12月12日Wang Eroxiao博士学术报告 [2009-05-07]
报告题目： Spectral Data of Finite Type Almost Complex Curves in 6-Sphere
报 告 人： 新加坡国立大学(Wang Eroxiao博士)
报告时间： 2008年12月12日下午4：30
报告地点： 理化大楼16008
欢迎感兴趣的师生参加！
Abstract: The talk will focus on the interesting background and a beautiful dictionary between a class of differential equations and Riemann surface (or algebraic curve) theory, thus for general audiences including graduate students. We will establish a bijective correspondence between finite type almost complex curves in S^6 and their spectral data, which consists of a hexagonal algebraic curve and a planar flow of line bundles in its Jacobian. We characterize the
spectral data by identifying various symmetries on them. We prove generic smoothness of these spectral curves, compute their genus, and compute the dimension of the moduli of such curves. Then we identify a Prym-Tjurin subtorus of the Jacobian, in which the direction of the flow must lie, and compute its dimension. Finally we characterize finite type special Lagrangian cones in C^3 as a subclass of such associative cones in terms of the spectral data. These computations are mainly motivated by Hitchin's recent work on Langland duality.
