Title：Lagrangian surfaces in R^4 and  in TS^2

Speaker：Wilhelm Klingenberg（Durham University）

Time：2017年10月31日（周二）   下午14:30-15:30

Room：东区管理科研楼  数学科学学院1518室

Abstract： Lagrangian surfaces are a tool in the study of the geometry and topology of the ambient symplectic four manifold. We will review the landmark result of M Gromov from 1985, where he proved that there are no embedded exact Lagrang ian tori in R^4. In analogy to this we then consider (necessarily exact) Lagrangian spheres in symplectic TS^2, which arise naturally in classical Differential Geometry. We will prove that the collection of such is locally a Banach manifold near sections with only one complex point. We will conclude by extracting corollaries in Differential Geometry and raise open problems in symplectic geometry of TS^2.