homological mirror symmetry conjecture

Target entity: homological mirror symmetry conjecture
Context triple: [Strominger–Yau–Zaslow conjecture, relatesTo, homological mirror symmetry conjecture]

• A. Simons Collaboration on Homological Mirror Symmetry
  The Simons Collaboration on Homological Mirror Symmetry is a research initiative that brings together mathematicians and physicists to advance the theory and applications of homological mirror symmetry.
• B. Strominger–Yau–Zaslow conjecture
  The Strominger–Yau–Zaslow conjecture is a proposal in mirror symmetry stating that mirror pairs of Calabi–Yau manifolds can be understood as dual special Lagrangian torus fibrations, providing a geometric explanation of mirror symmetry.
• C. Duistermaat–Heckman formula
  The Duistermaat–Heckman formula is a result in symplectic geometry that describes how the pushforward of the Liouville measure under a moment map behaves, showing it is piecewise polynomial and linking geometry with equivariant localization techniques.
• D. Calabi–Yau manifold
  A Calabi–Yau manifold is a special type of complex manifold with vanishing first Chern class that plays a central role in string theory compactifications and complex algebraic geometry.
• E. Donaldson–Thomas theory
  Donaldson–Thomas theory is a branch of algebraic geometry and mathematical physics that counts stable sheaves or ideal sheaves on Calabi–Yau threefolds, providing integer-valued invariants related to curve counting and string theory.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: homological mirror symmetry conjecture
Target entity description: The homological mirror symmetry conjecture, proposed by Maxim Kontsevich, posits a deep equivalence between the derived category of coherent sheaves on a Calabi–Yau variety and the Fukaya category of its mirror symplectic manifold, providing a categorical formulation of mirror symmetry.

• A. Simons Collaboration on Homological Mirror Symmetry
  The Simons Collaboration on Homological Mirror Symmetry is a research initiative that brings together mathematicians and physicists to advance the theory and applications of homological mirror symmetry.
• B. Strominger–Yau–Zaslow conjecture
  The Strominger–Yau–Zaslow conjecture is a proposal in mirror symmetry stating that mirror pairs of Calabi–Yau manifolds can be understood as dual special Lagrangian torus fibrations, providing a geometric explanation of mirror symmetry.
• C. Duistermaat–Heckman formula
  The Duistermaat–Heckman formula is a result in symplectic geometry that describes how the pushforward of the Liouville measure under a moment map behaves, showing it is piecewise polynomial and linking geometry with equivariant localization techniques.
• D. Calabi–Yau manifold
  A Calabi–Yau manifold is a special type of complex manifold with vanishing first Chern class that plays a central role in string theory compactifications and complex algebraic geometry.
• E. Donaldson–Thomas theory
  Donaldson–Thomas theory is a branch of algebraic geometry and mathematical physics that counts stable sheaves or ideal sheaves on Calabi–Yau threefolds, providing integer-valued invariants related to curve counting and string theory.
• F. None of above. chosen