On Characterizing Rare Events in Persistent Homology

Explore the characterization of rare events in persistent homology through this 53-minute conference talk. Delve into the complexities of multi-parameter persistent homology, examining the relevance of complicated indecomposables in real data analysis. Learn about large deviation principles in 1-parameter persistent homology and the law of large numbers in multi-parameter persistent homology. Discover applications in materials science, focusing on the analysis of silica glass structures under pressure. Gain insights into limit theorems for random cubical homology, including the law of large numbers and central limit theorem for Betti numbers. Investigate ongoing projects in random 2-persistent homology and discuss the implications for future research in topological data analysis.

Beyond TDA
Materials TDA
Hierarchical Structural Analysis of Silica Glass
How robust under pressure?
Persistent homology and persistence diagram
Multiparameter Persistent Homology
Pressurization and commutative ladder
Multiplicity on non-interval indecomposable
Numerical computation
Contents of the remaining parts
Limit theorems for random cubical homology
Random cubical set in R
LLN and CLT of Betti numbers
LLN of PD
Large deviation principle of Betti numbers
Toward large deviation principle of PD
Ongoing projects: random 2 persistent homology