Erica Klarreich in Quanta:
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.”
The Langlands program, originated by Robert Langlands in the 1960s, is a vast generalization of Fourier analysis, a far-reaching framework in which complex waves are expressed in terms of smoothly oscillating sine waves. The Langlands program holds sway in three separate areas of mathematics: number theory, geometry and something called function fields. These three settings are connected by a web of analogies commonly called mathematics’ Rosetta stone.
Now, a new set of papers has settled the Langlands conjecture in the geometric column of the Rosetta stone.
More here.
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