Tue, 14 Oct 2025
16:00
C3

Homotopy groups of Cuntz classes in C*-algebras

Andrew Toms
(Leverhulme Visiting Professor, University of Oxford)
Abstract

The Cuntz semigroup of a C*-algebra A consists of equivalence classes of positive elements, where equivalence means roughly that two positive elements have the same rank relative to A.  It can be thought of as a generalization of the Murray von Neumann semigroup to positive elements and is an incredibly sensitive invariant. We present a calculation of the homotopy groups of these Cuntz classes as topological subspaces of A when A is classifiable in the sense of Elliott.  Remarkably, outside the case of compact classes, these spaces turn out to be contractible.  

Song of the Week: Frédéric Chopin - Nocturne Op.9 No.1

In the week the Prince of Darkness Ozzy Osbourne died, here's a nocturne by Chopin. Actually Ozzy has been due to feature in the Bulletin for some time, but not necessarily in Song of the Week. Watch this space. 

RIP Ozzy (if appropriate in your case).

The pianist is Canadian Jan Lisiecki.

Waves on glaciers
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Short stories 2

And here's part two starring Ellie and Sienna from the Mirzakhani Society . If you wonder at the title (Etc.) the post was accompanied by the text: "Mathematicians are all the same. They look the same. They only like other mathematicians. They only like maths. They did nothing but maths from the age of two. Etc."

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From metric to action: An evaluation framework to translate infectious disease forecasts into policy decisions
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Where was your mathematical light bulb moment?

Where were you when you had that moment when things became mathematically clear (if they ever have).

We're looking to do a short series of films on places that inspire after the success of last year's places you go to get away from maths.

Drop Dyrol a line. We'll also be coming round with the camera so shut your doors if you don't fancy it.

Image: Caspar David Friedrich - Wanderer above the Sea of Fog

Strong gradient effects on neoclassical electron transport and the bootstrap current in large aspect ratio tokamaks
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UKRI & research culture

UKRI (UK Research and Innovation) has recently launched a Good Practice Exchange Survey to help develop a plan for research culture.

It’s targeted at anyone that has a passing interest or involvement in anything research culture related. It closes on 10 August.

L’Oréal-UNESCO For Women in Science UK and Ireland Young Talent Awards

The L’Oréal-UNESCO For Women in Science UK and Ireland Young Talent Awards is an annual programme that awards grants worth £25,000 to five outstanding early-career women scientists in the fields of Engineering, Life Sciences, Mathematics and Computer Science, Physical Sciences and Sustainable Development.  

The grants are designed to provide flexible and practical financial support to enable these women scientists to further their research and careers.

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