(This is a part of Seminars on Algebraic Surfaces and Related Topics.)
A vector bundle over a projective manifold is said to be pseudo-effective if the tautological line bundle of its Grothendieck projectivization is pseudo-effective. In this talk, I will show that a smooth non-uniruled projective surface S has pseudo-effective tangent bundle if and only if S is minimal and has vanishing second Chern class. Moreover, I will describe the non-rational ruled surface and its blow-up which has pseudo-effective tangent bundles. This is a joint work with Jia Jia and Yongnam Lee.