2013 Fiscal Year Final Research Report
Integrable systems and singular tropical curves
| Project/Area Number |
24840035
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Aoyama Gakuin University |
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Principal Investigator |
IWAO Shinsuke 青山学院大学, 理工学部, 助教 (70634989)
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| Project Period (FY) |
2012-08-31 – 2014-03-31
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| Keywords | トロピカル幾何 / 超離散可積分系 |
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| Research Abstract |
I studied the relation between the tropical mathematics and the ultradiscrete integrable systems. Tropical curves are geometrical objects defined by the use of piece-wise linear functions, which are realized as metric graphs. On the other hand, ultradiscrete integrable systems are "piece-wise linear differential equations" obtained from various integrale systems through the "ultradiscretization", which is some special limiting procedure.
In this study, I constructed the method for the initial value problems of various periodic ultradiscrete integrable systems.
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