mathematics building. It aims to provide an overview of the current status of classification programme, and introduce participants to key techniques at the heart of current research in this area.

Minicourses will be given by

Nate Brown (Structure of simple nuclear C*-algebras)

Marius Dadarlat (Classification results for simple nuclear tracially AF algebras)

Mikael Rørdam (The central sequence algebra and it's applications)

with an introductory lecture by

Wilhelm Winter.

A list of participants can be found here.

## Minicourses

Nate Brown (Structure of simple nuclear C*-algebras)

Over the last decade our understanding of simple nuclear C*-algebras has advanced enormously. From Kirchberg's third approximation theorem to nuclear dimension (in the sense of Winter and Zacharias) to the classification of wide classes of important examples, the results are deep and the pace has been fast and furious. In these lectures we will discuss some of the highlights and prospects for the future.

Marius Dadarlat (Classification results for simple nuclear tracially AF algebras)

We will give an introduction to the classification of simple separable
nuclear tracially AF algebras satisfying the UCT due to Huaxin Lin and
will discuss the K-theory techniques that are needed for this result.

As a prelude to this course Christian Voigt will give two background lectures on KK-theory.

Mikael Rørdam (The central sequence algebra and its applications)

The central sequence algebra has extensive applications in the theory of C*-algebras, and in particular within the classification programme. Roughly speaking, the central sequence algebra allows one to translate and approximate identity in the original C*-algebra into an exact identity in the central sequence algebra. The recent progress of Matui and Sato has carried the use of the central sequence algebra to a higher level. These developments, as well as the basic theory of the central sequence algebra, will be the topic of my lecture series. I will attempt to cover the following:

- Definitions and elementary properties of the central sequence algebra;

approximate divisibility; - absorption of strongly self-absorbing C*-algebras
- traces and ideals of the central sequence algebras; von Neumann quotients;
- property SI by Matui and Sato;
- applications to the Toms-Winter conjecture;

divisibility properties of the central sequence algebras; - properties of C*-algebras whose central sequence algebra has no characters

## Schedule

A pdf of the schedule is here. Abstracts and titles here.

**Mon 25 Aug**

9:00 Registration and coffee (Maths common room)

10:00 Introductory lecture: Winter (Maths 515)

10:50 Coffee (Maths common room)

11:20 Background session (maths 515)

12:20 Lunch (QM Union)

14:00 Voigt 1 (Maths 515)

14:50 Coffee (Maths common room)

15:30 Rørdam 1 (Maths 515)

16:30 Dickson (Maths 515)

16:55 Vignati

17:30 Pizza and Beer (Maths Common Room)

**Tues 26 Aug**

10:00 Voigt 2 (Maths 515)

10:50 Coffee (Maths common room)

11:20 Dadarlat 1 (Maths 515)

12:20 Lunch (QM Union)

14:00 Rørdam 2 (Maths 515)

14:50 Coffee (Maths common room)

15:30 Brown 1 (Maths 515)

16:30 Stammeier (Maths 515)

16:55 Kwasniewski (Maths 515)

**Wed 27 Aug**

10:00 Dadarlat 2 (Maths 515)

10:50 Coffee (Maths common room)

11:20 Rørdam 3 (Maths 515)

12:20 Lunch (QM Union)

**Thurs 28 Aug**

10:00 Dadarlat 3 (Maths 515)

10:50 Coffee (Maths common room)

11:20 Brown 2 (Maths 515)

12:20 Lunch (QM Union)

14:00 Rørdam 4 (Maths 515)

14:50 Coffee (Maths common room)

15:30 Barlak (Maths 515)

15:55 Wu (Maths 515)

16:30 Gabe (Maths 515)

16:55 Viola (Maths 515)

19:30 Masterclass Banquet

**Fri 29 Aug**

10:00 Rørdam 5 (Maths 515)

10:50 Coffee (Maths common room)

11:20 Brown 3 (Maths 515)

12:20 Lunch (QM Union)

14:00 Ando (Maths 515)

14:25 Castillejos (Maths 515)

14:50 Coffee (Maths common room)

15:30 Tornetta (Maths 515)

15:55 Gogic (Maths 515)