C*-algebra seminar - Page 4

Time and place: June 24, 2015 10:15 AM12:00 PM, NHA B735

Klaus Thomsen, Aarhus Universitet, Denmark, will give a talk with title "KMS states and ground states for generalized gauge actions on graph C*-algebras"

Time and place: June 17, 2015 2:15 PM4:00 PM, NHA B735

John Quigg, Arizona State University at Tempe, USA, will give a talk with title: Landstad duality and a theorem of Pedersen


In joint work with Steve Kaliszewski and Tron Omland, we show how a theorem of Pedersen characterizing exterior equivalent actions on a C*-algebra can be parlayed into an equivalence between two equivariant categories of C*-algebras. In one category, isomorphisms correspond to outer conjugacies of actions, while isomorphisms in the other category are equivariant isomorphisms of the crossed products that respect the generalized fixed point algebras. This category equivalence is a variation of Landstad's original characterization of actions up to equivariant isomorphism, where we now allow more morphisms. Time permitting, we will compare our "outer duality" with Landstad duality and also with Imai-Takai crossed-product duality.



Time and place: June 9, 2015 2:15 PM4:00 PM, NHA Building B738

Alfons van Daele (University of Leuven, Belgium) will give a talk with title:  Constructing locally compact quantum groups from pairs of *-algebras

Abstract: Let (A,\Delta)  be a finite-dimensional Hopf *-algebra. The dual B of A is again a finite-dimensional Hopf *-algebra. The entire structure of these two Hopf *-algebras is encoded in the *-algebras A and B and the pairing between the two. We will explain how this works. This is in fact true in many more, and more general situations.  In particular, we give an example constructed from a pair of subroups H,K of a group G with the property that the map (h,k)-> hk is a bijection from HxK to G. This method is used in a joined paper with Magnus Landstad where we construct a pair of locally compact quantum groups from such pairs of subgroups of a locally compact group G.


Time and place: May 27, 2015 2:15 PM4:00 PM, NHA 738

Adam Sørensen (UiO) will give a talk with title "Leavitt path algebras - a connection between pure algebra and operator algebras"

Abstract: We will discuss Leavitt path algebras, the purely algebraic cousins of the analytic graph C*-algebras. We will discuss similarities and differences, in particular recent work with Brownlowe on a purely algebraic version of Kirchberg's theorem that all exact C*-algebras embed into O_2.

Time and place: May 26, 2015 2:00 PM4:00 PM, NHA B735

Marco Matassa (UiO) will give a talk with title The Dolbeault-Dirac operator on quantized projective spaces, revisited

Abstract: In this talk I will present a new construction for the Dolbeault-Dirac operator on quantum projective spaces, the main result being the computation of its square. This clarifies and generalizes some results of D'Andrea-Dąbrowski. Moreover it gives a class of explicit examples of the general construction of Krähmer-Tucker Simmons, which deals with such operators on irreducible generalized flag manifolds.

Time and place: May 12, 2015 11:00 AM12:00 PM, B735

Roberto Conti (La Sapienza, Rome) will give a talk with title "C*-algebras and Fourier theory"

Time and place: May 6, 2015 2:15 PM4:00 PM, B735

Robert Yuncken (Univ. Clermont-Ferrand II, France) will give a talk with title: A groupoid approach to pseudodifferential operators

Abstract: Connes introduced the "tangent groupoid" of a manifold as a geometric device for linking a classical pseudodifferential operator to its symbol, yielding a novel proof of the Atiyah-Singer index theorem.  Since then, numerous variations on the tangent groupoid have been produced, each adapted to a different class of pseudodifferential operators.  In this talk we will consider the reverse problem: associating to a given tangent groupoid a pseudodifferential calculus.  We shall show that the kernels of classical pseudodifferential operators are precisely the essentially homogeneous fibrewise distributions on Connes' tangent groupoid.  This leads to a natural pseudodifferential calculus of subelliptic type on a manifold with a filtration on its Lie algebra of vector fields.

Time and place: Apr. 15, 2015 2:15 PM3:15 PM, NHA B735

Réamonn Ó Buachalla (IMPAN) will give a talk with title: Noncommutative Kähler structures on quantum homogeneous spaces


Building on the definition of a noncommutative complex structure for a general algebra A, I will introduce the notion of a noncommutative Kähler structure for A. In the special case where A is a quantum homogeneous space, I show that many of the fundamental results of classical Kähler geometry follow from the existence of such a structure: Hodge decomposition, Serre duality, the Hard Lefschetz theorem, the Kähler identities, and collapse of the Frölicher spectral sequence at the first page. We then apply these results to Heckenberger and Kolb's differential calculus for quantum projective space, and show that they have cohomology groups of at least classical dimension. Time permitting, I will also discuss the relationship of this work to Connes proposal to study positive Hochschild cocycles as a starting point for noncommutative complex geometry, and Fröchlich, Grandjean, and Recknagel's definition of a Kähler spectral tuple.

Time and place: Apr. 13, 2015 12:15 PM2:00 PM, NHA B735

Eduard Ortega, NTNU, will give a talk with title: Cuntz-Krieger uniqueness theorems

Abstract: I will make a little survey about Cuntz-Krieger uniqueness theorems and how they help to the study of the ideal structure of the rings to which one can apply them. In certain classes of (C*-)algebras this is described as topologically freeness or condition (L). However they are important classes of rings for which are not known Cuntz-Krieger type theorems. I will present a class of rings, that generalize Leavitt path algebras and Passman crossed products, for which I can totally characterize the Cuntz-Krieger uniqueness theorem.

Time and place: Apr. 8, 2015 2:15 PM3:00 PM, NHA B735

Erik Bédos will give a talk with title: On the Fourier-Stieltjes algebra of a C*-dynamical system

Abstract: When G is a discrete group, its Fourier-Stieltjes algebra B(G) may be described as the set of coefficient functions associated with unitary representations of G on Hilbert spaces. In a similar way, if Sigma=(A, G, alpha, sigma) is a unital discrete twisted C*-dynamical system, one may let the Fourier-Stieltjes algebra B(Sigma) consist of the functions from G x A into A that arise as coefficient functions of equivariant representations of Sigma on Hilbert A-modules. We will explain how B(Sigma) may be organized as an algebra with conjugation, and show that it may be represented as completely bounded multipliers on the full crossed product C*(Sigma). (This is also known to be true for the reduced crossed product). This is part of an ongoing project with Roberto Conti (Rome).

Time and place: Mar. 11, 2015 2:15 PM4:00 PM, NHA B71

Franz Luef (NTNU) will give  a talk with title "Sigma-models solitons on noncommutative spaces"

Abstract: Results from time-frequency analysis and Gabor analysis allow the construction of new classes of sigma-model solitons over the Moyal plane and over noncommutative tori, taken as source spaces, with a target space made of two points. A natural action functional leads to self-duality equations for projections in the source algebra. Solutions, having non-trivial topological content, are constructed via suitable Morita duality bimodules. This is joint work with L. Dabrowski and G. Landi.


Time and place: Mar. 4, 2015 2:15 PM4:00 PM, NHA B735

Bartosz K. Kwaśniewski (University of Southern Denmark, Odense) will talk on: Topological aperiodicity for product systems of C*-correspondences

Abstract:We introduce a semigroup of multivalued maps dual to a product system of $C^*$-correspondences over an Ore semigroup. Under a certain aperiodicity condition on the dual semigroup we obtain a uniqueness theorem and a simplicity criterion for the associated Cuntz-Pimsner algebra. These results generalize similar statements for crossed products by groups (R. J. Archbold, J. S. Spielberg) and Exel’s crossed products (R. Exel, A. Vershik). They also give interesting conditions for topological higher rank graphs, and apply to the new Cuntz $C^*$-algebra $\mathcal{Q}_\mathbb{N}$ arising from the `$ax+b$'-semigroup over natural numbers. (Based on joint work with Wojciech Szymański.)

Time and place: Feb. 25, 2015 2:15 PM4:00 PM, NHA B71

Adam P.W. Sørensen will talk on Nuclear dimension of UCT Kirchberg algebras

Abstract: Nuclear Dimension is a regularity property for C*-algebras that is based on the type of properties currently being taught in Topics in Operator Algebras. We will go over the definition and motivation and discuss known results.

Time and place: Feb. 18, 2015 2:15 PM3:15 PM, NHA B735
Time and place: Feb. 11, 2015 2:15 PM4:00 PM, NHA B735

Makoto Yamashita, Ochanomizu University, will give a talk with title: Drinfeld center and representation theory for monoidal categories

Abstract: Motivated by the recently found relation between central completely positive multipliers and the spherical unitary representations of the Drinfeld double for discrete quantum groups, we construct and analyze the representations of fusion algebra of rigid C*-tensor category from the unitary half-braidings. Through the correspondence of Drinfeld center and the generalized Longo-Rehren construction in subfactor theory, these representations are also related to Popa’s theory of correspondences and subfactors. This talk is based on joint work with Sergey Neshveyev.

Time and place: Dec. 4, 2014 2:15 PM4:00 PM, NHA B637

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.  

Time and place: Dec. 3, 2014 2:00 PM4:00 PM, NHA B71

Alfons van Daele, University of Leuven (Belgium), will give a talk with title: Separability idempotents and quantum groupoids

Time and place: Nov. 19, 2014 2:15 PM4:00 PM, NHA B71

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.

Time and place: Nov. 5, 2014 2:15 PM4:00 PM, NHA B71

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.


Time and place: Oct. 15, 2014 2:15 PM4:00 PM, NHA Hus, B71

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.


Time: Sep. 17, 2014 2:00 PM4:00 PM

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.

Time and place: Sep. 10, 2014 3:15 PM4:15 PM, B71, NHA

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.

Time and place: June 4, 2014 1:00 PM3:00 PM, NHA Hus, B71

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.

Time and place: June 3, 2014 1:15 PM3:00 PM, NHA B71

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.

Time and place: May 30, 2014 1:15 PM3:00 PM, NHA Hus, B71

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.