Proof of the geometric Langlands conjecture
Prueba de la conjetura de Langlands geométrica
- Date
- 2024 · confidence high
- Place
- Cambridge, Massachusetts (Harvard) and Bonn (Max Planck Institute)
- Credited to
- Dennis Gaitsgory, Sam Raskin and collaborators (nine authors)
- People
- 👤 Dennis Gaitsgory1973–👤 Sam Raskin1987–
- Field
- Knowledge & symbols
What was discovered
A series of five papers totalling around 900 pages that prove the geometric version (over curves and sheaves) of the Langlands programme, after three decades of work. Confirmation of mathematics's largest web of conjectures on one of its three fronts.
Gaitsgory received the 2025 Breakthrough Prize; full verification by the community is still ongoing.
What it led to
- advances in arithmetic and local Langlands
- connections with quantum field theory
- derived algebraic geometry
Built on
- Langlands program1967
- Langlands programme
- Drinfeld and Laumon
- derived algebraic geometry (Lurie)