Applications and Applied Perspectives of Hyperplane Arrangements

Reference No.	2026a005
Type/Category	Grant for Supporting the Advancement of Female Researchers-Workshop (I)
Title of Research Project	Applications and Applied Perspectives of Hyperplane Arrangements
Principal Investigator	Junyan Chu（Kyoto University, School of Science, SACRA・Postdoctoral fellow）
Research Period	November 9,2026. - November 13,2026.
Keyword(s) of Research Fields	Recent research demonstrates substantial progress in the application of hyperplane arrangements. In statistics and psychometrics, scholarship regarding ranking patterns in unfolding models has demonstrated how arrangement regions describe all possible rankings compatible with experimental or survey data; subsequent research has refined this using Coxeter-invariant arrangements and related combinatorial structures. Similarly, in preference and choice modeling, arrangements have been employed to represent heterogeneous preferences, where chambers encode distinct behavioral types while allowing for efficient geometric analysis. In information theory, a series of studies has clarified the relationship between hyperplane arrangements, coboundary polynomials, and weight enumerators of linear codes. This has led to new interpretations of error-correcting performance and polynomial invariants tailored to coding applications. Complementary computational work has resulted in software for logarithmic vector fields and arrangement-based vector field reconstruction, enabling the implementation of these concepts within concrete data-analysis pipelines.
Abstract for Research Report	While the theoretical foundations of hyperplane arrangements are deeply rooted in algebraic combinatorics and topology, their structural properties have recently emerged as powerful tools for solving practical problems across diverse fields. This workshop aims to highlight and further develop recent applications of hyperplane arrangements in mathematics, data science, and information security. Invited speakers will discuss applications in pattern recognition, probabilistic models, decision theory, and algebraic coding. By converging these complementary viewpoints, we seek to identify common geometric and combinatorial structures underlying these applications and formulate new problems where arrangement techniques can be effectively deployed. Expected outcomes include a clearer cross-disciplinary understanding of how hyperplane arrangements appear in practice, the initiation of concrete collaborative projects, and the training of early-career researchers through direct interaction with leading experts from Japan and abroad.
Organizing Committee Members (Workshop) Participants (Short-term Joint Usage)	CHU Junyan（Kyoto University・Postdoc） 鍛冶　静雄（京都大学・教授） 安田 雅哉（立教大学・教授） 中島 規博（名古屋工業大学・准教授） 沼田 泰英（北海道大学・教授）