Seminars - Page 6

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.  

Erik Alfsen will give a talk with title  "Finding decompositions of separable states"

Magnus Dahler Norling will give a second talk on the topic of inverse semigroup C*-algebras associated with left cancellative semigroups.

Magnus Dahler Norling will give a talk with title "Inverse semigroup C*-algebras associated with left cancellative semigroups".

Abstract: To each discrete left cancellative semigroup S one may associate a certain inverse semigroup I_l(S), often called the left inverse hull of S. We show how the full and the reduced C*-algebras of I_l(S) are related to the full and the reduced semigroup C*-algebras for S recently introduced by Xin Li, and give conditions ensuring that these algebras are isomorphic. Our picture provides an enhanced understanding of Li's algebras.  

Simen Rustad (UiO) will give a talk with title  "Construction of Bost-Connes type systems for function fields".

Abstract: I will try to indicate how Benoit Jacob's construction of a Bost-Connes  type system for function fields fits into a more general framework.  

Bora Yalkinoglu will give a talk entitled: Introduction to p-adic Bost-Connes systems.

Abstract: In this talk we want to give a gentle introduction into the recently emerging theory of p-adic Bost-Connes systems. In the first part of the talk, after reviewing the necessary background from p-adic analysis and number theory, we will explain recent work of Connes and Consani on certain p-adic representations of the classical BC-system. In the second part of the talk we will discuss recent work on generalizations of the work of Connes and Consani and, further, point out several open problems for further research.  

Thomas Timmermann, Westfälische Wilhelms-Universität Münster, Germany, will give a talk with title "Towards the dynamical quantum group SU_q(2) on the level of operator algebras"

Fred Shultz, Wellesley College (USA) will give a talk with title "Affine automorphisms of the convex set of separable states, and decompositions of separable states".

Roberto Conti , Università di Chieti-Pescara ‘G. D’Annunzio’, Italy, will give a talk on "Sectors of scaling limit nets and asymptotic morphisms".

Abstract: In the algebraic approach to 4D-QFT the main object of study is a local net, namely an isotonous correspondence between spacetime regions and operator algebras on a fixed Hilbert space satisfying physically motivated properties including Einstein causality. The so-called DHR superselection sectors of the net are then described by certain (inner equivalence classes of) *-endomorphisms of the C*-algebra of quasi-local observables. For any local net, one may also consider its associated scaling limit nets, carrying the information on the short distance limit of the given QFT (roughly, this is the algebraic version of the renormalization group). In this talk we will argue that the superselection sectors of a scaling limit net can be described in terms of suitable maps of the original theory, that are similar to the asymptotic morphisms appearing in E-theory of Connes and Higson. This is a new arena where concepts from AQFT and NCG are merged together, and provides a first step for an alternative (rigorous, model independent) approach to the notion of confinement. (This is joint work with G. Morsella).