Integrable systems and singular tropical curves

• Project/Area Number: 24840035
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Aoyama Gakuin University
• Principal Investigator: IWAO Shinsuke 青山学院大学, 理工学部, 助教 (70634989)
• Project Period (FY): 2012-08-31 – 2014-03-31
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000); Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: トロピカル幾何 / 超離散可積分系 / 離散可積分系 / 代数曲線

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.

Research Products

• [Journal Article] Tropical Krichever construction for the non-periodic box and ball system (2012)
  • Author(s): S. Iwao, H. Nagai and S. Isojima
  • Journal Title: J.Phys. A: Math. Theor. Volume: Vol. 45, No. 39 Issue: 39 Pages: 395202-395202
  • DOI: 10.1088/1751-8113/45/39/395202
  • Peer Reviewed
• [Journal Article] The two-dimensional periodic box-ball system and its fundamental cycle (2012)
  • Author(s): Shinsuke Iwao
  • Journal Title: Journal of Physics : Mathematical and Theoretical Volume: 45巻 Issue: 39 Pages: 395204-395204
  • DOI: 10.1088/1751-8113/45/39/395204
  • Peer Reviewed
• [Journal Article] 離散mKdV方程式の2重Casorati行列式解と特異曲線 (2012)
  • Author(s): 岩尾慎介
  • Journal Title: RIMS講究録別冊 Volume: B30巻 Pages: 101-118
  • Peer Reviewed
• [Presentation] Tropical geometry and integrable systems (2013)
  • Author(s): Shinsuke Iwao
  • Organizer: JSPS-DST Asian Academic Seminar 2013, Discrete Mathematics & its Applications
  • Place of Presentation: Graduate School of Mathematical Sciences, the University of Tokyo
  • Year and Date: 2013-11-08
  • Invited
• [Presentation] Tropical geometry and discrete integrable systems (2013)
  • Author(s): Shinsuke Iwao
  • Organizer: JSPS-DST Asian Academic Seminar 2013, Discrete Mathematics & its Applications
  • Place of Presentation: Graduate School of Mathematical Sciences, the University of Tokyo
  • Invited