It seeks a systematic mathematical explanation for a phenomenon called mirror symmetry first observed by physicists studying string theory.
Morphisms in the categories are given by the massless spectrum of open strings stretching between two branes[citation needed].
Among the participants were Paul Seidel from MIT, Maxim Kontsevich from IHÉS, and Denis Auroux, from UC Berkeley.
In his seminal address, Kontsevich commented that the conjecture could be proved in the case of elliptic curves using theta functions.
Following this route, Alexander Polishchuk and Eric Zaslow provided a proof of a version of the conjecture for elliptic curves.
In 2002 Hausel & Thaddeus (2002) explained SYZ conjecture in the context of Hitchin system and Langlands duality.
In 1990-1991, Candelas et al. 1991 had a major impact not only on enumerative algebraic geometry but on the whole mathematics and motivated Kontsevich (1994).