Transversal study on Ultradiscretizing phenomena in algebraic geometry, learning theory and biological mathematics
| Project/Area Number |
21540045
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | トロピカル幾何 / 特異点 / 代数幾何学 / 工程計画問題 / 代数学 / トポロジー / 圏 / K3曲面 / 代数幾何 / Z-アフィン幾何 / 反射的多面体 / 生体生命情報学 / 運動量写像 |
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| Research Abstract |
(1) For the fourteen unimodal exceptional hypersurface singularities, we have constructed algebraic cycles in the derived category of K3 surfaces, and shown that we can recover the Dynkin diagrams from their categorical intersection numbers.
(2) We have shown that the famous ninety-five families of weighted K3 hypersurfaces are, in fact, essentially seventy-five families by constructing concrete correspondences.
(3) We introduced a geometric point of view to the scheduling problems for the first time, showed that the change of critical paths occurred at a tropical hypersurface and developed totally new method to visualize the transition of paths.
(4) We did a topological classification of tropical elliptic curves.
(5) We discussed about algebro-geometric method for acquiring abilities by neural networks.
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Report
(5 results)
Research Products
(31 results)
