Developments and Applications of Geometric Singularity Theory

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K03458
• 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: Hokkaido University
• Principal Investigator: Ishikawa Goo 北海道大学, 理学研究院, 名誉教授 (50176161)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Keywords: フロンタル / 幾何学的制御理論 / サブリーマン幾何 / 特異曲線 / 接触構造 / 単純リー環 / 接分布 / 双対性

Outline of Final Research Achievements

As developments and applications of geometric singularities and, we have succeeded to classify singularities of parallels to developable surfaces. We have investigated singular curves of (3,5) and (4,7) distributions, the results of which are going to be published. During all periods of the research, we have performed international researches， further we have published the survey article on symplectic singularities and studied normal and tangential maps to frontals. Also we published papers on the topology of complements to affine line arrangements, on the duality of Cartan distributions, i.e. (2, 3, 5)-distributions　and published results on the complexity of Nash functions. Moreover we have wrote an integrated survey paper on frontal singularities.

Free Research Field

幾何学（特異点論）

Academic Significance and Societal Importance of the Research Achievements

幾何学的特異点論は，数学の中で最も歴史のある幾何学の中で，他分野との関連や応用上重要な視点となる特異点に注目することにより新しい視点を与え，学術的に幾何学の新しい側面に光を照らす研究であり学術的な意義は深く広い．また，空間識，あるいは，時空識の研究への応用が期待されていて，社会的意味も大きいと期待される．