2012 Fiscal Year Final Research Report
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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| Keywords | トロピカル幾何 / 特異点 |
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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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