Analysis on and geometry of singular spaces towards a geometric desingularization

奇异空间的分析和几何走向几何去奇异化

• 批准号: 8949-2008
• 负责人: Milman, Pierre
• 金额: $ 3.06万
• 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=513345
• 关键词: Analysis; geometry; singular; spaces; towards

Singularities express irregularities of form in many branches of mathematics in a way similar to what a singularity means in an everyday language. They are a basic object of study in most of the mathematics and its applications. Important features of form are often concentrated at singularities. The objective of my research is to find closer links between the geometry and analysis of singularities. A longer term objective would be a 'geometric desingularization', i.e. reconstruction of the entire process in terms of geometry and/or analysis.

奇点在数学的许多分支中表达形式的不规则性，其方式类似于奇点在日常语言中的含义。它们是大多数数学及其应用的基本研究对象。形式的重要特征往往集中在奇点上。我的研究目标是找到几何学和奇点分析之间更紧密的联系。更长期的目标是“几何去奇异化”，即在几何和/或分析方面重建整个过程。