Title: Minimal complexity of non-orientable Lagrangian surfaces in symplectic rational surfaces
Abstract: We discuss the existence and uniqueness of non-orientable Lagragians in symplectic 4-manifolds, especially symplectic rational surfaces.
The starting observation is that every mod 2 degree 2 homology class is represented by a non-orientable Lagrangian surface.
So a natural problem is to investigate the minimal complexity of such surfaces. For this problem we will focus on the existence of Lagrangian projective planes in symplectic rational surfaces. This is based on joint works with Bo Dai, Chung-I Ho, Weiwei Wu and Shuo Zhang.