Speaker: Tianjun Li（University of Minnesota）
Time: 16:00-17:00, Jul 4, 2025
Room: room 1124, Material Science Research Building (Section C)
We discuss the existence of non-orientable Lagragian surfaces in symplectic 4-manifolds. We first briefly review the orientable case which has been extensively studied. In the non-orientable case, given a mod 2 degree 2 homology class, three basic facts are
(i) it is always represented by a non-orientable Lagrangian surface,
(ii) the complexity satisfies Audin's Mod 4 congruence,
(iii) the complexity increases by 4 via Givental's local surgery.
So a natural problem is to investigate the minimal complexity of such surfaces subject to Audin's congruence. We investigate this problem for symplectic rational surfaces and focus on the existence of Lagrangian projective planes. This is based on joint works with Bo Dai, Chung-I Ho, Weiwei Wu and Shuo Zhang.
