Title: TGDA Mini-Course 2
Speaker: Yasu Hiraoka (Tohoku University, Advanced Institute for Materials Research, Sendai Japan)
Abstract: In this series of lectures, I present several research topics on random topology and machine learnings on persistent homology. Persistent homology is one of the important tools in topological data analysis and it characterizes shapes of data. In particular, it provides a tool called the persistence diagram that extracts multiscale topological features such as rings and cavities in data (e.g. atomic configurations, high dimensional digital images etc).
In talk #2, I discuss a higher dimensional generalization of Frieze’s zeta(3) theorem on the Linial-Meshulam process and the clique complex process. The key observation is to show a connection of the minimum spanning acycle to the lifetime of persistent homology.
Seminar URL: https://research.math.osu.edu/tgda/tgda-seminar.html