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  3. Yasuaki Hiraoka

InaRIS Fellow (2025-)

Yasuaki Hiraoka

Kyoto University Institute for Advanced Study, Kyoto UniversityProfessor*Profile is at the time of the award.

2025InaRISScience & Engineering

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Research topics
Challenge to human biology from mathematics
Keyword
Summary
In recent biology, comprehensive experiments are generating vast amounts of data, but there is a critical shortage of data analysis methods that enable us to discover biological principles from those data. While we deepen biological understandings by revealing the intrinsic data structures within species and the relative relationships between species, this mathematically corresponds to extracting invariants of spaces and mappings defined by the data, respectively. In this research, we address the biological question “What makes us human?” by developing mathematical data analysis methods to elucidate the principles of species differences.


Citation

Dr. Yasuaki Hiraoka has made groundbreaking contributions to interdisciplinary research, bridging mathematics with fields such as materials science and life sciences. As a global leader in topological data analysis (TDA), he has pioneered new theories and methodologies, driving the advancement of TDA research.

In this proposal, Dr. Hiraoka takes on an ambitious and fundamental question in life sciences: What makes us human? — a question tied to the principle of species-specific trait expression. Collaborating with experimental biologists, he aims to tackle this challenge using a diverse range of mathematical approaches. One of the central issues in the life sciences, known as the species difference problem, arises from the difficulty of directly applying findings from animal experiments to humans despite their genetic similarities. This discrepancy is not simply a matter of genetic resemblance but rather stems from differences in the spatial structure and dynamics of gene expression. From this perspective, mathematics has the potential to make a significant impact. To date, no mathematician has approached the species difference problem from this standpoint. Dr. Hiraoka is poised to be the first to do so in a rigorous and comprehensive manner.

His research strategy incorporates an exceptionally broad range of mathematical theories, including topology (with a focus on TDA), representation theory, microlocal analysis, probability theory, optimal transport theory, and the latest advances in data science. He has already achieved key milestones in this endeavor. His approach is particularly noteworthy because it extends beyond pure mathematical theory, fostering direct collaboration with experimental biologists under one roof. This cyclic interaction between mathematics and experimental science exemplifies the very essence of scientific inquiry. In practice, his research begins with noise reduction in biological data, followed by the application of various mathematical techniques to derive results that meet the expectations of biologists. This process not only advances our understanding of life science but also provides new mathematical insights, such as the development of decomposition theory for multiparameter persistent homology. His approach is thus highly bidirectional, facilitating a fruitful exchange between mathematics and life science.  

Dr. Hiraoka’s research is expected to make profound contributions to our understanding of species-specific trait expression, with far-reaching implications across science, technology, and society. Due to the abstract and universal nature of mathematics, once a mathematical theory is established, its applications often transcend a single discipline. His work in TDA has already led to significant breakthroughs in materials science, and its future applications are expected to expand even further. While contemporary research is increasingly shifting from deductive to inductive methodologies, Dr. Hiraoka seamlessly integrates both approaches, positioning his research as a potential new model for future scientific inquiry. Particularly striking is the emergence of unexpected mathematical advancements driven by challenges arising from practical applications.

From the perspectives of advancing mathematics, contributing to society, and fostering future researchers, Dr. Hiraoka’s proposal is highly deserved with the mission of the InaRIS Fellowship. It stands as a model example of the call’s theme: creating new mathematical methodologies for understanding nature and society.


Message from Fellow


I am deeply grateful for being selected as an Inamori Foundation InaRIS Fellow. While I feel fortunate to be able to spend 10 years working thoroughly on challenging themes, I simultaneously feel anxious about how much I will be able to uncover even with these 10 years. I intend to proceed steadily forward, never losing sight of my duties as a mathematician, and maintaining my gratitude towards all those who have supported me.

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