Abstract: 

We discuss the space of  symplectic forms of K\"ahler-type on closed manifolds, especially in dimension 4. The three properties investigated are: 

(1) connectedness up to diffeomorphism, 
(2) uniqueness of cohomologous forms up to diffeomorphism,
(3) openness in the space of symplectic forms. 
We also study holomorphically tamed symplectic forms, which are symplectic forms tamed by some integrable complex structure. In fact, properties of Kahler type forms are often established via understanding the potentially bigger space of holomorphically tamed forms. 
This is joint work with Shengzhen Ning.