I study topological data analysis and microlocal sheaf theory. Topological data analysis is a field to study the topology of data using various mathematical methods, such as persistent homology. Recently, it has been developed in combination with machine learning. Microlocal sheaf theory is a method to study sheaves on manifolds by analyzing them in cotangent bundles. I am interested in applying this theory to topology and symplectic geometry. I would also like to explore how we can use geometric or algebraic methods in machine learning.
|Keywords||Topological data analysis, Microlocal sheaf theory, Machine learning|
|Division||Division of Industrial and Mathematical Statistics|