演講者：顏聰文博士 (新加坡南洋理工大學數理科學院)

日   期：2026 年 05 月 27 日（星期三）13:30

地   點：國立高雄大學理學院 408 室

講   題：Topological and Geometrical Characterization of Three Types of Critical Events Across Multiple Length Scales

摘   要：

In this talk, we propose for stock markets to be model complex systems, where test metrics would be developed for later use in other complex systems. To illustrate this feasibility, we ask whether it is possible to discriminate between crashes, corrections, and bull runs. Noting that these are distinct market states, we apply topological data analysis (TDA) on S&P 500 and Taiwanese stocks. We found that the standard TDA indicators are not informative. Instead, crashes can be distinguished from corrections and bull runs by the degree distribution of their filtered networks between 1.0≤ϵ≤1.4, where ϵ is the TDA filtration parameter. These can also be distinguished using the number of links with negative Ollivier-Ricci Curvatures (ORCs) in their filtered networks between 0.7≤ϵ≤1.0. In other words, to distinguish between two states in a complex system, we cannot compare indicators at a single length scale, but must compare how they change with ϵ.