Young Researcher Meeting in Arithmetic and Dynamics

Reference No.	2025a018
Type/Category	Grant for Young Researchers and Students-Workshop (II)
Title of Research Project	Young Researcher Meeting in Arithmetic and Dynamics
Principal Investigator	Irokawa Reimi（Institute of Fundamental Mathematics, NTT Corporation・Researcher）
Research Period	February 18,2026. - February 20,2026.
Keyword(s) of Research Fields	complex dynamics; number theory; arithmetic dynamics; algebraic geometry
Abstract for Research Report	The purpose of this research workshop is to bring together young researchers from the fields of complex and arithmetic dynamics, providing a platform for exchanging information and discussing the current state of research, recent advancements, and potential applications, including industrial ones. Complex dynamics refers to the study of discrete dynamical systems involving analytic maps on complex manifolds, while arithmetic dynamics primarily investigates self-maps (or rational maps) on algebraic varieties from a number-theoretic perspective. Arithmetic dynamics is a relatively new field, with systematic studies beginning around the 1990s. However, over the past few decades, these two areas have significantly influenced each other and have advanced together, primarily through the development of non-archimedean dynamics, which lies at their intersection. For instance, conjectures classified as "unlikely intersections," such as the dynamical André-Oort conjecture, have emerged from examining complex dynamical systems through a number-theoretic lens. Additionally, problems related to the structure of rational orbits in dynamical systems heavily rely on the analysis of dynamical Green functions, which are classical objects in complex dynamics. Given these deep connections, continued collaboration between experts in complex and arithmetic dynamics is essential for further progress in these fields. However, despite their close relationship, each field is vast and multifaceted, making it challenging to acquire a comprehensive understanding of both. This research workshop aims to gather researchers from complex and arithmetic dynamics, as well as related fields, to share their findings and engage in discussions on new techniques and interconnections between these areas. By fostering such exchanges, we expect participants to gain fresh insights, uncover unexpected commonalities, identify new research directions, and explore potential applications in other disciplines.
Organizing Committee Members (Workshop) Participants (Short-term Joint Usage)	Irokawa Reimi（Institute of Fundamental Mathematics, NTT Corporation・Researcher） Sano Kaoru（Institute of Fundamental Mathematics, NTT Corporation・Research Scientist）