Editing Langlands program (section)

{{short description|Far-reaching conjectures connecting number theory and geometry}}
{{More footnotes|date=June 2022}}

In [[mathematics]],  the '''Langlands program''' is a set of [[conjecture]]s about connections between [[number theory]], the theory of [[automorphic forms]], and [[geometry]]. It was proposed by {{harvs|txt|authorlink=Robert Langlands|first=Robert|last=Langlands|year1=1967|year2=1970}}. It seeks to relate the structure of [[Galois group]]s in [[algebraic number theory]] to [[automorphic form]]s and, more generally, the [[group representation|representation theory]] of [[algebraic group]]s over [[local field]]s and [[Adele ring|adele]]s. It was described by [[Edward Frenkel]] as the "[[Grand Unified Theory|grand unified theory]] of mathematics."<ref>{{cite web |title=Math Quartet Joins Forces on Unified Theory |work=[[Quanta Magazine|Quanta]] |date=December 8, 2015 |url=https://www.quantamagazine.org/math-quartet-joins-forces-on-unified-theory-20151208/ }}</ref>