Visiting addressNiels Henrik Abels hus Moltke Moes vei 35 (map)
Supported by the Foundation for Danish-Norwegian cooperation.
Christian Voigt (Glasgow) will give a talk with title: The structure of quantum permutation groups
Abstract: Quantum permutation groups, introduced by Wang, are a quantum analogue of permutation groups. These quantum groups have a surprisingly rich structure, and they appear naturally in a variety of contexts, including combinatorics, operator algebras, and free probability. In this talk I will give an introduction to these quantum groups, and review some results on their structure. I will then present a computation of the K-groups of the C*-algebras associated with quantum permutation groups, relying on methods from the Baum-Connes conjecture.
Alfons van Daele, University of Leuven (Belgium), will give a talk with title: Separability idempotents and quantum groupoids
Martijn Caspers (Münster) will give a talk with title: The Haagerup property for arbitrary von Neumann algebras
Abstract: The Haagerup property is an approximation property for both groups and operator algebras that has important applications in for example the Baum-Connes conjecture or von Neumann algebra theory. In this talk we show that the Haagerup property is an intrinsic invariant of an arbitrary von Neumann algebra. We also discuss stability properties of the Haagerup property under constructions as free products, graph products and crossed products. Finally we discuss alternative characterizations in terms of the existence of suitable quadratic forms.
Marco Matassa (UiO) will give a talk with title: Dirac Operators on Quantum Flag Manifolds
Abstract: I will review the paper "Dirac Operators on Quantum Flag Manifolds" by Ulrich Krähmer. The aim is to define Dirac operators on quantized irreducible flag manifolds. These will yield Hilbert space realizations of some distinguished covariant first-order differential calculi.
Adam Sørensen (UiO) will give a talk with title: Almost commuting matrices
Abstract: Two matrices A,B are said to almost commute if AB is close to BA (in a suitable norm). A question of Halmos, answered by Lin, asks if two almost commuting self-adjoint matrices are always close to two exactly commuting self-adjoint matrices. We will survey what is known about this and similar questions, and report on recent work with Loring concerning how the questions change if we look at real rather than complex matrices.
Abstract: We show that the discrete duals of the so called free orthogonal quantum groups have the completely contractive approximation property, analogous to the free groups. The proof relies on the structure of representation categories of these quantum groups, on the C*-algebraic structure of SUq(2), and on the free product techniques of Ricard and Xu. This talk is based on joint work with Kenny De Commer and Amaury Freslon.
Abstract: Independence has been introduced as a regularity property for pairs of commuting injective group endomorphisms of a discrete abelian group with finite cokernel by Joachim Cuntz and Anatoly Vershik. We discuss various characterisations of this regularity property and show how the statements need to be adjusted when removing the restrictions that the group has to be abelian and that the cokernels have to be finite. Somewhat surprisingly, this leads to the concept of *-commutativity. This property is defined for pairs of commuting self-maps of an arbitrary set. As an examples of *-commutativity, we explain a construction related to the Ledrappier shift and indicate how one obtains examples for independent group endomorphisms from this construction. If time permits, we will point out instances where the two notions have been readily used to obtain C*-algebraic results. Roughly speaking, both notions are designed to give rise to pairs of doubly commuting isometries, which significantly simplifies the analysis of the constructed C*-algebras. This is particularly useful when one tries to generalise results from the case of a single transformation to an action generated by finitely many transformations.
Abstract: We talk about independent resolutions for dynamical systems on totally disconnected spaces. Building on earlier work by Cuntz, Echterhoff and Li that allows one to compute the K-theory of totally disconnected systems that admit a so called independent invariant regular basis, we show how any totally disconnected dynamical system admits a resolution of such systems, which in some cases allows for K-theory computations. Based on work by me and X. Li.
Marco Matassa (UiO) will give a talk with title: On dimension and integration for spectral triples associated to quantum groups
Abstract: Abstract: I will discuss some aspects of the notions of spectral dimension and non-commutative integral in the context of modular spectral triples. I will focus on two examples: the modular spectral triple for SU_q(2) introduced by Kaad and Senior and the family of spectral triples for quantum projective spaces introduced by D'Andrea and Dąbrowski.
Jens Kaad (Trieste), will give a talk with title "Joint torsion line bundles of commuting operators"
In this talk I’ll associate a holomorphic line bundle to any commuting tuple of bounded operators on a Hilbert space. The transition functions for this bundle are given by the joint torsion which compares determinants of Fredholm complexes. The joint torsion is an invariant of the second algebraic K-group of the Calkin algebra (bounded operators modulo trace class operators). The main step is to prove that the transition functions for the joint torsion line bundle are indeed holomorphic. This is carried out by studying the Quillen-Freed holomorphic determinant line bundle over the space of Fredholm complexes. In particular I will construct a holomorphic section of a certain pull-back of this bundle. The talk is based on joint work with Ryszard Nest.
Magnus D. Norling will give a talk with title "Universal coefficient theorem in KK-theory". This presentation is part of the final act of the course on "The Baum-Connes conjecture and KK-theory".
Bas Jordans will give a talk with title "Higson's characterization of KK-theory". This presentation is part of the final act of the course on "The Baum-Connes conjecture and Kasparov's KK-theory".
Roberto Conti (Sapienza Università di Roma) will give a talk with title: Asymptotic morphisms in local quantum physics and study of some models
We discuss a notion of asymptotic morphisms that is suitable for a description of superselection sectors of a scaling limit theory. In some models, this leads to interesting questions about the explicit form of certain modular operators. (This talk is based on joint work with D. Guido and G. Morsella).
Magnus Landstad will give a talk with title: Quantum groups from almost matched pairs of groups - the groupoid approach
Abstract: If G is a locally compact group with two closed subgroups H,K s.t. G=HK, then (H,K) is called a matched pair of subgroups. The construction of a quantum group from such a pair goes back a long time. We shall look at the more general case where the subgroups are almost matched (the complement of HK in G has measure 0), then a groupoid approach to the construction is very useful and many formulas are obtained for free.
I shall start with explaining the concepts needed (quantum groups, groupoids, etc) and then how the groupoid is constructed. Finally we shall look at the special case where G has a compact open subgroup.
This is joint work with A. Van Daele.
Antoine Julien (NTNU) will give a talk with title: Tiling spaces, groupoids and K-theory
In this talk, I will describe how spaces, groupoids and C*-algebras can be associated with aperiodic tilings. In some cases, it is possible to describe the structure of the groupoid combinatorially in terms of augmented Bratteli diagrams. (joint work with Jean Savinien) Time permitting, I will expose a strategy for computing the K-theory of the tiling algebra in terms of the K-theory of AF-algebras (work in progress).
Takuya Takeishi, University of Tokyo, will give a talk with title: Bost-Connes system for local fields of characteristic zero
Abstract: The Bost-Connes system, which describes the relation between quantum statistical mechanics and class field theory, was first constructed by Bost and Connes for the rational field, and generalized for arbitrary number fields by the contribution of many researchers. In this talk, we will introduce a generalization of the Bost-Connes sysmtem for local fields of characteristic zero, and introduce some properties.
Judith Packer, University of Colorado (Boulder), will give a talk with title "Noncommutative solenoids and their projective modules"
Abstract: ``Noncommutative solenoids" are certain twisted group $C^*$-algebras, where the groups in question are countably infinitely generated; these algebras can also be generated as direct limits of rotation algebras. From examining the range of the trace of the $K_0$-groups of the noncommutative solenoids, their finitely generated projective modules can be constructed. We also discuss a way to construct Morita equivalence bimodules between noncommutative solenoids that goes back to work of M. Rieffel, with the new wrinkle of $p$-adic analysis appearing. This work is joint with F. Latr\'emoli\'ere.
Bas Jordans (UiO) will give a talk with title: Real dimensional spaces in noncommutative geometry
In noncommutative geometry geometric spaces are given by spectral triples. In this talk we consider a generalisation of these spectral triples to semifinite spectral triples. In analogy to the classical case it is possible to construct the product of two semifinite spectral triples. We will construct this product and derive properties thereof. Also we will describe for each z\in(0,\infty) a semifinite spectral triple which can be considered as having dimension z. As an application these "z-dimensional" semifinite triples will be used for two regularisation methods in physics.
Yusuke Isono from the University of Tokyo will give a talk with title: Strong solidity of II_1 factors of free quantum groups
We generalize Ozawa's bi-exactness to discrete quantum groups and give a new sufficient condition for strong solidity, which implies the absence of Cartan subalgebras. As a corollary, we prove that II_1 factors of free quantum groups are strongly solid. We also consider similar conditions on non-Kac type quantum groups, namely, non finite von Neumann algebras.
Erik Bédos will give a talk with title: On equivariant representations of C*-dynamical systems
Let \Sigma=(A, G, \alpha, \sigma) denote a unital discrete twisted C*-dynamical system. In our recent work with Roberto Conti (Rome), it has emerged that the so-called equivariant representations of \Sigma on Hilbert A-modules play an interesting role, complementing the one played by covariant representations. We will discuss some aspects of this notion and illustrate its usefulness in the study of the crossed products associated with \Sigma.
Adam Skalski (IMPAN) will give a talk with title: Closed quantum subgroups of locally compact quantum groups and some questions of noncommutative harmonic analysis (based on joint work with Matt Daws, Pawel Kasprzak and Piotr Soltan)
Abstract: The notion of a closed subgroup of a locally compact group is a very straightforward concept, often featuring in classical harmonic analysis. I will discuss the possible extensions of this notion to the quantum setting, focusing on the comparison of the two definitions proposed by S. Vaes and S.L. Woronowicz. I will describe some reformulations of these definitions and explain how they can beshown to be equivalent in many cases; I will also mention certain connections to other problems of quantum harmonic analysis.
Nicolai Stammeier, Westfälische Wilhelms-Universität Münster, will give a talk with title: Product Systems of Finite Type for Certain Algebraic Dynamics and their C*-algebras
Abstract: Let P be a lattice-ordered semigroup with unit acting on a discrete, abelian group G by injective endomorphisms with finite cokernel. Building on the work of Jeong Hee Hong, Nadia S. Larsen and Wojciech Szymanski on product systems of Hilbert bimodules and their KMS-states, one can associate a product system to this dynamical system that turns out to be of finite type. Imposing two additional conditions on the dynamics, namely independence of the endomorphisms for relatively prime elements in P and exactness, we derive presentations of the Nica-Toeplitz algebra and the Cuntz-Nica-Pimsner algebra. Moreover, the latter has lots of nice descriptions and is shown to be a unital UCT Kirchberg algebra.
Roberto Conti, Universita La Sapienza (Rome), Italy, will give a talk with title: The dark side of the Cuntz algebras
Abstract: We provide an overview of our recent work on the automorphism group of Cuntz algebras and discuss a number of open problems. (Joint work with J.H. Hong and W. Szymanski).