Homological mirror symmetry

URI: https://gptkb.org/entity/Homological_mirror_symmetry
GPTKB entity
Statements (33)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:field gptkb:algebraic_geometry
gptkb:mathematics
mathematical physics
symplectic geometry
gptkbp:formedBy gptkb:Maxim_Kontsevich
1994
gptkbp:hasApplication gptkb:D-branes
gptkb:Calabi-Yau_manifolds
gptkb:topological_field_theory
enumerative geometry
gptkbp:hasConjectureStatus open
gptkbp:hasProofsOf gptkb:toric_varieties
gptkb:K3_surfaces
elliptic curves
quartic surfaces
https://www.w3.org/2000/01/rdf-schema#label Homological mirror symmetry
gptkbp:influenced gptkb:string_theory
representation theory
categorical geometry
gptkbp:referencedIn Kontsevich, M. (1994). Homological algebra of mirror symmetry. Proceedings of the International Congress of Mathematicians.
gptkbp:relatedTo gptkb:mirror_symmetry
gptkb:Fukaya_category
gptkb:derived_category_of_coherent_sheaves
gptkbp:state Fukaya category of a symplectic manifold is equivalent to the derived category of coherent sheaves on the mirror dual
gptkbp:surveyedBy Alexander Polishchuk, 2009
Denis Auroux, 2007
Maxim Kontsevich, 1994 ICM address
Paul Seidel, 2001
gptkbp:bfsParent gptkb:Fourier–Mukai_transform
gptkb:Mirror_symmetry
gptkb:Mirror_Symmetry
gptkbp:bfsLayer 7