Approximating shapes with algebraic spline geometry

用代数样条几何近似形状

• 批准号: 2601170
• 金额: --
• 依托单位: Swansea University
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2601170
• 关键词: Approximating; shapes; algebraic; spline; geometry

The overarching aim of the project is to explore tools from commutative algebra, algebraic geometry, and combinatorics to study approximation methods based on piecewise polynomial functions, also known as splines. The project will focus on algebraic aspects of multivariate spline functions, particularly those supported on triangulations and tetrahedral partitions. For this, we will combine elements from homological algebra, fat points schemes, and syzygies, along with methods from rigidity theory and symbolic computation, including computational algebraic geometry and Groebner bases.Throughout the project, the student will complement their background in algebra, and/or combinatorics & geometry and develop an understanding of the different methods to study multivariate spline functions. The project will be oriented towards the student's interest on theoretical or computational aspects of the topic.

该项目的首要目标是探索交换代数，代数几何和组合学的工具，以研究基于分段多项式函数（也称为样条）的近似方法。该项目将集中在代数方面的多元样条函数，特别是那些支持三角剖分和四面体分区。为此，我们将结合联合收割机元素从同调代数，胖点计划，和syzygies，沿着方法从刚性理论和符号计算，包括计算代数几何和Groebner基地。在整个项目中，学生将补充他们的背景代数，和/或组合学和几何和发展的不同方法来研究多元样条函数的理解。该项目将面向学生对该主题的理论或计算方面的兴趣。