中科院数学与系统科学研究院

数学研究所

学术报告

拓扑研讨班

报告人：陈伟彦 (清华大学)  

题  目：Topological complexity of enumerative problems

时  间：2023.09.27（星期三）14:30-16:30

地  点：数学院南楼N802

摘  要：How complex is the solution of a polynomial equation? One way to measure such complexity is provided by topological complexity in the sense of Smale, who proved that any algorithm that finds roots of a polynomial must be sufficiently complicated. However, finding roots of a polynomial is just one basic example of enumerative problems in algebraic geometry. In this talk, we will consider the problem of finding flex points on smooth cubic plane curves. We prove a lower bound for the topological complexity of this problem, and show that our bound is close to be best possible. This talk is based on joint work with Zheyan Wan.