# C*-algebra seminar

## Previous

Time and place: May 3, 2018 1:00 PM - 2:00 PM, Hurricane, Ullevål

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).

Time and place: Feb. 6, 2018 11:00 AM - 12:00 PM, Gates of Eden

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.

Time and place: Jan. 9, 2018 11:00 AM - 12:00 PM, Gates of Eden

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.

Time and place: Dec. 19, 2017 2:00 PM - 3:00 PM, Desolation row, Ullevål

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).

Time and place: Dec. 13, 2017 11:00 AM - 12:00 PM, Desolation Row, Sognsv. 77B

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.

Time and place: Nov. 6, 2017 12:45 PM - 1:45 PM, End of Line, Ullevål

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.

Time and place: Oct. 23, 2017 12:45 PM - 1:45 PM, Gates of Eden

Erik Bedos (UiO) will give a talk with title "On Exel-Pardo algebras as Cuntz-Pimsner algebras"

Abstract:

In a joint work with S. Kaliszweski and J. Quigg (https://arxiv.org/pdf/1512.07302.pdf, to appear in JOT), we consider a continuous action of a locally compact group G on a topological graph E, equipped with a G-valued continuous cocycle, and show how to construct a C*-correspondence from these data, giving rise to a Toeplitz algebra and a Cuntz-Pimsner algebra. In the talk we will sketch this construction, but restrict ourselves to the discrete case. We will also describe these algebras in terms of generators and relations when E is row-finite. As a corollary we get that the associated Cuntz-Pimsner algebra coincides with the C*-algebra recently introduced by Exel and Pardo when E is finite and sourceless.

Time and place: Oct. 16, 2017 12:45 PM - 1:45 PM, Gates of Eden, Ullevål

Nicolai Stammeier (Oslo) will give a talk with title: The inner structure of boundary quotients of right LCM semigroups

Abstract: In joint work with Roberto Conti, Stefano Rossi, and Valeriano Aiello, we use semidirect products built from algebraic dynamical systems to model right LCM semigroups to study various structural aspects in connection with a selection of distinguished subalgebras of the associated boundary quotients. Our two guiding examples are integral dynamics as considered in work of Barlak - Omland - Stammeier, and exact injective group endomorphisms of discrete abelian groups with finite cokernel as studied by Cuntz and Vershik.

Time and place: Sep. 19, 2017 12:45 PM - 1:45 PM, Gates of Eden

Adam Sørensen (UiO) will give a talk with title: C*-stable groups.

Abstract: In this talk we will look at when group C*-algebra have stable relations, which loosely speaking means that any almost representation of the group in a C*-algebra will be close to an exact representation. A particularly interesting case is if we assume the C*-algebra is finite dimensional. I will mostly discuss a collection of examples. The talk is based on ongoing joint work with Søren Eilers and Tatiana Shulman.

Time and place: Aug. 11, 2017 11:00 AM - 12:00 PM, room 108, Niels Henrik Abels hus

Please access the abstract for detailed information on the contents of this talk.

Time and place: June 27, 2017 11:00 AM - 12:00 PM, "Desolation Row", 3rd floor, Sognsv. 77

Prof. Lia Vas (University of the Sciences, Philadelphia, USA) will give a talk with title:

Algebraization of Operator Theory

Time and place: Mar. 15, 2017 10:15 AM - 12:00 PM, NHA 738

Adam Sørensen (Oslo) will give a talk with title: Overlapping qubits

Abstract: I will discuss the paper "Overlapping Qubits" by Chao, Reichardt, Sutherland, and Vidick (arXiv:1701.01062 - category: Quantum Physics!). Qubits are the bits of quantum computing. In the paper the authors take the point of view that a qubit mathematically is described by a pair of anticommuting reflections on a finite dimensional Hilbert space. Two qubits are independent if their defining operators commute. The central point of the paper is that when performing observations we should not expect two qubits to be exactly independent, rather we should expect them to be almost independent, i.e. the norms of the commutators should be small. This naturally leads to questions about almost commuting matrices, which is why I care. I will attempt to explain how questions of almost commuting matrices come up, and how the physicists answer them.

Time and place: Feb. 9, 2017 3:15 PM - 5:00 PM, NHA room 735

Elizabeth Gillaspy, p.t. Münster (Germany) will give a talk with title "Wavelets and spectral triples for higher-rank graphs"

Time and place: Dec. 15, 2016 10:15 AM - 12:00 PM, GHS room 3514

Ulrik Bo Rufus Enstad (Oslo) will give a talk with title: Connections between Gabor frames and Noncommutative Tori

Abstract: A Gabor frame is a special type of frame in the Hilbert space of square-integrable functions on the real line. Gabor frames provide robust, basis-like representations of functions, and have applications in a wide range of areas. They have a duality theory which is deeply linked to Rieffel’s work on imprimitivity bimodules over noncommutative tori. We explore several links between Gabor frames and noncommutative tori, and show how operator algebras can be used to give alternative proofs of theorems from time-frequency analysis.  This talk is based on my Master’s thesis written at NTNU, which reviews Franz Luef’s work on the connections between Gabor frames and modules over noncommutative tori, as well as some joint work with Franz Luef.

Time and place: Dec. 7, 2016 10:15 AM - 12:00 PM, NHA, seminarrom B81

John Quigg, Arizona State University (Tempe), USA, will give a talk with title "The Pedersen rigidity problem".

University of Abstract: If \alpha is an action of a locally compact abelian group G on a C*-algebra A, Takesaki-Takai duality recovers (A,\alpha) up to Morita equivalence from the dual action of \widehat{G} on the crossed product A\rtimes_\alpha G. Given a bit more information, Landstad duality recovers (A,\alpha) up to isomorphism. In between these, by modifying a theorem of Pedersen, (A,\alpha) is recovered up to outer conjugacy from the dual action and the position of A in M(A\rtimes_\alpha G). Our search (still unsuccessful, somehow irritating) for examples showing the necessity of this latter condition has led us to formulate the "Pedersen rigidity problem". We present numerous situations where the condition is redundant, including G discrete or A stable or commutative. The most interesting of these "no-go theorems" is for locally unitary actions on continuous-trace algebras. This is joint work with Steve Kaliszewski and Tron Omland.

Time and place: Nov. 30, 2016 10:15 AM - 12:00 PM, NHA B81

Abstract: We first discuss C*-simplicity and the unique trace property for discrete groups in light of recent years' development. In particular, we consider amalgamated free products, and give conditions for such to be (and fail to be) C*-simple. Then we define radical and residual classes of groups, and explain that there exists a radical detecting C*-simplicity, in a similar way as the amenable radical detects the unique trace property. The talk is based on joint work with Nikolay A. Ivanov from Sofia University, Bulgaria.

Time and place: Nov. 10, 2016 2:15 PM - 4:00 PM, B735

Michael Whittaker from University of Glasgow will give a talk with title:  New directions in self-similar group theory

Abstract: A self-similar group (G,X) consists of a group G acting faithfully on a homogeneous rooted tree such that the action satisfies a self-similar condition. In this talk I will generalise the above definition to faithful groupoid actions on the path space of more general graphs. This new definition allows us to work out the structure of the KMS state space of associated Toeplitz and Cuntz-Pimsner algebras. This is joint work with Marcelo Laca, Iain Raeburn, and Jacqui Ramagge.

Time and place: Nov. 9, 2016 10:15 AM - 12:00 PM, B81

Rasmus Bryder (University of Copenhagen) will give a talk with title: Twisted crossed products over C*-simple groups

Abstract: A twisted C*-dynamical system consists of a C*-algebra, a discrete group and a "twisted" action of the group on the C*-algebra, i.e., the group acts by automorphisms on the C*-algebra in a manner determined by a 2-cocycle of the group into the unitary group of the C*-algebra. Whenever the 2-cocycle (or twist) is trivial, the action is given by a group homomorphism of the group into the automorphism group of the C*-algebra. We consider twisted C*-dynamical systems over C*-simple groups (i.e.,groups whose reduced group C*-algebra is simple) and how C*-simplicity affects the ideal structure of reduced crossed products over such dynamical systems.

Time and place: Oct. 26, 2016 10:15 AM - 12:00 PM, B81
Time and place: Oct. 12, 2016 10:15 AM - 12:00 PM, B81

Andreas Andersson (UiO): An introduction to duality for compact groups in algebraic quantum field theory

Time and place: Sep. 14, 2016 10:15 AM - 12:00 PM, B81

Bartosz Kwasniewski (Odense) will give a talk with title: Paradoxicality and pure infiniteness of  C*-algebras associated to Fell bundles

Abstract: Abstract: In this talk we present conditions implying  pure infiniteness of the reduced cross-sectional $C^*$-algebra $C^*_r(\mathcal{B})$ of a Fell bundle $\mathcal{B}$ over a discrete group $G$. We introduce notions of aperiodicity, $\mathcal{B}$-paradoxicality and  residual $\mathcal{B}$-infiniteness.  We discuss their relationship with similar conditions studied, in the context of crossed products, by the following duos: Laca, Spielberg; Jolissaint, Robertson; Sierakowski, R{\o}rdam;  Giordano, Sierakowski and Kirchberg, Sierakowski.    (based on  joint work with Wojciech Szyma{\'n}ski)

Time and place: Sep. 7, 2016 10:15 AM - 12:00 PM, B801

Abstract: Exploring connections between subfactors and conformal field theories, Vaughan Jones recently observed that planar algebras give rise to unitary representations of the Thompson group F, and more generally,  to unitary representations of the group of fractions of certain categories. Remarkably, this procedure applies to oriented link invariants. In particular, a suitably normalized HOMFLYPT polynomial is a positive definite function on the oriented Thompson group. (Based on joint work with V. Aiello and V. Jones.)

Time and place: June 16, 2016 10:15 AM - 12:00 PM, NHA B735

In this talk I will present a paper by D. Bisch, R. Nicoara and S. Popa where continuous families of irreducible subfactors of the hyperfinite II_1 factor which are non-isomorphic, but have all the same standard invariant are constructed. In particular, they obtain 1-parameter families of irreducible, non-isomorphic subfactors of the hyperfinite II_1 factor with Jones index 6, which have all the same standard invariant with property (T).

Time and place: May 19, 2016 2:15 PM - 4:00 PM, NHA B735

Abstract: This talk addresses some of the fundamental barriers in the theory of computations. Many computational problems can be solved as follows: a sequence of approximations is created by an algorithm, and the solution to the problem is the limit of this sequence (think about computing eigenvalues of a matrix for example). However, as we demonstrate, for several basic problems in computations such as computing spectra of operators, solutions to inverse problems, roots of polynomials using rational maps, solutions to convex optimization problems, imaging problems etc. such a procedure based on one limit is impossible. Yet, one can compute solutions to these problems, but only by using several limits. This may come as a surprise, however, this touches onto the boundaries of computational mathematics. To analyze this phenomenon we use the Solvability Complexity Index (SCI). The SCI is the smallest number of limits needed in order to compute a desired quantity. The SCI phenomenon is independent of the axiomatic setup and hence any theory aiming at establishing the foundations of computational mathematics will have to include the so called SCI Hierarchy. We will specifically discuss the vast amount of classification problems in this non-collapsing complexity/computability hierarchy that occur in inverse problems, compressed sensing problems, l1 and TV optimization problems, spectral problems, PDEs and computational mathematics in general.

Time and place: May 4, 2016 2:15 PM - 4:00 PM, NHA B735

Abstract:  In a recent work with R. Conti (La Sapienza Univ., Rome), we have introduced a notion of positive definiteness for certain functions associated to a (unital, discrete) C*-dynamical system. We will sketch the proof of a Gelfand-Raikov type theorem for such functions and use it to construct complete positive maps on the full and the reduced C*-crossed products of the system. We will also explain how a natural definition of amenability for C*-dynamical systems emerges from our work.

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