abstract:In mathematics the Langlands program is a web of far-reaching and influential conjectures that relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles. It was proposed by .
As its name suggests, the FundamentalLemmais a technical point, but one that had stymied mathematiciansfor decades. Ngo'sbreakthroughmakesotheradvances in theLanglandsProgram look possible.