Homological mirror symmetry

Homological mirror symmetry (HMS) is a conjectural framework in mathematical physics and algebraic geometry that relates certain aspects of symplectic geometry and algebraic geometry. It emerges primarily from the work of Maxim Kontsevich in the late 1990s. The conjecture provides a deep relationship between the geometry of a space and the derived category of coherent sheaves on that space, particularly in the context of mirror symmetry—a phenomenon that originated in string theory.