Mathematical sciences and applications of expander graphs 2

Reference No.	2026a024
Type/Category	Grant for Young Researchers and Students-Short-term Joint Research
Title of Research Project	Mathematical sciences and applications of expander graphs 2
Principal Investigator	Shohei Satake（Kumamoto University・Associate Professor）
Research Period	September 7,2026. - September 11,2026.
Keyword(s) of Research Fields	Expander graphs, Information science, Mathematical sciences, Academia–industry collaboration
Abstract for Research Report	Expander graphs are a class of sparse graphs exhibiting strong local connectivity, a combination of properties that is both theoretically intriguing and practically powerful. Due to their efficient information dissemination and rapid mixing properties, expanders play a fundamental role in information science, with applications ranging from post-quantum cryptography to quantum error-correcting codes. In recent years, major industrial players such as Google have intensified research on expanders, further highlighting their potential in areas including cryptography and machine learning. Consequently, the theoretical foundation of expander graphs has become a key driver of innovation in modern information science. Two central challenges define the current research landscape. First, the development of construction methods remains a core issue. Algebraic constructions provide explicit and well-structured graphs but often rely on deep results in group theory and number theory, making spectral analysis—particularly the evaluation of the second eigenvalue—highly nontrivial. In contrast, combinatorial and algorithmic constructions avoid these difficulties but tend to lack structural transparency. Bridging this gap requires hybrid approaches that integrate the strengths of both methodologies. Second, the expansion of application domains is essential. The utility of expander graphs in cryptography, coding theory, and machine learning is closely tied to their spectral and structural properties. While expanders have shown promise in areas such as cryptographic hash functions, quantum LDPC codes, and graph neural networks, their full potential remains underexplored. In particular, industry collaboration in Japan is still limited, and systematic frameworks for application-driven research are yet to be fully established. This project addresses these challenges through two primary objectives: (1) the development of hybrid construction methods that unify algebraic and combinatorial techniques, enabling both efficient construction and tractable analysis; and (2) the expansion of application domains through strengthened collaboration with academia and industry, including the promotion of joint research and concrete industrial use cases. The expected outcome is a substantial advancement in both the theoretical understanding and practical deployment of expander graphs, fostering stronger integration between academic research and industrial innovation.
Organizing Committee Members (Workshop) Participants (Short-term Joint Usage)	Yusuke Aikawa（University of Tokyo・Assistant professor） Yasuhiko Ikematsu（Kyushu University・Associate Professor） Cid Reyes Bustos（NTT Institute for Fundamental Mathematics・Research Scientist） Hyungrok Jo（Yokohama National University・Assistant Professor） Masato Mimura（Tohoku University・Associate Professor） Shohei Satake（Kumamoto University・Associate Professor）