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: TBA
Abstract: TBA
Speaker: Hannes Thiel (Chalmers University of Technology and University of Gothenburg)
Title: TBA
Abstract: TBA
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.
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