New Directions in Computational Algebraic Geometry

计算代数几何的新方向

• 批准号: 0200729
• 负责人: Bernd Sturmfels
• 金额: $ 24.97万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-07-01 至 2005-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0200729&HistoricalAwards=false
• 关键词: New; Directions; Computational; Algebraic; Geometry

This project develops new algorithms and new applications forcomputational algebraic geometry. If focusses on the followingfour specific topics: Computing amoebas, toric algebra of graphicalmodels, semi-definite programming and the real Nullstellensatz.It involves tools from combinatorics, commutative algebra andsymbolic computation, specifically the method of Grobner bases.The investigator also writes two books, one on Solving Systems of Polynomial Equations, and the other on Combinatorial Commutative Algebra.This project develops new algorithms and new applications forcomputational algebra. The research in this project is partlycollaborative with researchersin other fields, and it has applications to Statistics, Bioinformaticsand Computer Science. The use of algebraic methods plays an increasingly important role for the analysis of the U.S. census data provided by theNational Institute for Statistical Sciences, and this project providesfoundational research for this application. In Computer Science, thesetechniques are used in machine learning and artificial intelligence.

该项目为计算代数几何开发新算法和新应用。如果重点关注以下四个具体主题：计算阿米巴、图形模型的环面代数、半定规划和实 Nullstellensatz。它涉及组合学、交换代数和符号计算的工具，特别是 Grobner 基的方法。研究人员还写了两本书，一本是关于多项式方程组的求解，另一本是关于组合的 交换代数。该项目开发计算代数的新算法和新应用。 该项目的研究部分是与其他领域的研究人员合作的，它应用于统计学、生物信息学和计算机科学。代数方法的使用对于国家统计科学研究所提供的美国人口普查数据的分析发挥着越来越重要的作用，该项目为此应用提供了基础研究。在计算机科学中，这些技术用于机器学习和人工智能。