Mathematicians recently proved a central component of the Langlands program, an ambitious effort to develop a “grand unified theory” of mathematics. The monumental proof of the geometric Langlands conjecture totaled more than 800 pages and marked the culmination of 30 years of work by nine mathematicians.
You can watch Quanta’s video explainer about the full Langlands program here: https://www.youtube.com/watch?v=_bJeKUosqoY
Read the Quanta Magazine Article:
https://www.quantamagazine.org/monumental-proof-settles-geometric-langlands-conjecture-20240719/
PAPER
- D. Gaitsgory, S. Raskin D. Arinkin, D. Beraldo, J. Campbell, L. Chen, J. Faergeman, D. Gaitsgory, K. Lin, S. Raskin and N. Rozenblyum (2024) "Proof of the geometric Langlands conjecture" - https://people.mpim-bonn.mpg.de/gaitsgde/GLC/
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00:00 Introduction
01:01 What is the Langlands Programs?
01:35 Fourier theory and analysis
02:23 Fourier transform, building blocks and labels
04:37 Sheaves as building blocks
05:49 Geometric Langlands and eigensheaves
06:30 Gaitsgory and his fundamental diagram
07:01Poincaré sheaf and the solution to conjecture
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