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 |
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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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 / 結び目不変量 / 代数的完全可積分系 / スペクトル曲線 / ヤコビ多様体 / 双曲幾何 / 複素体積 |
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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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Report
(5 results)
Research Products
(37 results)
