CAREER: Free Resolutions

职业：自由解决方案

• 批准号: 0347342
• 负责人: Irena Peeva
• 金额: $ 40.08万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-01 至 2009-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0347342&HistoricalAwards=false
• 关键词: CAREER; Free; Resolutions

DMS-0347342Irena PeevaThe proposed research deals with the structure of freeresolutions and their applications in Commutative Algebra,Algebraic Geometry, and Topological Combinatorics. Resolutions will be studied over polynomial rings and theirquotients. In essence constructing a resolution over a ring Rconsists of repeatedly solving systems of R-linear equations.From another point of view, resolutions provide a homological method for studying the structure of modules. The idea to associate a resolution to a module was introduced in Hilbert's famous 1890 and 1893 papers. This CAREER project focuses especially on Castelnuovo-Mumford regularity and Koszulness of toric varieties,lower bounds on Betti numbers, asymptotic structure of infinite freeresolutions, free resolutions over rings with restricted powers,and monomial resolutions.Peeva will organize a workshop and a summer school on resolutions.She plans to organize other conferences as well. Such conferences provide a forum for discussion of recent developments and fosterresearch. This CAREER project also aims to aid undergraduate andgraduate students, and postdoctoral fellows to discover the beautyin mathematical ideas, to inspire them, and lead them to exploreexciting open problems and conjectures. Peeva is also writing a book on resolutions.

DMS-0347342Irena Peeva建议研究自由解的结构及其在交换代数、代数几何和拓扑组合中的应用。我们将研究多项式环及其商上的归结。在环R上构造归结实质上是重复求解R-线性方程组，从另一个角度来看，归结为研究模的结构提供了一种同调方法。把分解与模联系起来的想法是在希尔伯特著名的1890年和1893年的论文中提出的。这个职业项目特别关注环簇的Castelnuovo-Mumford正则性和Koszulness，Betti数的下界，无限自由解的渐近结构，有限幂的环上的自由分解，以及单项分解。Peeva将组织一个关于决议的研讨会和暑期学校。她还计划组织其他会议。这类会议为讨论最新发展和促进研究提供了一个论坛。这个职业项目还旨在帮助本科生、研究生和博士后发现数学思想中的美，启发他们，并引导他们探索令人兴奋的开放问题和猜想。佩瓦还在写一本关于决心的书。