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Studies in Commutative Algebra and Computational Algebra

Studies in Commutative Algebra and Computational Algebra
交换代数和计算代数研究
批准号:
0097093
负责人:
Wolmer Vasconcelos
金额:
$11.34万
依托单位国家:
美国
项目类别:
Continuing Grant
财政年份:
2001
资助国家:
美国
项目状态:
已结题
起止时间:
2001-06-01 至 2005-05-31

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中文摘要
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英文摘要
This proposal concerns problems in commutative algebra, algebraic geometry and computational algebra. These problems range from the explicit construction of algorithms in algebra and the development of settings to analyze their complexity to the construction and analysis of several classes of singular varieties. The investigator is: (a) developing methods to construct integral closures of algebras, ideals and modules, and understanding their complexity, including the introduction of non-Turing models of complexity; (b) developing families of numerical signatures (multiplicities, volumes) of rings and algebras that play in local rings and arbitrary algebras a role similar to Castelnuovo--Mumford's regularity in graded structures; (c) carrying out an algebraization of blowup algebras and of algebras associated to commuting sets of elements of Lie algebras with the major aim of finding its properties of Cohen-Macaulay type (including rational singularity), arguably the most efficient packaging of an algebraic structure.The mathematical problems with which this proposal is concerned come from the overlapping areas of commutative algebra, algebraic geometry and computational algebra. The research program is focused on the search for generic and numerical solutions of sets of polynomial and analytic equations, such as those that apply to such diverse areas as algebraic geometry, combinatorics, cryptography, control/coding theory and robotic motion. The investigator studies the fine structure of these algebraic systems, and he develops methods and algorithms for solving them. At the same time he is seeking to break the computational logjam of several problems of computer algebra through a more fundamental understanding of their structure.
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Complexity of Algebraic Structures
  • 批准号:
    0855601
  • 项目类别:
    Standard Grant
  • 资助金额:
    $12.92万
  • 财政年份:
    2009
  • 负责人:
    Wolmer Vasconcelos
  • 依托单位:
Complexity in Commutative Algebra
  • 批准号:
    0500359
  • 项目类别:
    Standard Grant
  • 资助金额:
    $0.0万
  • 财政年份:
    2005
  • 负责人:
    Wolmer Vasconcelos
  • 依托单位:
Studies in Commutative Algebra and Computational Algebra
  • 批准号:
    9801413
  • 项目类别:
    Continuing Grant
  • 资助金额:
    $11.5万
  • 财政年份:
    1998
  • 负责人:
    Wolmer Vasconcelos
  • 依托单位:
Mathematical Sciences: Studies in Commutative Algebra and Its Applications to Computational Algebra
  • 批准号:
    9500786
  • 项目类别:
    Continuing Grant
  • 资助金额:
    $18.0万
  • 财政年份:
    1995
  • 负责人:
    Wolmer Vasconcelos
  • 依托单位:
海外基金