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New Shape Opens ‘Wormhole’ Between Numbers and Geometry

3 hours ago

Created a post 52 points @theafh

New Shape Opens ‘Wormhole’ Between Numbers and Geometry

@rohanphadte 41 minutes

Replying to @theafh 🎙

Sizable article - write down a few highlights about the Langlands program.

> Mathematics has received a rare gift, in the form of a mammoth 350-page paper posted in February that will change the way researchers around the world investigate some of the field’s deepest questions.

> The work is a collaboration between Laurent Fargues of the Institute of Mathematics of Jussieu in Paris and Peter Scholze of the University of Bonn.

> It opens a new front in the long-running “Langlands program,” which seeks to link disparate branches of mathematics — like calculus and geometry — to answer some of the most fundamental questions about numbers.

> The Langlands program is a sprawling research vision that begins with a simple concern: finding solutions to polynomial equations like x2 − 2 = 0 and x4 − 10x2 + 22 = 0.

> “The Langlands program is a network of conjectures that touch upon almost every area of pure mathematics,” said Caraiani.

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@jesuslop 2 hours

Replying to @theafh 🎙

It's about Scholze work on perfectoid spaces. A nice intro talk in Spanish is at https://cienciastv.org.mx/2020/08/el-mundo-perfectoide-adria...

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