## Fall 2019

## : 4th December 2019. 10.15 in 656

Speaker: Zahra Afsar (University of Sydney)

Title: $C^*$-algebras of self-similar actions of groupoids on higher-rank graphs and their equilibrium states

Abstract. In a joint work with N. Brownlowe, J. Ramagge and M.F. Whittaker, we introduce the notion of a self-similar action of a groupoid $G$ on a finite higher-rank graph. To such an action, we associate two $C^*$-algebras: the Toeplitz algebra and the Cuntz–Pimsner algebra. We study the KMS states of these algebras in natural dynamics. We then illustrate our results by introducing the notion of a coloured-graph automaton, which we use to construct examples of self-similar actions. We compute the unique KMS states of the Cuntz–Pimsner algebra for some concrete examples.

## 13 November, kl. 10. in 656

Speaker: Eirik Berge (NTNU)

Title: The Affine Wigner Distribution

Abstract: In this talk I will present a notion of Wigner distribution in the time-scale setting that have been introduced several times under different disguises in the literature. I will begin by introducing the necessary background and relate the topic to the more well-known (time-frequency) Wigner distribution. Although these different Wigner distributions share many similarities, there are also important differences that I will emphasize. It turns out that the structure of the affine Wigner distribution is (maybe not surprising considering the name) intimately related to the affine group. I will present a few results that illuminate the structure of the affine Wigner distribution and draw parallels with the (time-frequency) Wigner distribution. There are several open questions remaining and I will discuss some of them at the end if time permits. The original material is joint work with Stine M. Berge and Franz Luef.

## 30th October 10.15 in 656

Speaker: Petter Nyland (NTNU)

Title: Matui's AH-conjecture for Étale Groupoids

Abstract: Around 2015, Hiroki Matui introduced two conjectures concerning minimal étale groupoids over Cantor spaces. Such groupoids serve as models for a great many unital simple C*-algebras. The HK-conjecture relates the homology groups of the groupoid with the K-groups of its reduced groupoid C*-algebra. Whereas the AH-conjecture relates the (abelianization of) the topological full group of the groupoid with its homology groups. I will give an introduction to these two conjectures, but focus mostly on the AH-conjecture–––as this has been my research focus of late.

## 23 October 10.15 in 656

Speaker: Eirik Skreittingland

Title: Accumulated Cohen's class distributions

Abstract: In 1988, I. Daubechies introduced a class of operators called time-frequency localization operators. Given a compact domain C in the time-frequency plane R^2, the associated localization operator acts on a signal f in L^2(R) by localizing f to C in time and frequency. In this talk we will consider a recent generalization of such operators called mixed-state localization operators. Our main goal is to show how the domain C can be approximated from the first few eigenfunctions of the associated mixed-state localization operator. The most important tool will be the quantum harmonic analysis of R. F. Werner, which allows us to find and exploit a connection between mixed-state localization operators and Cohen’s class of time-frequency distributions. In particular, it allows us to define an object called the accumulated Cohen’s class distribution, and this is the object that we will use to approximate the domain C. The talk is based on joint work with F. Luef.

## 16th October 10.15 in 656

Speaker: Eusebio Gardella(University of Münster)

Title: Structure and classification of amenable group actions

Abstract: we study actions of amenable groups on classifiable C*-algebras, with the ultimate goal of describing its internal structure (regularity) and classifying them when they are strongly outer. We will report on progress in this line of research, old and new, with a particular focus on the case where the underlying algebra is strongly self-absorbing.

## 9th October 10.15 in 656

Speaker: Jim Tao from NTNU.

Title: A twisted local index formula for curved noncommutative two tori

Abstract: We consider the Dirac operator of a general metric in the canonical conformal class on the noncommutative two torus, twisted by an idempotent (representing the K-theory class of a general noncommutative vector bundle), and derive a local formula for the Fredholm index of the twisted Dirac operator. Our approach is based on the McKean-Singer index formula, and explicit heat expansion calculations by making use of Connes' pseudodifferential calculus. As a technical tool, a new rearrangement lemma is proved to handle challenges posed by the noncommutativity of the algebra and the presence of an idempotent in the calculations in addition to a conformal factor. This work is joint with Farzad Fathizadeh and Franz Luef.

## 2nd October 10.15 in 656

Speaker: Are Austad (NTNU)

Title: Weighted Feichtinger algebras and smoothness in noncommutative geometry

Abstract: A central notion in Connes' noncommutative geometry is the notion of smoothness (or regularity). Given a spectral triple for a C*-algebra, smoothness is a requirement on dense *-subalgebras. Based on recent developments in KK-theory we define smoothness on Hilbert C*-modules. Moreover, we show that for certain twisted group C*-algebras, namely those arising from time-frequency analysis on locally compact abelian groups, we can create arbitrarily smooth structures on the twisted group C*-algebra as well as on the associated Heisenberg modules. Indeed, smoothness for Heisenberg modules turns out to be equivalent to a statement on Gabor frames with atoms with well-localized time-frequency distributions.

## 11th September 10.15 in 656

Speaker: Eduard Ortega (NTNU)

Title: The tight groupoid of a left-cancellative category Abstract: We will see how to associate an étale groupoid to a left-cancellative category. Examples and applications will be shown. In the first session we will focus on explaining the general construction, while in the second we will focus on examples, in particular of self-similar groups. This is a joint work with Enrique Pardo.

## Fall 2016

## 31st Aug. 14.15 in 734

**Speaker**: Eduard Ortega (NTNU).

**Title**: Cuntz-Krieger Uniqueness Theorem

**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 algebras 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. Later I will expose part of the recent progress of the on-going project with Carlsen and Kwasniewski about topologically freeness of C*-correspondences.

## 17th Aug. 10.15 in 734

**Speaker**: Anatoly N. Kochubei (Institute of Mathematics, National Academy of Sciences of Ukraine).

**Title**: Non-Archimedean Duality: Algebras, Groups, and Multipliers

**Abstract**: We develop a duality theory for multiplier Banach-Hopf algebras over a
non-Archimedean field K. As examples, we consider algebras corresponding to
discrete groups and zero-dimensional locally compact groups with K-valued Haar
measure, as well as algebras of operators generated by regular representations
of discrete groups.

## Spring 2016

## 3rd May. 10.15 in 734

**Speaker**: Sayan Chakraborty

**Title**: K-theory of some noncommutative orbifolds

**Abstract**: I will consider noncommutative tori with finite group actions on those and compute K-theories of the crossed products. I will also talk about how one can produce projective modules over the tori and will compute the traces of these modules. If time permits, I will also talk about cyclic cohomology of these algebras and its pairing the K-theory elements.

## 19th Apr. 10.15 in 734

**Speaker**: Stuart White

**Title**: Amenability, Quasidiagonality and the UCT

**Abstract**: Quasidiagonality is a concept originating in work of Halmos in operator theory; it asks for block diagonal approximations of an operator algebra. It's a pretty mysterious property of a somewhat topological nature, and as noted by Rosenberg and Voiculescu quasidiagonality always entails some level of amenability. In this talk (based on joint work with Aaron Tikuisis and Wilhelm Winter) I'll discuss a kind of converse: how do we get quasidiagonality from amenability and what consequences does this have for group algebras and for simple amenable C*-algebras. No prior familiarity with quasidiagonality will be assumed.

## 12th Apr. 10.15 in 734

**Speaker**: Antoine Julien

**Title**: Spectral triples and wavelets associated to representations of Cuntz algebras

**Abstract**: I will survey some results on the construction of spectral triples and Laplace operators on Cantor sets (namely by Pearson and Bellissard). This construction, in some cases turns out to be related to wavelet bases associated to representations of Cuntz algebras.
This is a joint work with C. Farsi, E. Gillaspy, S. Kang and J. Packer.

## 15th mar. 10.15 in 734

**Speaker**: Mads Sielemann Jakobsen

**Title**: The Feichtinger algebra S0.

**Abstract**: In this talk I will give an overview of the Feichtinger algebra.
It is a function space which lies in the intersection
of C_0 and L^{1} and it is a Wiener-Amalgam, Co-orbit,
and Modulation space as well as a Segal algebra.
As such, it enjoys a wealth of properties which makes it
a very interesting (Banach) space of functions. In particular it
is the smallest Banach space which is invariant under time-
frequency shifts. It is heavily used in time-frequency analysis, and finds
applications in generalized stochastic processes and is a good
space of test-functions and provides a shortcut to the theory of
distributions and Fourier analysis.
The presentation is based on an ongoing project of mine where I
try to make sense of the large body of litteratur on this subject
(mostly by H.G. Feichtinger and K. Gröchenig). Among the results
that will be presented in this talk many are known, however there
are some details which are new.

## 23rd feb. 10.15 in 734

**Speaker**: Erik Bakken (NTNU)

**Title**: Stochastic Methods for Finite Approximations over Local Fields

**Abstract**: We show that over a local field a continuous-time random walk converges to a Brownian motion in the sense of weak convergence of probability measures. This is used to approximate the spectrum of a quantum Hamiltonian over a local field. The talk is based on joint work with Trond Digernes and David Weisbart.

## 12th january, kl. 10.15 in 734

**Speaker**: Siegfried Beckus

**Title**: Spectral Approximation of Schrödinger Operators: Continuous Behavior of the Spectra.

**Abstract**: I will speak about the work with Jean about the characterization
of the continuous behavior of the spectra which is related to
C*-algebras. The second part will be about Schroedinger operators and
the application of the previous results.