The SYZ conjecture is an attempt to understand the mirror symmetry conjecture, an issue in theoretical physics and mathematics. The original conjecture was proposed in a paper by Strominger

Andrew Strominger

Andrew Eben Strominger is an American theoretical physicist who works on string theory and son of Jack L. Strominger. He is currently a professor at Harvard University and a senior fellow at the Society of Fellows...

, Yau

Shing-Tung Yau

Shing-Tung Yau is a Chinese American mathematician working in differential geometry. He was born in Shantou, Guangdong Province, China into a family of scholars from Jiaoling, Guangdong Province....

, and Zaslow, entitled "Mirror Symmetry is T-duality".

Along with the homological mirror symmetry conjecture

Homological mirror symmetry

Homological mirror symmetry is a mathematical conjecture made by Maxim Kontsevich. It seeks a systematic mathematical explanation for a phenomenon called mirror symmetry first observed by physicists studying string theory.-History:...

, it is one of the most explored tools applied to understand mirror symmetry in mathematical terms. While the homological mirror symmetry is based on homological algebra

Homological algebra

Homological algebra is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology and abstract algebra at the end of the 19th century, chiefly by Henri Poincaré and...

, the SYZ conjecture is a geometrical realization of mirror symmetry.
In string theory

String theory

String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...

, mirror symmetry relates type IIA and type IIB theories.