Past Functional Analysis Seminar

10 June 2021
16:45
Cornelia Drutu

Further Information: 

Part of UK virtual operator algebras seminar: https://sites.google.com/view/uk-operator-algebras-seminar/home

Abstract

In this talk I will discuss a number of topics at the interface between C* algebras and Geometric Group Theory, with an emphasis on Kazhdan projections, various versions of amenability and their connection to the geometry of groups. This is based on joint work with P. Nowak and J. Mackay.

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  • Functional Analysis Seminar
10 June 2021
16:00
Adam Dor On

Further Information: 

Part of UK virtual operator algebras seminar: https://sites.google.com/view/uk-operator-algebras-seminar/home

Abstract

We showcase some newly emerging connections between the theory of random walks and operator algebras, obtained by associating concrete algebras of operators to random walks. The C*-algebras we obtain give rise to new and interesting notions of ratio limit space and boundary, which are computed by appealing to various works on the asymptotic behavior of transition probabilities for random walks. Our results are leveraged to shed light on a question of Viselter on symmetry-unique quotients of Toeplitz C*-algebras of subproduct systems arising from random walks.

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  • Functional Analysis Seminar
27 May 2021
16:45
Soren Eilers

Further Information: 

Part of UK virtual operator algebras seminar: https://sites.google.com/view/uk-operator-algebras-seminar/home

Abstract

The graph C*-algebra construction associates a unital C*-algebra to any directed graph with finitely many vertices and countably many edges in a way which generalizes the fundamental construction by Cuntz and Krieger. We say that two such graphs are C*-equivalent when they define isomorphic C*-algebras, and give a description of this relation as the smallest equivalence relation generated by a number of "moves" on the graph that leave the C*-algebras unchanged. The talk is based on recent work with Arklint and Ruiz, but most of these moves have a long history that I intend to present in some detail.

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  • Functional Analysis Seminar
27 May 2021
16:00
Emily Peters

Further Information: 

Part of UK virtual operator algebras seminar: https://sites.google.com/view/uk-operator-algebras-seminar/home

Abstract

In this talk I will explain how a subfactor (ie an inclusion of type II_1 factors) give rise to a diagrammatic algebra called the Temperley-Lieb-Jones algebra. We will observe the connection between the index of the subfactor, and the TLJ algebra. In the TLJ algebra setting, we will observe that indices below four are discrete, while any number above four can be an index.

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  • Functional Analysis Seminar
29 April 2021
16:00
Andreas Thom

Further Information: 

Part of UK virtual operator algebras seminar: https://sites.google.com/view/uk-operator-algebras-seminar/home

Abstract

n this talk we consider a p-isometrisability property of discrete groups. If p=2 this property is equivalent to unitarisability. We prove that any group containing a non-abelian free subgroup is not p-isometrisable for any p∈(1,∞). We also discuss some open questions and possible relations of p-isometrisability with the recently introduced Littlewood exponent Lit(Γ).

  • Functional Analysis Seminar
27 April 2021
15:00
Bram Mesland

Further Information: 

Part of UK virtual operator algebras seminar: https://sites.google.com/view/uk-operator-algebras-seminar/home

Abstract

The observation that the Dirac operator on a spin manifold encodes both the Riemannian metric as well as the fundamental class in K-homology leads to the paradigm of noncommutative geometry: the viewpoint that spectral triples generalise Riemannian manifolds. To encode maps between Riemannian manifolds, one is naturally led to consider the unbounded picture of Kasparov's KK-theory. In this talk I will explain how smooth cycles in KK-theory give a natural notion of noncommutative fibration, encoding morphisms noncommutative geometry in manner compatible with index theory.

  • Functional Analysis Seminar
18 February 2021
16:45
Evgenios Kakariadis

Further Information: 

Part of UK virtual operator algebras seminar: https://sites.google.com/view/uk-operator-algebras-seminar/home

Abstract

Continuous product systems were introduced and studied by Arveson in the late 1980s. The study of their discrete analogues started with the work of Dinh in the 1990’s and it was formalized by Fowler in 2002. Discrete product systems are semigroup versions of C*-correspondences, that allow for a joint study of many fundamental C*-algebras, including those which come from C*-correspondences, higher rank graphs and elsewhere.
Katsura’s covariant relations have been proven to give the correct Cuntz-type C*-algebra for a single C*-correspondence X. One of the great advantages of Katsura's Cuntz-Pimsner C*-algebra is its co-universality for the class of gauge-compatible injective representations of X. In the late 2000s Carlsen-Larsen-Sims-Vittadello raised the question of existence of such a co-universal object in the context of product systems. In their work, Carlsen-Larsen-Sims-Vittadello provided an affirmative answer for quasi-lattices, with additional injectivity assumptions on X. The general case has remained open and will be addressed in these talk using tools from non-selfadjoint operator algebra theory.

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  • Functional Analysis Seminar
18 February 2021
16:00
Sam Kim

Further Information: 

Part of UK virtual operator algebra seminar: https://sites.google.com/view/uk-operator-algebras-seminar/home

Abstract

The recent work on nc convex sets of Davidson, Kennedy, and Shamovich show that there is a rich interplay between the category of operator systems and the category of compact nc convex sets, leading to new insights even in the case of C*-algebras. The category of nc convex sets are a generalization of the usual notion of a compact convex set that provides meaningful connections between convex theoretic notions and notions in operator system theory. In this talk, we present a duality theorem for norm closed self-adjoint subspaces of B(H) that do not necessarily contain the unit. Using this duality, we will describe various C*-algebraic and operator system theoretic notions such as simplicity and subkernels in terms of their convex structure. This is joint work with Matthew Kennedy and Nicholas Manor.

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  • Functional Analysis Seminar
3 December 2020
16:00
Vern Paulsen

Further Information: 

Part of UK virtual operator algebras seminar: https://sites.google.com/view/uk-operator-algebras-seminar/home

Abstract

There are many constructions that yield C*-algebras. For example, we build them from groups, quantum groups, dynamical systems, and graphs. In this talk we look at C*-algebras that arise from a certain type of game. It turns out that the properties of the underlying game gives us very strong information about existence of traces of various types on the game algebra. The recent solution of the Connes Embedding Problem arises from a game whose algebra has a trace but no hyperlinear trace.


Assumed knowledge: Familiarity with tensor products of Hilbert spaces, the algebra of a discrete group, and free products of groups.

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  • Functional Analysis Seminar

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