Some research progress on symplectic birational geometry

In the 1980s, the Japanese mathematician Mori established his minimal model program. The point of the program is to classify algebraic varieties into two classes: uniruled and non-uniruled varieties. For the uniruled varieties, one tries to understand the structure of fibrations with Fano fibers, and for the non-uniruled varieties, one hopes to find their minimal models. Symplectic birational geometry is a field to study the classification of symplectic manifolds under symplectic birational equivalence, and to extend Mori's minimal model program to symplectic category. In this paper, we survey some recent progress on symplectic birational geometry, including birational cobordism, uniruled and rationally connected symplectic manifolds, Kodaira dimension of symplectic 4-manifolds, and birational geometry of almost complex manifolds.