Nachi Avraham-Re'em
Spatial Poisson suspensions in Polish group actions
In the ergodic theory of non-locally compact Polish groups, there is an important distinction between spatial actions (a Borel action with an invariant measure) and near or Boolean actions (each group element corresponds to a measure preserving transformation that is defined almost everywhere). In this talk, I will present the Poisson suspension construction, in which a probability preserving action is constructed out of an infinite measure preserving action, and in light of the above distinction, I will present a construction of the classical Poisson point process in such a way that spatial continuous actions admit spatial Poisson suspension.
Two applications are: (1) a partial answer to an open question of Glasner, Tsirelson & Weiss about spatial actions of Lévy groups; (2) the diffeomorphisms group of a smooth manifold admits an ergodic, free, spatial action on a standard probability space.
This is a joint work with Emmanuel Roy (Université Paris 13, LAGA).
Siegfried Beckus
Spectral convergence rates and the underlying dynamics
We study spectral estimates of dynamical defined operators. This has various applications in mathematical physics and it is connected to similar results obtained via continuous fields of C*-algebras.
Stine Marie Berge
QHA and Quantization for the Shearlet Group
In this talk we will delve into quantum harmonic analysis for the shearlet group. In this context, we will define a quantization scheme that works well with the group convolution. If time permits, we will see how this relates to the Wigner distribution for the shearlet group.
Michael Björklund
Quasi-morphisms and approximate lattices
In this talk we discuss how one can construct uniform approximate lattices from (cohomologically non-trivial) quasi-morphisms, and show that the corresponding hulls do not admit any invariant probability measures, and always project to a non-trivial Furstenberg boundary. No prior knowledge of approximate lattices or quasi-morphisms will be assumed.
Based on joint work with Tobias Hartnick (Karlsruhe).
Eusebio Gardella
Classifiability of crossed products
To every action of a discrete group on a compact Hausdorff space one can canonically associate a C*-algebra, called the crossed product. There are numerous results in the literature that describe the structure of this C*-algebra in terms of the dynamical system, making its study very accessible. In this talk, we will focus on one of the central notions in the realm of the classification of simple, nuclear C*-algebras, namely Jiang-Su stability. We will review the existing results and report on the most recent progress in this direction, going beyond the case of free actions both for amenable and nonamenable groups.
The talk will report on joint works with Geffen, Kranz and Naryshkin, and with Geffen, Gesing, Kopsacheilis and Naryshkin.
Franz Luef
Heisenberg modules in quantum time-frequency analysis
Quantum time-frequency analysis is based on a projective representation of phase space on the Hilbert-Schmidt operators. This adds to the quantum harmonic analysis setting the time-frequency aspect. There is also a theory of Gabor frames in this setting, which we link with Heisenberg modules. This is joint work with Henry McNulty (NTNU Trondheim).
Simon Machado
Approximate lattices: structure and beyond
Approximate lattices are aperiodic generalisations of lattices of locally compact groups. They were first introduced by Yves Meyer in locally compact abelian groups before being investigated in a broader setting by Björklund and Hartnick. Since then their structure has been thoroughly investigated.
In this talk I will survey what is known of the structure of approximate lattices. I will highlight some objects - coming from ergodic theory, model theory, bounded cohomology or the structure of arithmetic lattices - that appear in their study. I will also formulate open problems and conjectures related to approximate lattices.
Bram Mesland
Groupoid C*-algebras in solid state physics
In this talk I will give an overview of some recent uses of groupoid C*-algebras in solid state physics. A solid material can be modelled by an abstract discrete point set embedded in a topological group. The ambient group encodes the physical symmetries of the system under study. Because of the absence of any internal structure in the discrete point set, groupoids naturally presents themselves. The associated C*-algebra encodes the physical observables and its K-theory classifies observable physical quantities. These techniques give insight into certain classes of architected materials as well interacting particle systems. Based on joint work with E. Prodan.
Felix Pogorzelski
Symbolic substitutions and spectral approximation
Consider a discrete Schrödinger operator with aperiodic potential on the
Cayley graph of the Heisenberg group. Can one study its spectrum? This is a general and in many ways open program. One approach is to work with approximations via finite-volume or periodic analogs. For potentials arising as fixed points of symbolic substitution systems, we present sufficient and necessary conditions for (in fact exponential) convergence of the spectra in the Hausdorff metric. Based on two joint works including Ram Band, Siegfried Beckus, Tobias Hartnick and Lior Tenenbaum.
Jonathan Taylor
Functoriality of groupoid C*-algebras
With the exception of some specific classes of examples, continuous functors between étale groupoid do not lift functorially to homomorphisms of their algebras. One alternative approach to this is to consider a different class of morphism, such as actors: a special class of actions of groupoids. Buneci and Stachura demonstrated that such morphisms lift covariantly to morphisms of the associated algebras. If the groupoids concerned are effective, we are able to reconstruct actors from *-homomorphisms of reduced/effective groupoid C*-algebras, if they interntwine conditional expectations. This leads to an equivalence of categories between effective étale groupoids and Cartan pairs of C*-algebras (with the appropriate definitions of morphism).
José Luis Romero
Sampling, interpolation, and repulsive point processes
The problems of sampling and interpolation concern the relation between functions in a given class and their values on a distinguished set (samples). The two main questions are: Is every function determined by its samples? Can a function with prescribed samples be found?
A random point process is repulsive if the statistics of disjoint observation regions are negatively correlated. As a consequence of repulsion, a typical realization of such a process is better distributed than a Poissonian one.
I will present classical and recent results on sampling and interpolation, and discuss why repulsive point processes are often good candidates to solve both problems. As a case in point, I will focus on the planar Coulomb gas (Boltzmann-Gibbs distribution) and investigate its statistics at low temperatures by means of sampling and interpolation properties for weighted polynomials, as well as discrepancy estimates based on fine spectral estimates for Toeplitz operators. (Joint work with Yacin Ameur and Felipe Marceca).
Jordy Timo van Velthoven
Density inequalities for coherent state subsystems of amenable
groups
The talk concerns various density conditions for reproducing
properties of coherent state systems for amenable groups. In particular,
a sharp density inequality for complete systems associated to
approximate lattices will be outlined.
The talk is based on joint work with Ulrik Enstad
Mike Whittaker
Limit spaces of Katsura groupoids
Takeshi Katsura proved that every Kirchberg algebra arises, up to strong Morita equivalence, from a C*-algebra associated to two integer matrices. Exel and Pardo realised that Katsura's construction gives rise to a self-similar group(oid) action on the path space of a graph, and that Katsura's C*-algebra is the associated Cuntz-Pimsner algebra of the self-similar action.
In this talk, we introduce Katsura groupoids and construct their limit spaces, in the sense of Nekrashevych. Under mild conditions, these are circle bundles fibred over a Cantor set. We prove these embed in the plane and explain how an inverse limit construction gives rise to an algebra that is Poincaré dual to Katsura's original algebra. We will also show how this is related to a recent construction of Putnam, and use the limit space viewpoint to answer a question he asked.
This is joint work with Jeremy Hume.