Organized research on computational complexity via algebraic geometry
| Project/Area Number |
17K19954
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| Research Category |
Grant-in-Aid for Challenging Research (Exploratory)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Information science, computer engineering, and related fields
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| Research Institution | Kwansei Gakuin University (2019-2020)
Tohoku University (2017-2018) |
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Principal Investigator |
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| Project Period (FY) |
2017-06-30 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥6,370,000 (Direct Cost: ¥4,900,000、Indirect Cost: ¥1,470,000)
Fiscal Year 2019: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2018: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 計算理論 / 代数幾何学 / 群の表現論 / 計算複雑度 / 表現論 / 計算幾何学 / 計算階層 |
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| Outline of Final Research Achievements |
Our grand challenge is the integration of mathematics and theory of computing. In particular, we aim at construction of collaborating research between researchers of mathematics (mainly algebraic geometry and group representation theory) and theory of computing, and pursue joint study focusing on GCT (Geometric Complexity Theory). We organized bi-monthly seminar held at Komaba campus of University of Tokyo. Moreover, we promoted international joint study, and participated to a joint seminar at Max Plank Institute in Germany, where Tokuyama and three other Japanese joint researchers gave invited talks. We also invited Prof. Ikenmeyer (U. Liverpool, UK) and Mr. Fisher (PhD student) to have joint study and series of lectures in Sendai, Kyoto, and Tokyo.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究では、数学と情報科学分野の研究連携の推進を目指し、代数幾何学と群の表現論を計算複雑度解明に活用するGCTを中心とした、組織的な研究を行った。トップレベル研究者による定例セミナーと国際的な先端研究者や研究機関との国際共同研究を実施し、新しい成果を得た。一例として、一般化行列式を用いたWeylの公式の拡張は、数学的に基本的な公式の拡張であるのみならず、統計物理学や量子計算等の多くの分野への波及が期待される。また、数学と情報科学分野の連携に関して広く活動し、JST俯瞰セミナー等数多くの意義の高い啓蒙を行った。
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Report
(5 results)
Research Products
(25 results)
