Homological mirror symmetry conjecture

URI: https://gptkb.org/entity/Homological_mirror_symmetry_conjecture
GPTKB entity
Statements (32)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:appliesTo gptkb:Calabi–Yau_manifolds
gptkbp:category1 gptkb:derived_category_of_coherent_sheaves
gptkbp:category2 gptkb:Fukaya_category
gptkbp:field gptkb:algebraic_geometry
mathematical physics
symplectic geometry
gptkbp:formedBy gptkb:Maxim_Kontsevich
1994
gptkbp:hasApplication gptkb:D-branes_in_string_theory
enumerative geometry
gptkbp:hasProofsOf gptkb:toric_varieties
elliptic curves
quartic surfaces
https://www.w3.org/2000/01/rdf-schema#label Homological mirror symmetry conjecture
gptkbp:influenced gptkb:string_theory
derived algebraic geometry
categorical approaches in geometry
gptkbp:notablePerson gptkb:Alexander_Polishchuk
gptkb:Paul_Seidel
gptkb:Ludmil_Katzarkov
gptkb:Dmitri_Orlov
Denis Auroux
gptkbp:relatedConcept gptkb:A-model
gptkb:B-model
gptkbp:relatedTo gptkb:mirror_symmetry
gptkb:topological_field_theory
string duality
gptkbp:state derived category of coherent sheaves on a Calabi–Yau manifold is equivalent to the Fukaya category of its mirror
gptkbp:surveyedBy Maxim Kontsevich, 1994 ICM address
gptkbp:bfsParent gptkb:Maxim_Kontsevich
gptkbp:bfsLayer 6