2013 Fiscal Year Final Research Report
Tropical geometry, non-commutative geometry and integrable systems
| Project/Area Number |
22740111
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Chiba University (2011-2013)
Suzuka University of Medical Science (2010) |
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Principal Investigator |
INOUE YAMAZAKI Rei (井上 玲) 千葉大学, 理学(系)研究科(研究院), 准教授 (30431901)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | トロピカル幾何 / クラスター代数 / セルオートマトン / 差分方程式 / 可積分系 / 結び目 |
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| Research Abstract |
We solved a problem on the box-ball system: the general isolevel set of the box-ball system is isomorphic to the Jacobian variety of a tropical curve, which links quantum group with tropical geometry. We also studied applications of cluster algebra: we constructed the Poisson structure of cluster algebra which includes preceding results. We apply it to study the discrete Lotka-Volterra equation. Based on a relation between punctured surface and cluster algebra, we study the complex volume of once-punctured torus bundles on S1 and two bridge knot complements in S3. We also formulated the conjecture on the complex volume of knot complement in terms of cluster algebra.
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