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HLF Blogs – Michael Atiyah’s Favourite Manifold

This week, Katie and Paul are blogging from the Heidelberg Laureate Forum – a week-long maths conference where current young researchers in maths and computer science can meet and hear talks by top-level prize-winning researchers. For more information about the HLF, visit the Heidelberg Laureate Forum website.

As part of the HLF, the Laureates are participating in press conferences throughout the week, and being bombarded with questions by well-meaning journalists and bloggers. Unlike most press conferences, where participants often have a specific topical thing they’re there to speak to the press about, the Laureates can be asked about any of their past projects, on any area of maths they’ve worked on, and many of them have a very long and illustrious career to speak of.

It can be difficult then, to be put on the spot by a taxing question, especially if you’re not expecting it. I’ve been surprising the topologists whose press conferences I’ve attended with a deceptively deep but simple question: What’s your favourite manifold?

Best way to explain topology: now officially ‘using baked goods’

Nobel Prize news!

The 2016 Nobel Prize in Physics has been awarded to a trio of physicists: Michael Kosterlitz, Duncan Haldane and David Thouless“for theoretical discoveries of topological phase transitions and topological phases of matter”.

And here’s the maths angle – their work is in the field of topological physics, which relates strange matter (superconductors, superfluids and the like) to topology, via the interesting way the properties of the materials change in phases, like the different fundamental shapes of objects in topology. None of the material we’ve taken a cursory glance at so far yields a simple explanation of how these two things are linked, but they have explanatory PDFs on the Nobel website if you’d like a dig around: Popular (PDF) and Advanced (PDF).

Also, impressively many newspaper headlines seem to have failed to notice that ‘strange matter’ is actually a thing in physics, and consequently mangled it in their explanations.

Cue of course an amazing press conference in which Nobel Committee for Physics member Thors Hans Hansson holds up a bun, a bagel and a pretzel to explain the difference. Classic topology.

More information

Official Nobel press release

British scientists win Nobel prize in physics for work so baffling it had to be described using bagels, at The Telegraph (bonus points for ‘Noble prize’ typo, if it’s not been corrected yet)

Physics prize explanations on the Nobel website: Popular (PDF) and Advanced (PDF)


Review: Cakes, Custard and Category Theory by Eugenia Cheng


We’ve often mentioned category theorist and occasional media-equation-provider Eugenia Cheng on the site, and she’s now produced a book, Cakes, Custard and Category Theory, which we thought we’d review. In a stupid way.

Mary Ellen Rudin (1924-2013)

Mary Ellen Rudin, one of the pioneers of set-theoretical topology, passed away this week. She was 88.

Topology Gossip

Brubeck is a database of topological information, à la the classic Counterexamples in Topology. It contains descriptions of several important topological spaces and properties and the interrelationships between each of them.

This is quite interesting. Brubeck, by James Dabbs, is a bit like Number Gossip but for topological spaces: it presents you with a search box into which you can type a list of properties you want a topology to have or not have, and it returns a list of matches. It also automatically geenerates proofs (really simple implication trees) based on theorems it’s been told and the facts it is given about spaces, and displays its working-out graphically.

Site: Brubeck

Source: /r/math

All metro systems eventually have the same shape

The BBC and Scientific American report on a paper looking, “in an exploratory manner,” at the limiting shape of metro systems serving large cities. The BBC linked to the actual paper, which is nice of them. The Scientific American article goes into a bit more detail, though.

The authors contend that rather than the shape of subway networks being decided by central planning, which would produce a variety of shapes, the eventual shape of a subway network converges on an emergen structure consisting of a dense core with branches radiating from it.