topology – Quanta Magazine

Monumental Proof Settles Geometric Langlands Conjecture

Erica Klarreich — Fri, 19 Jul 2024 14:02:17 +0000

A group of nine mathematicians has proved the geometric Langlands conjecture, a key component of one of the most sweeping paradigms in modern mathematics. The proof represents the culmination of three decades of effort, said Peter Scholze, a prominent mathematician at the Max Planck Institute for Mathematics who was not involved in the proof. “It’s wonderful to see it resolved.

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How Failure Has Made Mathematics Stronger

Jordana Cepelewicz — Wed, 22 May 2024 14:15:33 +0000

Reading a math paper is a bit like having dinner at a nice restaurant. The entrée might taste delicious, but it doesn’t tell the full story of how it was made. Clever recipes that end up tasting funky don’t make the menu; undercooked dishes are (usually) not served to customers. But missteps in both conception and execution are important parts of the process. Danny Calegari, a topologist at the...

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Strangely Curved Shapes Break 50-Year-Old Geometry Conjecture

Jordana Cepelewicz — Tue, 14 May 2024 14:12:40 +0000

In an old Indian parable, six blind men each touch a different part of an elephant. They disagree about what the elephant must look like: Is it smooth or rough? Is it like a snake (so thinks the man touching the trunk) or a fan (as the man touching the ear proposes)? If the blind men had combined their insights, they might have been able to give a correct account of the nature of the elephant.

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Mathematicians Marvel at ‘Crazy’ Cuts Through Four Dimensions

Jordana Cepelewicz — Mon, 22 Apr 2024 15:22:13 +0000

The central objects of study in topology are spaces called manifolds, which look flat when you zoom in on them. The surface of a sphere, for instance, is a two-dimensional manifold. Topologists understand such two-dimensional manifolds very well. And they have developed tools that let them make sense of three-dimensional manifolds and those with five or more dimensions. But in four dimensions...

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Topologists Tackle the Trouble With Poll Placement

Lyndie Chiou — Tue, 26 Mar 2024 13:50:38 +0000

In Georgia’s 2020 gubernatorial election, some voters in Atlanta waited over 10 hours to cast a ballot. One reason for the long lines was that almost 10% of Georgia’s polling sites had closed over the preceding seven years, despite an influx of about 2 million voters. These closures were disproportionately concentrated in predominantly Black areas that tended to vote Democratic.

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