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.

可集成的系统包括一类特殊的部分差分（或差异）方程组。它们出现在几种情况下以略有不同的形式出现，包括随机矩阵理论，Riemann表面和连接的模量空间，随机过程和反问题。所有这些实例的一个共同点是根据矩阵值分析函数的特定边界价值问题进行重新重新制定的可能性，或者现在通常称为Riemann-Hilbert问题（RHP）。拟议的研究旨在促进对RHP的一般理解，以及它们在几个杰出问题上的应用。