Arrangementer - Side 4

Seung-Hyeok Kye (Seoul National University, Korea) will give a talk titled: Indecomposable exposed multi-linear maps and separable states with unique decomposition.

Roberto Conti (Sapienza University of Rome, Italy) will give a talk titled: Endomorphisms of simple C*-algebras generated by isometries.

Sanaz Pooya (Stockholm), Sweden, will give a talk titled: On the Baum–Connes assembly map for certain semi-direct products.

Sven Raum (Stockholm), Sweden, will give a talk with title: C*-superrigidity of 2-step nilpotent groups

Camila Fabre Sehnem (Florianopolis), Brasil, will give a talk with title :

On $C^*$-algebras associated to product systems

Connes' embedding problem is one of the long standing open problems in Operator Algebras. Since it was raised in 1976, several equivalent formulations, seemingly unrelated to it, have been found, also in other areas of mathematics. In particular, it is equivalent to the (weak) Tsirelson problem in Quantum Information Theory. 

The aim of the winter school is to upgrade the knowledge of all operator algebraists at NTNU and UiO, in particular master and PhD students, on these important topics and to review some of the recent developments.  

This course is a part of the project "Pure Mathematics in Norway, 2018-2022", supported by the Trond Mohn Foundation (earlier called the Bergen Research Foundation) and the Tromsø Research Foundation.    

An abstract of the talk is available here.

Noncommutative geometry aims to use geometric insight in studying phenomena that are beyond the reach of classical geometry and analysis, using functional analysis and algebra as primary rigorous tools. Over the years it has been applied to a variety of problems, from index theory for foliations, to the Novikov conjecture, quantum Hall effect, standard model, analysis on quantum groups, and many more. The goal of the one-day seminar is to use the opportunity provided by the visit of Adam Rennie from Australia to report on recent advances in the area. Another goal is to strengthen ties between the operator algebra groups in Oslo and Trondheim.

The seminar is part of the project "Pure Mathematics in Norway, 2018-2022", supported by the Trond Mohn Stiftelse (earlier called Bergen Research Foundation) and the Tromsø Research Foundation.     

Prof. Masaki Izumi, Kyoto University, Japan, will give a talk with title:

The classification of poly-Z group actions on Kirchberg algebras

Abstract: We completely classify outer actions of a poly-Z group G on any Kirchberg algebra A in terms of a principal Aut(A x K)-bundle over the classifying space BG. This is joint work with Hiroki Matui.

Becky Armstrong, University of Sydney, Australia, will give a talk with title:

Simple graph algebras

Abstract: Since their introduction twenty years ago, C*-algebras associated to directed graphs have become a popular tool for investigating various classes of C*-algebras, because analytical properties of these C*-algebras depend on much simpler combinatorial properties of the underlying graphs. One such analytical property is simplicity, which plays a fundamental role in the classification program for C*-algebras. In this talk I will first recall the characterisation of simplicity for directed graph C*-algebras. I will then describe the results of my PhD research, in which I characterise simplicity of twisted C*-algebras of topological higher-rank graphs in terms of the underlying graphical and cohomological data. These C*-algebras are constructed using groupoid techniques for the purpose of this simplicity characterisation, but I will also briefly describe two product-system models for twisted C*-algebras of topological higher-rank graphs. (This is joint work with my PhD supervisors, Nathan Brownlowe and Aidan Sims.)

This is the third and last lecture by Anders C. Hansen (Cambridge Univ. and UiO) on this topic. Vegard Antun (UiO) will also contribute to the lecture.

Added June 06: Slides from the lectures are now available here.

This is the second in a series of three lectures by Anders C. Hansen (Cambridge Univ. and UiO) on this topic. Vegard Antun (UiO) will also contribute to the lectures.

Added June 06: Slides from the lectures are now available here.

This is the first in a series of three lectures by Anders C. Hansen (Cambridge Univ. and UiO) on this topic. Vegard Antun (UiO) will also contribute to the lectures.

Added June 06: Slides from the lectures are now available here.

Kurusch Ebrahimi-Fard (NTNU) will give a talk with title: Moment-cumulant relations in noncommutative probability and shuffle-exponentials

Abstract: In this talk we consider monotone, free, and boolean moment-cumulant relations from the shuffle algebra viewpoint. Cumulants are described as infinitesimal characters over a particular combinatorial Hopf algebra, which is neither commutative nor cocommutative. As a result the moment-cumulant relations can be encoded in terms of shuffle and half-shuffle exponentials. These shuffle exponentials and the corresponding logarithms permit to express monotone, free, and boolean cumulants in terms of each other using the pre-Lie Magnus expansion. If time permits we will revisit additive convolution in monotone, free and boolean probability and related aspects. Based on joint work with F. Patras (CNRS).

Zahra Afsar (University of Wollongong, Australia) will give a talk with title: Nica-Toeplitz-algebras of *-commuting local homeomorphisms and equilibrium states

Abstract: Given a family of *-commuting local homeomorphisms on a compact space, we can build a compactly aligned product system of Hilbert bimodules. The product system has a Nica-Toeplitz algebra which carries a gauge action of a higher-dimensional torus, and there are many possible dynamics obtained by composing with different embeddings of the real line in this torus. In this work, which is a joint work with Prof. Astrid an Huef and Prof. Iain Raeburn, I will talk about the equilibrium states of these dynamics. If time allows, I will also provide some examples from higher rank graph theory and reconcile our results with those existing ones.

Elizabeth Gillaspy from the University of Montana at Missoula, USA, will give a talk with title " Finite decomposition rank and strong quasidiagonality for virtually nilpotent groups "

Abstract: In joint work with Caleb Eckhardt and Paul McKenney, we show that the C*-algebras of discrete, finitely generated, virtually nilpotent groups G are strongly quasidiagonal and have finite decomposition rank. Thus, the only remaining step required to show that primitive quotients of such virtually nilpotent groups G are classified by their Elliott invariant is to check that these C*-algebras satisfy the UCT. Our proof of finite decomposition rank relies on a careful analysis of the relationship between primitive ideals of C*(G) and those of C*(N), where N is a finite-index normal subgroup of G. In the case when N is also nilpotent, we obtain a decomposition of C*(G) as a continuous field of twisted crossed products, which enables us to prove finite decomposition rank of C*(G) by analyzing the decomposition rank of the fibers.  

Antoine Julien, Universitetet i Nord, will give a talk with title:  Rieffel-type projections in higher-dimensional rotation algebras

Abstract: Rieffel first built a non-trivial projection in the rotation algebra by considering a certain C*-module over this algebra, and exploiting the Morita equivalence which it implements. In this talk, I will present how it is possible to extend these ideas to construct explicitly projections in higher-dimensional noncommutative tori. Precisely, our techniques can be applied to the NC tori which are associated with an R^d-flow on a 2d-torus, or equivalently which are given by the crossed product of C(T^d) by Z^d. I will also hint on how this result can be interpreted as constructing Gabor atoms associated with some lattices in the time-frequency space R^{2d}. This is a joint work with Franz Luef (NTNU).

Abstract: Recently, Steve Kaliszewski, Tron Omland, and I have been investigating the following theorem of Pedersen: two actions of a compact abelian group on C*-algebras A and B are outer conjugate if and only if there is an equivariant isomorphism between the crossed products that respects the positions of A and B. We upgraded this to nonabelian groups (using coactions on the crossed products), and then searched for examples showing that the last condition (on the positions of A and B) is necessary. We failed. This lead us to formulate the "Pedersen Rigidity Problem": if the crossed products of A and B are equivariantly isomorphic, are the actions on A and B outer conjugate? We have been finding numerous "no-go theorems", which give various sufficient conditions for Pedersen Rigidity. Quite recently we have done this for ergodic actions of a compact group, assuming that the actions have "full spectrum". In fact, these actions are (not just outer) conjugate if and only if the dual coactions are. I will summarize our progress on the Pedersen Rigidity Problem and outline the proof of the no-go theorem for these compact ergodic full-spectrum actions.

Pawel Kasprzak (Warzaw) will give a talk with title " Quantum actions on discrete quantum spaces"

Abstract:

To any action of a compact quantum group on a von Neumann algebra which is a direct sum of factors we associate an equivalence relation corresponding to the partition of a space into orbits of the action. We show that in case all factors are finite-dimensional (i.e. when the action is on a discrete quantum space) the relation has finite orbits.  We then apply this

i) to generalize the classical theory of Clifford, concerning the restrictions of representations to normal subgroups, to the framework of quantum subgroups of discrete quantum groups, itself extending the context of closed normal quantum subgroups of compact quantum groups; ii) to the context of idempotent states showing that the  algebra of invariant elements is finite dimensional if and only if the corresponding state is normal. Joint work with K. De Commer, A. Skalski and P. Sołtan.