"Applications of Homological Algebra in Algebra, Geometry, and Physics"

“同调代数在代数、几何和物理中的应用”

• 批准号: 36739-2012
• 负责人: Buchweitz, RagnarOlaf
• 金额: $ 2.91万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508870
• 关键词: Applications; Homological; Algebra; Geometry; Physics

No two maple leaves are alike and neither are two snow flakes. However, nobody will mistake the former for the latter. This simple metaphor is at the basis of the deformation and classification theory of mathematical structures. Given an algebraic or geometric object that is specified by axioms, structural data, or equations, what remains of the structure and which aspects change if one (slightly) varies the defining parameters? The instruments and techniques mathematicians employ to answer these questions are contained in the ever expanding toolbox of homological algebra, which strives to classify that which is of equal shape or form, i.e. ``homological''.

没有两片枫叶是一样的，也没有两片雪花是一样的。但是，没有人会把前者误认为后者。这个简单的比喻是数学结构的变形和分类理论的基础。给定一个由公理、结构数据或方程指定的代数或几何对象，如果（稍微）改变定义参数，结构的哪些方面会改变？数学家用来回答这些问题的工具和技术包含在不断扩大的同调代数工具箱中，该工具箱致力于对具有相同形状或形式的东西进行分类，即“同调的”。