Tropical geometry and integrable systems

该提案寻求资金支持一个关于可积系统和热带几何的国际会议。对于英国在可积系统研究领域的传统强势地位来说，保持纯粹数学家和应用数学家之间的积极交流以及与新兴研究课题的联系至关重要。热带几何这个相对年轻的学科是代数几何中一个新兴的领域，它与组合几何和枚举几何有很强的重叠。中心是min- +代数和热带曲线的概念，当取所谓的孤子方程的超离散极限时，它们分别出现在可积系统的领域中。提议的会议宣布的目标是连接两个可整合的热带社区，并“启动”对每个领域发展的相互认识，一个寻找共同语言的讨论过程，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资助申请。它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见解在科学，应用和纯粹应用中的潜力。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，在系统遗传学中，人们试图对动物和人类的遗传密码进行分类。提议的会议是探索与可积系统相关的热带几何应用新途径的第一步。后者出现在非线性光学和电信、等离子体物理、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.