Enhao Liu
| Position | Program-Specific Researcher |
|---|---|
| Group name | Hiraoka Group |
| Research Field | topological data analysis |
| Awards | Best Poster Award, ICMMA2022 (2022) |
| ORCID | https://orcid.org/0009-0009-3592-2228 |
| Personal Website | https://sites.google.com/view/enhaoliu |
| Joined | 2025/10/01 |
Research Overview
My research area is applied topology, with a focus on topological data analysis (TDA). TDA studies datasets through their underlying shape, allowing us to detect topological features and encode them in concise descriptors—such as persistence diagrams/barcodes and mapper graphs—that are useful for inference and learning.
I currently focus on persistent homology, one of the main tools in TDA. My work draws on the representation theory of algebras, probability, and statistics. In the standard one-parameter context, I used to investigate applying the persistent homology theory to high-dimensional, low-sample-size data in some practical and specified settings, motivated by the single-cell RNA sequencing data analysis. In generalized persistent homology (e.g., multiparameter persistence), data analysis is substantially harder than in the one-parameter case because of algebraic complications. I have developed both theoretical and computational aspects for studying some invariants of persistent homology, which are closely related to the algebraic (homological) approximation of the persistent homology obtained. I am continuing to develop this line of work.
Biography
Enhao Liu obtained his PhD in Mathematics from Kyoto University in 2025, where he specialized in topological data analysis (TDA). In October 2025, he joined the Kyoto University Institute for Advanced Study (KUIAS) as a program-specified researcher at the Institute for the Advanced Study of Human Biology (ASHBi). His research interests focus on developing mathematical methods for analyzing complex data using topological approaches.
Publications
Yasuaki Hiraoka, Yusuke Imoto, Shu Kanazawa, Enhao Liu. Curse of Dimensionality on Persistence Diagrams. Foundations of Data Science. 2025. doi: 10.3934/fods.2025008