Schedule and practical information

Søren Eilers

Title: The classification problem for Cuntz-Krieger algebras

Abstract:

The classification problem for Cuntz-Krieger algebras has a long and prominent history. Indeed, Rørdam’s classification in 1995 of the simple such C*-algebras by appealing to results in symbolic dynamics paved the way for the sweeping generalization by Kirchberg and Phillips to all simple, nuclear, separable and purely infinite C*-algebras, and Restorff’s generalization in 2006 to the case of Cuntz-Krieger algebras with finitely many ideals (equivalently, of real rank zero) was a key inspiration for the recent surge in results concerning nonsimple purely infinite C*-algebras.

I will explain how recent progress on the understanding of this problem - arising from the ambition to generalize Restorff's result to all unital graph C*-algebras - leads to a complete classification of the entire class of Cuntz-Krieger algebras. This is joint work with Restorff, Ruiz and Sørensen.

Adam P. Wie Sørensen

Title: The Cuntz splice

Abstract:

In the classification program for graph C*-algebras the Cuntz splice plays a special role. It is a way to transform a graph the clearly doesn't change the K-theory of the graph C*-algebra, but it is hard to see if it preserves the isomorphism class of the graph C*-algebra. We will discuss how the Cuntz splice came about, when we can Cuntz splice and why writing down a concrete isomorphism is hard.

We will touch on joint work with Eilers-Restorff-Ruiz and Johansen.

Franz Luef

Title: From noncommutative geometry to signal analysis

Abstract: The talk discusses some aspects of the connection between noncommutative geometry and signal analysis. In particular, the interpretation of vector bundles over noncommutative tori in terms of frames for Hilbert spaces.

Sara Malacarne

Title: Woronowicz's Tannaka-Krein duality and free orthogonal quantum groups

Abstract:

Given a finite dimensional Hilbert space $H$ and a collection of operators between its tensor powers satisfying certain properties, we give a category-free proof of the existence of a compact quantum group $G$ with a fundamental representation $U$ on $H$ such that the intertwiners between the tensor powers of~$U$ coincide with the given collection of operators. We then explain how the general version of Woronowicz's Tannaka-Krein duality can be deduced from this.

Marco Matassa

Title: Commutation relations for quantum root vectors of cominuscole parabolics

Abstract:

In this talk I will discuss a result on the structure of certain quantized algebras coming from Lie theory, which are of interest in non-commutative geometry. The result is that for two quantum root vectors, belonging respectively to the quantized nilradical and the quantized opposite nilradical, their commutator belongs to the quantized Levi factor. This generalizes the classical result for Lie algebras. Recall that quantum root vectors depend on the choice of reduced decomposition of the longest word of the Weyl group. I will show that this result does not hold for all such choices.

Antoine Julien

Title: Flow equivalence for higher dimensional subshifts

Abstract:

I will present some results obtained in collaboration with Lorenzo Sadun. We could relate orbit equivalences between minimal, aperiodic tiling spaces to the theory of tiling deformations, and provide a cohomological picture of such orbit equivalences modulo conjugacy. In the symbolic setting, such orbit equivalences between tiling spaces correspond to flow equivalences between subshifts. These results can be seen as an extension to higher dimensions of a theorem of Parry and Sullivan.

Eduard Ortega

Title: Continuous orbit equivalence of reducible subshifts.

Abstract:

There exist several notions of equivalence of shifts of finite type. Those notions can be reflected in the operator algebras world in terms of isomorphism classes of the Cuntz-Krieger algebras. There are many positive results when the subshifts are irreducible, but few is known in the general case. We will explore the world of reducible subshifts, and explain recent results about connections between the different equivalence relations. This is a joint work with Carlsen, Eilers and Restorff

Bass Jordans

Title: Convergence to the boundary for random walks on discrete quantum groups.

Abstract:

For classical random walks there exist two boundaries: the Poisson boundary and the Martin boundary. The relation between these two boundaries is described by the so-called "convergence to the boundary". For random walks on discrete quantum groups both the Poisson boundary and Martin boundary are defined and a non-commutative analogue of convergence to the boundary can be formulated. However, no proof is known for a such a theorem. In this talk we will discuss both the classical and quantum version of convergence to the boundary, explain how these are related and we consider the case of SUq(2).

Magnus Landstad

Title: An exotic problem.

Abstract: Given a locally compact group G, I will start with a description of interesting C*-algebras between the full group algebra C*(G) and the reduced group algebra C*_r(G). They are related to subalgebras or ideals in the dual space B(G) of C*(G). The problem I am going to study is whether span{E\cap P(G)}=E when E is a G-invariant subspace of B(G) and P(G)= all positive definite functions in B(G). (Joint work with Steve Kaliszewski and John Quigg)

Erik Bakken

Title: Convergence of Random Walks and Finite Approximation in a non-Archimedean Setting.

Abstract: In 1987 Volovich introduced $p$-adic physics. In this talk I will present how stochastic methods can be used to approximate the spectrum of certain quantum Hamiltonians over the $p$-adics. This is based on joint work with T. Digernes and D. Weisbart.

Tron Ormland

Title: C*-algebras arising from integral dynamics.

Abstract: We investigate certain C*-algebras arising from sets of mutually relatively prime natural numbers. In particular, since these are always UCT Kirchberg algebras, our main goal is describe the K-theory.

This is joint work with Selcuk Barlak (Münster/Odense) and Nicolai Stammeier (Münster/Oslo).