geometric Langlands program

URI: https://gptkb.org/entity/geometric_Langlands_program

GPTKB entity

Statements (50)

Predicate	Object
gptkbp:instanceOf	gptkb:logic
gptkbp:field	gptkb:algebraic_geometry gptkb:mathematics number theory representation theory
gptkbp:focusesOn	automorphic forms Galois representations sheaves moduli spaces of bundles
gptkbp:generalizes	gptkb:classical_Langlands_program
gptkbp:hasApplication	gptkb:quantum_field_theory gptkb:string_theory
https://www.w3.org/2000/01/rdf-schema#label	geometric Langlands program
gptkbp:influencedBy	gptkb:algebraic_geometry mathematical physics number theory representation theory
gptkbp:notableContributor	gptkb:David_Kazhdan gptkb:Edward_Frenkel gptkb:Vladimir_Drinfeld gptkb:Alexander_Beilinson gptkb:Dennis_Gaitsgory gptkb:Roman_Bezrukavnikov
gptkbp:notableWork	Beilinson-Drinfeld's work on chiral algebras Kapustin-Witten's work on S-duality and gauge theory Frenkel-Gaitsgory-Vilonen's work on Hecke eigensheaves
gptkbp:originatedIn	1980s
gptkbp:relatedTo	gptkb:S-duality_in_physics gptkb:categorical_Langlands_correspondence gptkb:geometric_Satake_equivalence gptkb:global_geometric_Langlands_correspondence gptkb:Langlands_program gptkb:D-modules gptkb:Hitchin_fibration gptkb:arithmetic_Langlands_program local geometric Langlands correspondence perverse sheaves moduli stack of bundles
gptkbp:studies	Hecke operators correspondence between local systems and automorphic sheaves moduli of G-bundles categorical equivalences duality of reductive groups
gptkbp:uses	gptkb:category_theory gptkb:D-modules algebraic curves perverse sheaves
gptkbp:bfsParent	gptkb:Alexander_Beilinson gptkb:Dennis_Gaitsgory
gptkbp:bfsLayer	5