Geometry of moduli spaces and of integrable systems

模空间和可积系统的几何

• 批准号: 44871-2010
• 负责人: Hurtubise, Jacques
• 金额: $ 2.91万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=521718
• 关键词: Geometry; moduli; spaces; integrable; systems

My research deals with two linked areas of mathematics, both having deep roots in geometry as well as in theoretical physics. The first, that of integrable Hamiltonian systems, dates back to the nineteenth century, with important contributions from many of the leading mathematicians of the period; it has its origins in the study of classical mechanical systems such as the solar system. It has come to the fore more recently because of the appearance of the structure in hidden ways in such phenomena as water waves and non-linear optics, as well as in some of the more advanced constructions of theoretical physics. My work aims at understanding the

我的研究涉及两个相互关联的数学领域，两者都深深植根于几何学和理论物理学。第一个是可积的哈密顿系统，可以追溯到世纪，当时许多著名数学家都做出了重要贡献;它起源于对太阳系等经典力学系统的研究。最近，由于在水波和非线性光学等现象中，以及在一些更先进的理论物理学结构中，这种结构以隐藏的方式出现，它才脱颖而出。我的工作旨在了解