Title: TGDA Mini-Course 1
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 #1, I show a recent result about convergence of persistence diagrams on stationary point process in R^N. Several limit theorems such as strong laws of large numbers and central limit theorems for random cubical homology are also shown here.
Seminar URL: https://research.math.osu.edu/tgda/tgda-seminar.html
