ProvedAlgebra·2024
Geometric Langlands Conjecture
The 'grand unification' connecting number theory, algebraic geometry, and representation theory.
The Langlands program is often called the 'grand unified theory of mathematics.' The geometric Langlands conjecture establishes an equivalence between D-modules on BunG and quasi-coherent sheaves on LocSysĞ. Gaitsgory led a 30-year effort culminating in 5 papers totaling 800+ pages.
Summary
The Langlands program is often called the 'grand unified theory of mathematics.' The geometric Langlands conjecture establishes an equivalence between D-modules on BunG and quasi-coherent sheaves on LocSysĞ. Gaitsgory led a 30-year effort culminating in 5 papers totaling 800+ pages.