Arrangementer - Side 8

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

Abstract:

 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

Abstract:

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

Abstract:

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

Abstract:

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).

Gunther Cornelissen, Utrecht University (The Netherlands) will give a talk with title "Dynamical systems and point counting"

Abstract: Counting the points of a curve over finite fields doesn't determine the curve up to isomorphism; this is analogous to the famous fact that you cannot "hear the shape of a drum". I will show how to remedy this by counting points in a weighted way (namely, using abelian L-series). The method of proof is through the theory of dynamical systems, and - curiously - arose from a study of a quantum statistical mechanical system.  

Makoto Yamashita, p.t. University of Copenhagen, will give a talk with title "Tannaka-Krein duality of quantum homogeneous spaces"

Abstract: We study ergodic actions of compact quantum groups on operator algebras  (quantum homogeneous spaces) from the categorical point of view. The language of Rep(G)-module C*-categories gives a reconstruction theorem of quantum homogeneous spaces, which also captures the equivariant Morita equivalence and the equivariant homomorphisms.  For the case of quantum SU(2), the universality of Rep(SUq(2)) allows us to obtain a combinatorial description of quantum homogeneous spaces and their properties. Based on joint work with Kenny De Commer (arXiv:1211.6552, arXiv:1212.3413).  

Magnus Dahler Norling, UiO, will give a talk with title: The K-theory of some reduced inverse semigroup C*-algebras

Abstract: We use a recent result by Cuntz, Echterhoff and Li about the K-theory of certain reduced C*-crossed products to describe the K-theory of C*_r(S) when S is an inverse semigroup satisfying certain requirements. A result of Milan and Steinberg allows us to show that C*_r(S) is Morita equivalent to a crossed product of the type handled by Cuntz, Echterhoff and Li. We apply the results to graph inverse semigroups and the inverse semigroups of one-dimensional tilings.

Fred Shultz, Wellesley College, USA will give a talk with title "Decomposing separable states".

This is the first in a joint seminar series organised by the Operator Algebra group (UiO), Several Complex Variable group (UiO) and the CAS group.  The plan is to have seminars every other week.  

Abstract: This talk will begin with a brief introduction to entanglement and its applications, since that motivates the mathematics to be discussed.  In the title of this talk, a state is a positive linear functional on the tensor product of the algebras of m x m and n x n complex matrices.  Such a state is separable if it is a convex combination of product states. An interesting open problem is to give a useful criterion for a state to be separable. A related problem is to give a systematic way to find a decomposition of a separable state into a convex combination of product states.  This talk will describe such a decomposition for a class of separable states that is of both physical and mathematical interest.  This decomposition is also applicable to a class of completely positive maps (which correspond to certain quantum channels). This is joint work with Erik Alfsen.  

Magnus Landstad (NTNU) will give a talk with title: Exotic group C*-algebras and noncommutative duality.

Abstract: It  has long been known that for a (non-amenable) locally compact group G there are many C*-algebras between the full and reduced group C*-algebra. First I will discuss to what extent these intermediate algebras can be called group C*-algebras. Then I will look at algebras between the full and reduced crossed product, and the various types of coactions (full, maximal, normal) a group can have. To make arguments a little simpler, we shall assume G to be discrete.

Yoshiko Ogata, University of Tokyo, will give a talk with title: Approximating macroscopic observables in quantum spin systems with commuting matrices

Abstract: Macroscopic observables in a quantum spin system are spatial means of local observables in a UHF algebra. One of their properties is that they commute asymptotically as the system size goes to infinity. It is not true that any given set of asymptotically commuting matrices can be approximated by commuting ones in the norm topology. The main statement of this talk is that this is true for macroscopic observables.  

Jyotishman Bhowmick, UiO, will give a talk with title: Deformation of operator algebras by Borel cocycles

Abstract:Given a coaction of a locally compact group on a C^* algebra and fixing a cocycle on G, we discuss a method to deform A into another C^* algebra, thus generalizing  the works of Kasprzak, Yamashita and Rieffel. This is a joint work with S. Neshveyev and A.S. Sangha.

Stuart White (University of Glasgow, UK) will talk on "Z-stability and central sequences".

Abstract: Over recent years, tensorial absorption of the Jiang-Su algebra $\mathcal Z$ has become a particularly prominent property of $C^*$-algebras. In this talk, I'll explain what this means, and why this is the case; I'll also discuss methods for establishing ``$\mathcal Z$''-stability using central sequence, and some more general properties of central sequence algebras. The talk will end with a recent result showing that for a simple separable unital nuclear C*-algebra, whose extremal traces are compact and of finite covering dimension $\mathcal Z$-stability can be detected by a comparison property of the Cuntz semigroup (this result is joint work with Andrew Toms and Wilhelm Winter, which has also been independently discovered by Eberhard Kirchberg and Mickael Rørdam, and by Yasuhiko Sato).  

Dana Williams, Dartmouth College (USA) will talk on "Equivalence theorems and linking groupoids".

Abstract: The Kolmogorov decomposition of positive scalar valued kernels has played an important role in applications of operator theory to function theory.  It has been vastly generalised, finding its apotheosis in the result of Baretto, Bhat, Liebscher and Skeide which states that a positive $L(A,B)$-valued kernel, $A$ and $B$ $C^*$-algebras, has a Kolmogorov decomposition if and only if it is completely positive; that is, the restriction of the kernel to any finite set of index points gives a completely positive map.  The result may be viewed as a generalisation of the Stinespring dilation theorem from single point to multi-point index sets.  This talk presents the analogue of the Haagerup-Paulsen-Wittstock decomposition theorem for $L(A,B)$-valued kernels (where now $B$ is assumed to be injective).  It happens that in general complete boundedness of the kernel (ie, complete boundedness of the map resulting from restriction of the kernel to any finite index set) is not quite enough to ensure a decomposition: a certain regularity condition must also hold.  This condition can be seen to be automatic if the kernel is completely positive or the index set is countable.  This is joint work with Tirthankar Bhattacharyya and Chris Todd.  

Dávid Kunszenti-Kovács, Tübingen University (Germany) will give a talk with title "The Jacobs-deLeeuw-Glicksberg decomposition and ergodic theorems".

Abstract: We present the classical decomposition theorem for contractions on Hilbert spaces due to Jacobs, deLeeuw and Glicksberg, and show how it can be used to prove ergodic theorems. We then prove a new version of this decomposition, adapted to the context of W*-algebras, with consequences for W*-dynamical systems. Finally we take a look at how the characterizations given in the original decomposition theorem can be further strengthened.  

John Quigg, University of Arizona (Tempe), USA, will give a talk with title "Exotic group C*-algebras"

Abstract: We study C*-algebras between C*(G) and C*_r(G), focusing on the aspects relevant to noncommutative crossed-product duality.