abstract:In the theory of automorphic forms, an area of mathematics, the fundamental lemma relates orbital integrals on a reductive group over a local field to stable orbital integrals on its endoscopic groups. It was conjectured by in the course of developing the Langlands program.
As its name suggests, the FundamentalLemmais a technical point, but one that had stymied mathematiciansfor decades. Ngo'sbreakthroughmakesotheradvances in theLanglandsProgram look possible.