Activities

The thematic semester will be composed of several activities:
  1. Inaugural Colloquium (13/03/2019).
  2. School I (11-15/03/2019).
  3. Workshop I (18-22/03/2019).
  4. School II (06-10/05/2019).
  5. Workshop II (13-17/05/2019).
  6. International Conference (17/06-21/06/219).
  7. Visitor Program and Running Seminar.

Inaugural Colloquium :

Speaker: Joachim Cuntz, WWU Münster, Germany.
Title: The ring of integers and C*-algebras.
Abstract: Among the most basic structures in mathematics are the sets of natural numbers and of integers with their operations of addition and multiplication. These structures give rise, in a completely natural way, to C*-algebras with intriguing properties. The study of these C*-algebras and in particular of their K-theoretical invariants reveals close connections with algebraic number theory. These connections can be extended, from the usual ring of integers to rings of algebraic integers in number fields.

School I (11-15/03/2019):

The aim of this school is to introduce and develop several topics around the classification of operator algebras and amenability of groups and spaces. The school will be divided into three courses:

  1. Course I: Stefaan Vaes (KU-Leuven, Belgium)
    Title: Type III factors, free Araki-Woods factors and their (non-)classification
    Abstract: The course starts with a basic introduction to von Neumann algebras of type III, the modular theory of Tomita-Takesaki and Connes' classification of amenable factors. I then introduce Shlyakhtenko's free Araki-Woods factors, which are free probability analogs of the injective type III factors. I present Shlyakhtenko's classification of the almost periodic free Araki-Woods factors and the more recent non almost periodic classification results from a joint work with Houdayer and Shlyakhtenko. I will finally show that this also gives rise to unclassifiably many nonisomorphic free Araki-Woods factors (joint work with Sasyk and Törnquist).

  2. Course II: Tullio Ceccherini-Silberstein (U. Sannio, Italy)
    Title: Amenability of groups.
    Abstract: In these lectures, I would like to present the notion of amenability (of discrete groups), introduced in 1929 by John von Neumann in relation to the study of the Banach-Tarski paradox. Since then, the notion of amenability has been extended to other different settings and nowadays plays a fundamental role in Harmonic Analysis, Functional Analysis, and Operator Algebras, in Geometric and Combinatorial Group Theory, in Ergodic Theory and Dynamical Systems, as well as in Probability, Statistical Mechanics, and Mathematical Physics. I'll present some characterizations of amenability (for discrete groups), combining methods from Functional Analysis, Combinatorics & Graph Theory, Probability & Random Walks, Combinatorial and Geometric Group Theory, and Dynamical Systems.Time permitting, I'll also discuss the notion of amenability for discrete metric spaces.

    PROGRAMME:

    1. Definitions, examples, and properties of the class of amenable groups.
    2. The Folner condition
    3. Paradoxical decompositions and the Tarski alternative theorem (including the Rado-Hall marriage theorem for bipartite graphs).
    4. The Markov-Kakutani type theorem for amenable groups.
    5. The Kesten criterion.
    6. The Grigorchuk cogrowth criterion.
    7. The Ornstein-Weiss theorem and applications: entropies.
    8. Cellular automata and the Garden of Eden theorem for amenable groups.
    9. Amenability for discrete metric spaces.
  3. Course III: Hannes Thiel (WWU-Münster, Germany)
    Title: Structure and classification of amenable C*-algebras.
    Abstract: A series of spectacular breakthroughs over the past three years led to the completion of the decades-long effort to classify simple, amenable C*-algebras by K-theory. We will discuss these results and the connections to the regularity conjecture of Toms-Winter on the structure of simple, amenable C*-algebras. We will also study the Cuntz semigroup, which is a geometric refinement of K-theory that has been used to obtain structure and classification results for non-simple C*-algebras.

Workshop I (18-22/03/2019):

Following the first school, the first workshop will treat the operator algebra venue of the semester. Nevertheless, some talks will be dedicated to the quantum information side of the semester. Confirmed talks are still to be announced.

There will be a chance to present a talk in the workshop. However, in order to favour interaction among the participants, the number of talks will be limited.

School II (06-10/05/2019):

In this school we will high-light several important interactions between operator algebras and the theory of quantum information. The school will be divided again into three parts and interactions between these parts will be remarked during the course.

  1. Speaker: Magdalena Musat, U. Copenhagen, Denmark
    Title: Infinite dimensional phenomena in the analysis of quantum information theory.
    Abstract: To be announced.

  2. Speaker: Ion Nechita, U. Toulouse, France
    Title: Applications of random matrices to quantum information theory.
    Abstract: To be announced.

  3. Speaker: Vern Paulsen, U. Waterloo, Canada
    Title: Operator algebras and nonlocal games.
    Abstract: To be announced.

Workshop II (13-17/05/2019):

As with the first school and workshop, this second workshop is to be thought as a follow-up to the second school. Nevertheless, some of the talks held here will belong to the operator algebra half of the semester. Confirmed talks are again still to be announced.

There will be a chance to present a talk in the workshop. However, in order to favour interaction among the participants, the number of talks will be limited.

INVITED SPEAKERS:

  • Ivan Bardet (Université Lyon I)
  • Marius Junge (University of Illinois at Urbana-Champaign)
  • Barbara Kraus (Universität Innsbruck)
  • Ludovico Lami (University of Nottingham)
  • Alexander Müller-Hermes (University of Copenhagen)
  • Ion Nechita (Université Paul Sabatier, Toulouse)
  • Ivan Todorov (Queen’s University Belfast)
  • Ignacio Villanueva (Universidad Complutense de Madrid)
  • Andreas Winter (Universitat Autònoma de Barcelona)