Speaker: Siegfried Echterhoff (University of Münster)
Title: TBA
Abstract: TBA
Speaker: Piotr Nowak (Polish Academy of Sciences)
Title: Cocycles and positive functionals in higher cohomology
Abstract: The GNS is a fundamental tool in operator algebras and group cohomology, where it provides a correspondence between positive functionals on one hand, and unitary representations and associated 1-cocycles on the other.
I will present a generalization of the GNS construction, for which the correct setting turns out to be higher unitary cohomology of a group. Our higher cocycle GNS construction provides a correspondence between positive functionals on certain subspaces of the algebras of matrices with group ring coefficients on one hand, and unitary representations and associated higher cocycles on the other.
As applications we prove new characterizations of higher property (T), via an extension property of positive functionals, as well as in terms of an algebraic spectral gap for the upper Laplacian.
This joint work with Antonio Lopez Neumann.
Speaker: Narutaka Ozawa (Research Institute for Mathematical Sciences, Kyoto University)
Title: Selfless (group) C*-algebras
Abstract: I will discuss the selfless property for C*-algebras, with particular emphasis on group C*-algebras. After recalling the basic framework and motivation, I will explain some results and examples mainly arising from groups.
Speaker: Francesc Perera (Universitat Autònoma de Barcelona)
Title: TBA
Abstract: TBA
Speaker: Jean Renault (Université d'Orléans)
Title: Noncommutative solenoids and their projective modules
Abstract: Noncommutative p-solenoids are a p-adic version of noncommutative tori. Their study is analogous to that of rotation algebras and relies on it. I shall give a classiffcation, up to isomorphism and up to Morita equivalence, of noncommutative p-solenoids in terms of their angle of rotation, when this angle is irrational. I shall also give a geometrical construction of their projective modules. This is a joint work with Paulo Carrillo Rouse and Laurent Guillaume.
Speaker: Kasia Rejzner (University of York)
Title: TBA
Abstract: TBA
Speaker: Karen Strung (Czech Academy of Sciences)
Title: Purely infinite orbit-breaking constructions
Abstract: Orbit-breaking in topological dynamical systems was introduced by Ian Putnam in his study of the C*-algebras associated to Cantor minimal systems. By breaking an orbit at a single point, Putnam was able to construct all simple unital AF algebras as subalgebras by way of a Cantor minimal system. Since then, orbit-breaking algebras have been used to construct dynamical models for many stably finite "classifiable" C*-algebras.
In this talk, I introduce orbit-breaking of a surjective local homeomorphism. The C*-algebraic output is a simple and purely infinite C*-algebra embedded in the Cuntz algebra on two generators or its stabilization. We can realise all stable UCT Kirchberg algebras in this way. The construction also provides Cartan subalgebras of arbitrarily high (finite) dimension. Furthermore, if A and B are stable UCT Kirchberg algebras with K_*(A)=G_*, K_*(B) = H_*, we show that a group homomorphism from G_* to H_* gives rise to an explicit embedding of A into B.
This is joint work with Robin Deeley and Ian Putnam.
Speaker: Nóra Szakács (University of Manchester)
Title: TBA
Abstract: TBA
Speaker: Takuya Takeishi (Kyoto Institute of Technology)
Title: Boundary actions of outer automorphism groups of Thompson-like groups
Abstract: This talk presents a recent result of the speaker on the C*-simplicity of the outer automorphism groups of Higman–Thompson groups. More generally, for every Cuntz–Krieger groupoid, there is a topologically free boundary action of the outer automorphism group of its topological full group on the Hilbert cube. This is a joint work with C. Bruce and X. Li.
Speaker: Hannes Thiel (Chalmers University of Technology and University of Gothenburg)
Title: Comparison in dynamical systems and type semigroups
Abstract: Dynamical comparison means that an inequality between open sets detected by all invariant measures can be upgraded to a geometric comparison, by cutting one set into pieces and moving them disjointly into the other. It is the dynamical analogue of strict comparison for C*-algebras. Comparison is known to hold for many minimal systems, but not in general.
We show that a weak form of dynamical comparison always holds: comparison of open sets by invariant measures leads to geometric comparison after removing a set that is uniformly small with respect to all invariant measures. As an application, we show that a minimal system has dynamical comparison if and only if all of its amplifications do, if and only if its type semigroup is almost unperforated.
This is joint work with Bartosz Kwaśniewski, Akshara Prasad, and Jianchao Wu.
Speaker: Hang Wang (East China Normal University)
Title: Approximately Macroscopically Unique States and the Synthetic Spectrum of Quantum Systems
Abstract: The transition from quantum mechanics to the classical macroscopic world remains a profound puzzle in physics. To mathematically characterize this emergence of classicality, David Mumford proposed the concept of Approximately Macroscopically Unique (AMU) states, which behave classically for a set of almost-commuting macroscopic observables. In this talk, I will present recent joint work with Huaxin Lin to rigorously establish the existence of AMU states for quantum systems consisting of unbounded self-adjoint operators with small commutators. To tackle the inherent lack of exact joint eigenvectors for non-commuting observables, we employ the framework of the synthetic spectrum. To bring these abstract concepts down to earth, we will walk through explicit calculations of fundamental physical paradigms, showing exactly how this mathematical machinery works in practice.
Speaker: Daniel Beltita
Title: C*-rigidity for Lie groups
Abstract: We will discuss the question of the extent to which a given Lie group can be distinguished from other Lie groups in terms of its corresponding unitary representation theory. In particular, we prove that the Heisenberg groups are strongly $C^*$-rigid, that is, they are uniquely determined within the class of connected, simply connected Lie groups, in terms of the Morita equivalence class of their group $C^*$-algebras. The presentation is based on joint work with Ingrid Beltita.
Speaker: Soham Chakraborty (École Normale Supérieure)
Title: A Lie theoretic approach to the existence and uniqueness problem for trace scaling flows on full factors.
Abstract: In this talk we shall see how some Lie algebraic techniques can be used to show that if the outer automorphism group of a full II_infinity factor M is a Lie group, then the number of distinct trace scaling flows on M is either zero, one or a continuum. This can then be extended to all locally compact groups using the Gleason-Yamabe theorem. We use this to give the first example of a continuum of pairwise distinct full III_1 factors with the same continuous core. The talk is based on joint work with Sergiu Novac.
Speaker: Jorge Pérez Garcia (Spanish National Research Council)
Title: Schur vs Fourier multipliers
Abstract: The connection between Schur and Fourier multipliers has been a source of inspiration in noncommutative analysis for the last decade and a half. In this talk, we will present an example of a function defining (S_p)-bounded Herz–Schur multipliers but not an (L_p)-bounded Fourier multiplier, for (1<p<\infty). This shows that the equivalence between Herz–Schur and Fourier multipliers proved by Neuwirth and Ricard (2010) cannot, in general, be extended to nonamenable groups.
This is joint work with Adrián M. González-Pérez, Javier Parcet, and Simeng Wang.
Speaker: Ayoub Hafid (University of Tokyo)
Title: Concepts of coarse geometry and Higher index theory on quantum metric spaces.
Abstract: We recall two different concepts of quantum metric spaces, one based on Lipschitz seminorms (by Rieffel and Latremoliere) and the other based on quantum relations (by Kuperberg and Weaver) and introduce a link between them. We then introduce examples of these spaces and show how we can generalize concepts from coarse geometry and higher index theory. In particular we show how a higher index taking value in the K-groups of a Roe algebra can be constructed for locally compact quantum metric spaces under some mild conditions on the commutators of their elements. We finally introduce the Moyal plane as a first example where this theory applies.
Speaker: Malay Mandal (Indian Institute of Science Education and Research, Bhopal)
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Speaker: Micheal O Cobhthaigh (University of Virginia)
Title: Tensor GUE Models, Graph Products, and the MF Property
Abstract: I will discuss a strong convergence result on graph products of tracial C*-algebras. We utilize a GUE model on overlapping tensor supports to encode the graph relations, while operator valued Fock and Toeplitz–Pimsner constructions identify the resulting strong limit. This yields MF permanence results under suitable exactness hypotheses. This is joint work with Nicholas Sweeney.
Speaker: Hridoyananda Saikia (University of Haifa)
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Speaker: Ryo Toyota (University of Copenhagen)
Title: Geometric property of warped cones
Abstract: A warped cone is a construction of metric spaces associated with a dynamical system, whose large-scale geometry reflects dynamical properties of the underlying action. In particular, the expansion property of warped cones can be characterized in terms of spectral gap of the action. In this talk, we discuss when a warped cone has geometric property (T), a strengthening of the expansion property. We explain that the warped cone associated with any free isometric action on a compact Riemannian manifold does not have geometric property (T). In contrast, in the non-isometric setting, the natural action of $SL_n(\mathbb{Z})$ on the torus gives rise to a warped cone with geometric property (T). Part of this talk is based on joint work with Jintao Deng.