Fields medal for Peter Scholze about fractals

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Offline RedshiftRider

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« on: August 01, 2018, 06:15:19 PM »
I just heard via the radio that the mathematician Peter Scholze was awarded with the fields medal for his findings on perfectoid spaces, a type of fractal.

Unfortunately my connection here is pretty slow so I have not been able to read a bit more about it.

Offline Fraktalist

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« Reply #1 on: August 01, 2018, 08:08:45 PM »
thx for the info -seems to be quite important news:

If anyone who understands them could give an ELI5 (explain like I'm 5) on those perfectoid spaces that would be awesome and probably helping many here.

Offline RedshiftRider

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« Reply #2 on: August 01, 2018, 08:16:34 PM »
Thank you Fraktalist.

Yes a eli5 would definitely be useful, the perfectoid spaces seem pretty conplicated to me.

Offline claude

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« Reply #3 on: August 04, 2018, 09:03:12 PM »
The youngest for the four winners, Germany’s Peter Scholze, became a professor at the age of just 24, and has been described by previous award committees as “already one of the most influential mathematicians in the world.”

Among his achievements, Scholze invented the theory of perfectoid spaces – which are noted in his citation for the Fields medal, and have been described as a class of fractal structures allowing problems to be moved from one number system to another, making them easier to solve.

“Geometry is the study of space and shape,” said Kevin Buzzard of Imperial College London. “One technique that geometers have introduced is the idea of studying a complicated space by mapping a simpler space onto it. For example, a line is a simpler object than a circle. But if you imagine wrapping a line up into a spring shape and compressing the spring, you have found a way of mapping a line into a circle. Geometers might use this technique to analyse questions about circles, by turning them into perhaps more complex questions about lines.”

Perfectoid spaces, he says, turns this logic on its head. “The counterintuitive idea introduced by Scholze is that to study a geometric object, you might instead want to find a mapping from a space which is so grotesque and twisted that in some sense it cannot be twisted up any more. The result is that instead of ending up having to solve complicated questions about simple objects, you have to solve simple questions about extremely complicated objects.”

Offline gerrit

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« Reply #4 on: August 06, 2018, 03:10:30 AM »
I don't understand what his work has to do with fractals, apart from some journalist throwing in that word.

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