A construction of symplectic 4-manifold with positive signature is one of the main interest in the geography problem of symplectic 4-manifolds.
A surface bubdle over surface with section is related to a relaltion in surface mapping class group as a product of commutators and boundary parallel Dehn twists and a computation of signature is coming from a local signature formula.
In the tallk we will explain how to construct a surface bundle over surface with positive signature for almost all pair of $(g, h)$ except 18 cases. Most details are based on the article written by Baykur and Korkmaz.