| Project/Area Number |
25800037
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
Kalman Tamas 東京工業大学, 理学院, 准教授 (00534041)
|
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 低次元トポロジー / 結び目理論 / 代数組み合わせ論 / knot theory |
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| Outline of Final Research Achievements |
The interior polynomial can be associated, among other things, to hypergraphs. There is a natural duality, called the transpose, of hypergraphs: it simply interchanges the vertices and the hyperedges. I had conjectured for some time that the interior polynomial of a hypergraph and its transpose agree. In joint work with A. Postnikov we proved this statement by interpreting the interior polynomial as the Ehrhart polynomial of the so called root polytope. This was also the last remaining step for the proof that the coefficients of the interior polynomial occur among those of the Homfly polynomial of certain links, which in turn proved that these coefficients can be derived from Floer homology groups, as predicted in my research program.
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