[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 77 (1002ﾚｽ)
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625(2): 現代数学の系譜 雑談 ◆yH25M02vWFhP 11/09(日)16:02 ID:QrKJGO9s(15/26) AAS
つづき
In the case of the geometric Langlands conjecture, the proposed one-to-one correspondence is between two very different sets of objects, analogous to these spectrums and waves: on the spectrum side are abstract algebraic objects called representations of the fundamental group, which capture information about the kinds of loop that can wrap around certain complex surfaces; on the “wave” side are sheaves, which, loosely speaking, are rules assigning vector spaces to points on a surface. Gaitsgory has dedicated much of the last 30 years to the geometric Langlands conjecture. In 2013 he wrote an outline of the steps required for a proof, and after more than a decade of intensive research in 2024 he and his colleagues published the full proof, comprising over 800 pages spread over 5 papers. This is a monumental advance, expected to have deep implications in other areas of mathematics too, including number theory, algebraic geometry and mathematical physics.
2025 New Horizons in Mathematics Prize
Sam Raskin, Yale University
For contributions to the geometric Langlands program, including the theory of the Whittaker model and the proof of the geometric Langlands conjecture in characteristic 0.
外部ﾘﾝｸ:people.mpim-bonn.mpg.de
Proof of the geometric Langlands conjecture
This page contains five papers, the combined content of which constitutes the proof of the (categorical, unramified) geometric Langlands conjecture.
This is a collaborative project of D. Arinkin, D. Beraldo, J. Campbell, L. Chen, J. Faergeman, D. Gaitsgory, K. Lin, S. Raskin and N. Rozenblyum.
Papers:
省7
636(1): 現代数学の系譜 雑談 ◆yH25M02vWFhP 11/09(日)16:35 ID:QrKJGO9s(16/26) AAS
>>624-625
さて
Geometric Langlands correspondence
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
（Scholzeさん）
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.”
(引用終り)
1）これが、査読され雑誌掲載されたかどうかを 追跡したが
省11
638: 11/09(日)16:52 ID:CA6TFgJW(32/64) AAS
>>624-625
ホッブス世田は、くだらんコピペをする暇があったら
・コーシー列の定義と解析学における意義
・線形独立の定理と線形代数学における意義
を理解するほうが先だろう
公式だけ覚えればOKみたいな
「ガリ勉高校生の一夜漬け勉強法」
では現代数学はちょっとも理解できんよ
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