Construction and uniqueness of asymptotically symmetric Einstein spaces

2023 Fiscal Year Final Research Report

• Project/Area Number: 20K03584
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 11020:Geometry-related
• Research Institution: Osaka University
• Principal Investigator: MATSUMOTO Yoshihiko 大阪大学, 大学院理学研究科, 准教授 (00710625)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Keywords: 微分幾何学 / 漸近的対称空間 / アインシュタイン計量 / 共形幾何学 / CR幾何学

Outline of Final Research Achievements

I conducted research related to the "Einstein filling problem," which is the problem of constructing the corresponding "asymptotically symmetric Einstein spaces" for a given geometric asymptotic boundary. This project is connected to the idea known as "bulk-boundary correspondence" or "holographic principle" in high-energy physics and differential geometry. While many of the initially set goals remain as topics requiring continued examination, certain results have been achieved regarding two issues that arose during the course of the research. These achievements were documented in papers and presented and discussed at both domestic and international research conferences.

Free Research Field

微分幾何学

Academic Significance and Societal Importance of the Research Achievements

本課題で実施した研究は純粋数学に属するもので、近い未来に実用的な意味で社会に役立つことは期待しづらい。しかし、人類の共有する知的地平を広げるという点において意義がある。ひいては、国際社会において日本が文化的な敬意を得ることにも、多少の貢献があるかもしれない。
学術的には、世界的にみて新しく、国内外の研究者と協力して発展させられる可能性のある、将来にわたる研究の題材を提供したものと信ずる。また、物理学には何らかの形で直接的な影響をもたらす可能性もあると期待される。