Tropical geometry and integrable systems

该提案寻求资金支持一次关于可积系统和热带几何的国际会议。由于英国在可积系统研究领域传统上的强大地位，在纯数学家和应用数学家之间保持积极的沟通并与新兴的新研究课题联系是至关重要的。相对年轻的热带几何学科是代数几何中的一个新兴领域，与组合学和计数几何有很强的重叠。中心是最小+代数和热带曲线的概念，它们在取所谓的孤子方程的超离散极限时独立地出现在可积系统的范围内。拟议会议宣布的目标是将可积和热带两个社区联系起来，“启动”对每个领域的发展的相互认识，一个寻找共同语言的讨论过程，并从长远来看，形成共同的研究兴趣，从而产生高质量的论文和超越传统学科界限的拨款申请。这将有助于英国在数学科学方面的强大研究地位，并增加其利用新的数学洞察力在科学、应用和纯科学中应用的潜力。热带几何已经在统计科学和生物学中找到了应用，更具体地说，人们试图对动物和人类的遗传密码进行分类的系统发育学。拟议的会议是探索与可积系统相关的热带几何应用的新途径的第一步。后者出现在例如非线性光学和电信、等离子体物理以及海洋、大气和行星科学的研究中。

The proposal seeks funding to support an international conference on integrable systems and tropical geometry. For the UK's traditionally strong standing in the research area of integrable systems it is vital to maintain an active communication between pure and applied mathematicians and to connect with emerging new research topics. The relatively young discipline of tropical geometry is such an emerging field within algebraic geometry having strong overlaps with combinatorics and enumerative geometry. Central are the notions of the min-plus algebra and tropical curves which independently appeared in the area of integrable systems when taking the so-called ultradiscrete limit of soliton equations. The declared aim of the proposed conference is to connect the two communities, integrable and tropical, and "jump start" a mutual awareness of developments in each field, a discussion process to find a common language and in the long term the formulation of common research interests resulting in high quality papers and grant applications transgressing traditional subject boundaries. It will contribute to the UK's strong research position in the mathematical sciences and increase its potential to harness new mathematical insight for applications in the sciences, applied and pure.Tropical geometry has already found applications in statistical sciences and biology, more specifically phylogenetics where one tries to classify the genetic codes of animals and humans. The proposed conference is a first step to explore new avenues for applications of tropical geometry related to integrable systems. The latter appear for instance in the study of nonlinear optics and telecommunication, plasma physics, and ocean, atmospheric and planetary sciences.