Past Functional Analysis Seminar

2 July 2020
16:00
to
17:30
Nigel Higson

Further Information: 

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

Abstract

Abstract: John Roe was a much admired figure in topology and noncommutative geometry, and the creator of the C*-algebraic approach to coarse geometry. John died in 2018 at the age of 58. My aim in the first part of the lecture will be to explain in very general terms the major themes in John’s work, and illustrate them by presenting one of his best-known results, the partitioned manifold index theorem. After the break I shall describe a later result, about relative eta invariants, that has inspired an area of research that is still very active.


Assumed Knowledge: First part: basic familiarity with C*-algebras, plus a little topology. Second part: basic familiarity with K-theory for C*-algebras.

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  • Functional Analysis Seminar
18 June 2020
16:45
Matthew Kennedy

Further Information: 

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

Abstract

Since the work of von Neumann, the theory of operator algebras has been closely linked to the theory of groups. On the one hand, operator algebras constructed from groups provide an important source of examples and insight. On the other hand, many problems about groups are most naturally studied within an operator-algebraic framework. In this talk I will give an overview of some problems relating the structure of a group to the structure of a corresponding C*-algebra. I will discuss recent results and some possible future directions.

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  • Functional Analysis Seminar
18 June 2020
16:00
Ivan Todorov

Further Information: 

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

Abstract

The study of non-local games has involved fruitful interactions between operator algebra theory and quantum physics, with a starting point the link between the Connes Embedding Problem and the Tsirelson Problem, uncovered by Junge et al (2011) and Ozawa (2013). Particular instances of non-local games, such as binary constraint system games and synchronous games, have played an important role in the pursuit of the resolution of these problems. In this talk, I will summarise part of the operator algebraic toolkit that has proved useful in the study of non-local games and of their perfect strategies, highlighting the role C*-algebras and operator systems play in their mathematical understanding.

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  • Functional Analysis Seminar
4 June 2020
16:45
Hannes Thiel

Further Information: 

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

Abstract

The Cuntz semigroup is a geometric refinement of K-theory that plays an important role in the structure theory of C*-algebras. It is defined analogously to the Murray-von Neumann semigroup by using equivalence classes of positive elements instead of projections.
Starting with the definition of the Cuntz semigroup of a C*-algebra, we will look at some of its classical applications. I will then talk about the recent breakthroughs in the structure theory of Cuntz semigroups and some of the consequences.

  • Functional Analysis Seminar
4 June 2020
16:00
Ana Khurkho

Further Information: 

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

Abstract

After recalling some motivation for studying highly-connected graphs in the context of operator algebras and large-scale geometry, we will introduce the notion of "asymptotic expansion" recently defined by Li, Nowak, Spakula and Zhang. We will explore some applications of this definition, hopefully culminating in joint work with Li, Vigolo and Zhang.

  • Functional Analysis Seminar
21 May 2020
16:45
Alain Valette

Further Information: 

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

Abstract

We will introduce the Baum-Connes conjecture without coefficients, in the setting of discrete groups, and try to explain why it is interesting for operator algebraists. We will give some idea of the LHS and the RHS of the conjecture, without being too formal, and rather than trying to define the assembly map, we will explain what it does for finite groups, for the integers, for free groups, and finally for wreath products of a finite group with the integers (the latter result is joint work with R. Flores and S. Pooya; it raises a few open questions about classifying the corresponding group C*-algebras up to isomorphism).

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  • Functional Analysis Seminar
21 May 2020
16:00
Kirstin Courtney

Further Information: 

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

Abstract

In January of this year, a solution to Connes' Embedding Problem was announced on arXiv. The paper itself deals firmly in the realm of information theory and relies on a vast network of implications built by many hands over many years to get from an efficient reduction of the so-called Halting problem back to the existence of finite von Neumann algebras that lack nice finite-dimensional approximations. The seminal link in this chain was forged by astonishing results of Kirchberg which showed that Connes' Embedding Problem is equivalent to what is now known as Kirchberg's QWEP Conjecture. In this talk, I aim to introduce Kirchberg's conjecture and to touch on some of the many deep insights in the theory surrounding it.

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  • Functional Analysis Seminar
14 May 2020
16:00
Francesca Arici

Further Information: 

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

Abstract

In 1997 Pimsner described how to construct two universal C*-algebras associated with an injective C*-correspondence, now known as the Toeplitz--Pimsner and Cuntz--Pimsner algebras. In this talk I will recall their construction, focusing for simplicity on the case of a finitely generated projective correspondence. I will describe the associated six-term exact sequence in K(K)-theory and explain how these can be used in practice for computational purposes. Finally, I will describe how, in the case of a self-Morita equivalence, these exact sequences can be interpreted as an operator algebraic version of the classical Gysin sequence for circle bundles.

  • Functional Analysis Seminar
30 April 2020
16:45
Christian Bonicke

Further Information: 

UK Virtual operator algebras seminar by zoom: https://sites.google.com/view/uk-operator-algebras-seminar/home

Abstract

Having its roots in classical operator theoretic questions, the theory of extensions of C*-algebras is now a powerful tool with applications in geometry and topology and of course within the theory of C*-algebras itself. In this talk I will give a gentle introduction to the topic highlighting some classical results and more recent applications and questions.

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  • Functional Analysis Seminar

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