Short··0:22·Algebraic and complex geometry
Quantum Geometric Langlands: OpenAI Claims the Irrational Level
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About this video
The quantum geometric Langlands conjecture says a group G and its Langlands dual group are two views of the same mathematics: twisted D-modules on Bun_G of a curve at level c should match those for the dual group at level -1/(rc). OpenAI claims a proof of the unramified equivalence for every connected simple complex group, every smooth projective curve and every irrational level, including non-real levels; this is OpenAI's preprint and has not yet been peer reviewed.
Paper (OpenAI, catalogue result 069):
- Global quantum geometric Langlands at irrational level: github.com/openai/math/blob/main/preprints/Global-quantum-geo…
The rods are the real root systems of Spin(7) and its dual Sp(6) (r = 2), and the dual level is computed exactly as -1/(2c).
The animation illustrates the result; it is not a proof.
Gradient Damage: mathematics you can see, equations you can hear.
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Every result explained: gradientdamage.com/p/069
About the problem
Algebraic and complex geometry·OpenAI Math·Result 069
Global quantum geometric Langlands at irrational level
Proves the unramified de Rham quantum geometric Langlands equivalence for every connected simple complex algebraic group on every smooth projective connected complex curve, at every shifted level c ∈ ℂ∖ℚ. It identifies the full derived categories of twisted D-modules for the group and its Langlands dual, retaining all global forms and connected components.
Topics
quantum geometric Langlandsgeometric LanglandsLanglands programLanglands dualityLanglands dual groupquantum Langlandsirrational levelD-modulesBun_Galgebraic curvesRiemann surfacesroot systemsS-dualityrepresentation theoryalgebraic geometryOpenAIOpenAI mathAI mathematicsAI proofmathsmathematicsmath shorts3D animation
