IKE, Yuichi

Title
Associate Professor
Field
Mirolocal sheaf theory, topological data analysis
Research interests
Applications of microlocal sheaf theory to geometry, persistent homology
Current research

I study microlocal sheaf theory and topological data analysis, especially persistent homology. Microlocal sheaf theory is a method to study sheaves on manifolds by analyzing them in cotangent bundles. I apply this theory to topology and symplectic geometry. Recently, I have been interested in studying non-smooth objects in symplectic geometry with sheaves. Topological data analysis is a field for studying the topology of data using various mathematical methods, such as persistent homology. I have studied the mathematical structure of persistent homology and its applications in combination with machine learning.

Selected publications
  1. (with T. Asano) Completeness of derived interleaving distances and sheaf quantization of non-smooth objects, Math. Ann. 390 (2024), 2991--3037.
  2. (with M. Carrière, F. Chazal, M. Glisse, H. Kannan, Y. Umeda) Optimizing persistent homology based functions, Proceedings of the 38th International Conference on Machine Learning (ICML 2021).
  3. (with M. Carrière, F. Chazal, T. Lacombe, M. Royer, Y. Umeda) PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures, Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics (AISTATS 2020).
  4. (with T. Asano) Persistence-like distance on Tamarkin's category and symplectic displacement energy, J. Symp. Geom. 18 (2020), no. 3, 613--649.

Memberships, activities and

Awards

The Japan Society for Industrial and Applied Mathematics