Integrable systems in Geometry, Asymptotics and Inverse Problems

几何、渐近和反问题中的可积系统

• 批准号: RGPIN-2016-06660
• 负责人: Bertola, Marco
• 金额: $ 2.91万
• 依托单位: Concordia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635311
• 关键词: Integrable; systems; Geometry; Asymptotics; Inverse

Integrable systems consist in a special class of overdetermined sets of partial differential (or difference) equations. They appear in several contexts in slightly different guises, including Random Matrix Theory, Moduli Spaces of Riemann surfaces and connections, Stochastic Processes and Inverse problems. A common thread to all these instances is the possibility of reformulation in terms of a particular boundary value problem for matrix-valued analytic functions, or what is now commonly referred to as a Riemann-Hilbert problem (RHP). The proposed research seeks to both advance the general understanding of RHPs as well as their application to several outstanding problems.

可积系统由一类特殊的超定偏微分（或差分）方程组组成。它们以略有不同的形式出现在多种环境中，包括随机矩阵理论、黎曼曲面和连接的模空间、随机过程和逆问题。所有这些实例的共同点是根据矩阵值解析函数的特定边值问题重新表述的可能性，或者现在通常称为黎曼-希尔伯特问题（RHP）。拟议的研究旨在增进对 RHP 的一般理解及其在几个突出问题上的应用。