理学院数理讲坛（2013年第四十二讲）
题目：Classification of soliton graphs for Kadomtsev-Peviashvili hierarchy
报告人：黄继辉博士(美国俄亥俄州立大学)
时间：2013年12月31日（周二）下午3：00-4：00
地点：北楼311报告厅
欢迎老师和学生参加！
黄继辉博士，本科毕业于清华大学，博士就读于美国俄亥俄州立大学数学系，师从知名专家Yuji Kodama教授从事数学物理和组合学的交叉研究，报告内容如下：
The Kadomtsev-Peviashvili equation can be used to describe shallow water waves, whose solution is induced by a Grassmannian point. It provides an excellent model for the resonant interaction of those waves, and we use soliton graph to express these patterns. For $Gr_{1,n}^{>0}$ and $Gr_{2,n}^{>0}$ cases, the soliton graphs can be constructed from the triangulations of $n$-gon. But generally, not many things are known, even for $Gr_{3,n}^{>0}$ case. We are trying to classify all possible soliton graphs for Top Grassmannian cells. To do this, we introduce multi-time scales to consider the KP hierarchy, and consider the soliton graphs as the dual ones to certain subdivision of zonotopes. Using the topology representation of Zonotopal Tilings, we obtain the polyhedral fan whose regions give different type of soliton graphs. We will also give a brief introduction of the soliton graphs of lower dimension Grassmannian cells for infinity $t_3$ time.