Fundamentals and Applications of Mathematics

数学基础与应用

• 批准号: 10304004
• 负责人: NISHIKAWA Seiki
• 金额: $ 20.62万
• 依托单位: Tohoku University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10304004/
• 关键词: Mathematical science; Global analysis; Symplectic geometry; Combinatorics; Class field theory; Group theory; Singularities; Integrable system; 微分幾何学; リー群; 幾何構造; 微分方程式; 組み合わせ論; トポロジー; 特異点; 表現論; 等質空間; 極小曲面; シンプレクティック幾何学; CR幾何学; 過剰決定系; 幾

The main objective of this project was twofold. One was to execute intensive cooperative researches beyond the borders of specific research fields with the aim of strengthening the foundation of mathematical sciences and its applications. The other was to promote the publication of the "Advanced Studies in Pure Mathematics" series (ASPM for short) in order to establish the prompt distribution of research results in official publication form.As its outcomes, two international conferences were organized and accomplished with great success, and the following eight proceedings of international conferences were edited and published.A. International Conferences :(1) Minimal Surfaces, Geometric Analysis and Symplectic Geometry, held at the Japan-America Mathematics Institute, Johns Hopkins University in March, 1999.(2) The Fifth Pacific Rim Geometry Conference, held at Tohoku University in July, 2000.B. Proceedings :(1) Arrangements - Tokyo 1998, ASPM Vol. 27(2) Singularities - Sapporo 1998, ASPM Vol. 29(3) Class Field Theory - Its Centenary and Prospect, ASPM Vol. 30(4) Groups and Combinatorics - in memory of Michio Suzuki, ASPM Vol. 32(5) Minimal Surfaces, Geometric Analysis and Symplectic Geometry, ASPM Vol. 34(6) Proceedings of The Fifth Pacific Rim Geometry Conference, Tohoku Math. Publ., No. 20(7) Surveys on Integrable Systems in Differential Geometry, to be published in 2002(8) Lie Groups, Geometric Structure and Differential Equations - One Hundred Years after Sophus Lie-, to be published in 2002

该项目的主要目标是双重的。一是跨特定研究领域开展深入合作研究，加强数学科学基础及其应用。二是推动《纯数学高等研究》系列丛书（简称ASPM）的出版，建立研究成果以官方出版形式及时发行的制度。其成果是组织了两次国际会议，取得了丰硕的成果。成功，编辑出版了以下八篇国际会议论文集。国际会议：（1）最小曲面、几何分析和辛几何，1999年3月在约翰·霍普金斯大学日美数学研究所举行。（2）第五届环太平洋几何会议，2000年7月在东北大学举行.B.会议记录：(1) 安排 - 东京 1998 年，ASPM 第 1 卷。 27(2) 奇点 - 札幌 1998 年，ASPM 第 1 卷。 29(3) 类场论——百年历史与展望，ASPM Vol. 29(3) 30(4) 群与组合 - 纪念铃木道雄，ASPM Vol. 30(4) 群与组合学 - 纪念铃木道雄，ASPM Vol. 32(5) 最小曲面、几何分析和辛几何，ASPM 第 1 卷。 34(6) 第五届环太平洋几何会议论文集，东北数学。 Publ.，No. 20(7) Surveys on Integrable Systems in Differential Geometry，将于 2002 年出版(8) Lie Groups, Geometric Structure and Differential Equations - One Hundred Years after Sophus Lie-，将于 2002 年出版

项目成果

Seiki Nishikawa: "Proceedings of the Fifth Pacific Rim Geometry Conference, Tohoku Mathematical Publications, No.20"Mathematical Institute, Tohoku University. 205 (2001)

Seiki Nishikawa：“第五届环太平洋几何会议论文集，东北数学出版物，第 20 期”东北大学数学研究所。

Eiichi Bannai: "Groups and Combinatorics-in memory of Michio Suzuki Advanced Studies in Pure Mathematics, Vol.32"Mathematical Society of Japan. 483 (2001)

版内英一：《群与组合学——纪念铃木道夫纯数学高等研究》，第 32 卷，日本数学会。

Jean-Paul Brasselet: "Singularities - Sapporo 1998"Kinokuniya Company,Ltd.. 322 (2000)

Jean-Paul Brassellet：“奇点 - 札幌 1998”纪伊国屋有限公司。322 (2000)

Eiichi Bannai: "Some results on modular forms-Subgroups of the modular group whose ring of modular forms is a polynomial ring"Advanced Studies in Pure mathematics. 32. 245-254 (2001)

Eiichi Bannai：“关于模形式的一些结果-其模形式环是多项式环的模群的子群”纯数学高级研究。

Kenji Fukaya: "Floer homology and mirror symmetry II"Advanced Studies in Pure Mathematics. 34(in printing). (2002)

Kenji Fukaya：《弗洛尔同调与镜像对称 II》纯数学高级研究。