Topological data analysis from a practical and mathematical perspective

1. Topological data analysis and its applications
In this talk, I will explain some methods in topological data analysis (TDA) and their applications. First I recall persistent homology, which is a central tool to analyze the "shape" of a point cloud set. Then I show several applications to material science and time-series analysis. I also talk about our collaborative research with Inria on noise-robust persistent homology and an automated vectorization method of persistence diagrams.

2. Persistence-like distance on sheaf category and displacement energy
In this talk, I will talk about relation among sheaf theory, persistence modules, and symplectic geometry. We introduce a persistence-like distance on Tamarkin sheaf category and prove a stability result with respect to Hamiltonian deformation of sheaves. Based on this result, we propose a new sheaf-theoretic method to give a lower bound of the displacement energy of compact subsets of a cotangent bundle.
This is a joint work with Tomohiro Asano.