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URLﾘﾝｸ(en.wikipedia.org)
Geometric Langlands correspondence
Status
A claimed proof of the categorical unramified geometric Langlands conjecture was announced on May 6, 2024 by a team of mathematicians including Dennis Gaitsgory.[7][8]
The claimed proof is contained in more than 1,000 pages across five papers and has been called "so complex that almost no one can explain it".
Even conveying the significance of the result to other mathematicians was described as "very hard, almost impossible" by Drinfeld.[9]
Breakthrough Prize なんだね（下記）
URLﾘﾝｸ(en.wikipedia.org)
Dennis Gaitsgory (born 17 November 1973) is an Israeli-American mathematician. He is a mathematician at Max Planck Institute for Mathematics (MPIM) at Bonn and is known for his research on the geometric Langlands program.
Honors and awards
In 2025, he received the Breakthrough Prize in Mathematics.[3]
（Scholzeさん）
URLﾘﾝｸ(www.quantamagazine.org)
Quanta magazine
Monumental Proof Settles Geometric Langlands Conjecture
Erica Klarreich July 19, 2024
The proof represents the culmination of three decades of effort, said Peter Scholze(opens a new tab), a prominent mathematician at the Max Planck Institute for Mathematics who was not involved in the proof. “It’s wonderful to see it resolved.”
Dennis Gaitsgory (left) and Sam Raskin led the nine-person team that proved the geometric Langlands conjecture.
URLﾘﾝｸ(breakthroughprize.org)
Breakthrough Prize 2025 April 5, 2025 – Los Angeles
Mathematics
Dennis Gaitsgory wins the Breakthrough Prize in Mathematics for his central role in the proof of the geometric Langlands conjecture. The Langlands program is a broad research program spanning several fields of mathematics. It grew out of a series of conjectures proposing precise connections between seemingly disparate mathematical concepts. Such connections are powerful tools; for example, the proof of Fermat’s Last Theorem reduces to a particular instance of the Langlands conjecture. These Langlands program equivalences can be thought of as generalizations of the Fourier transform, a tool that relates waves to frequency spectrums and has widespread uses from seismology to sound engineering.
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