Speaker：Weiyi Zhang （Warwick University）

Time：2018年6月15日（周五）    下午 16:00--17:30

Room：东区管理科研楼   数学科学学院1418室

Abstract：An almost complex manifold is a smooth manifold equipped with a smooth linear complex structure on each tangent space. Every complex or symplectic manifold is an almost complex manifold, but not vice versa.

Transversality is the notion of general position in manifold topology. It could be used to define the multiplicity of a zero for a smooth function with more than one variables. We will discuss differential topology of almost complex manifolds, explain how to use transversality statements for smooth manifolds to formulate and prove corresponding results for an arbitrary almost complex manifold. The examples include intersection of almost complex manifolds, pseudoholomorphic maps and zero locus of certain harmonic forms. Using these results, we are able to define and study Kodaira dimension for almost complex manifolds (joint with Haojie Chen). It could also be applied to get upper bounds for eigenvalues of Laplacian on almost complex manifolds (work of my student Louis Bonthrone).

An undergraduate student who has taken Prof. Zuoqin Wang's Manifold class should be able to understand a large portion of the talk.