Combinatorial Algebraic Geometry

这个项目涉及代数几何、交换代数和符号计算中的组合问题。这个项目的一个重要部分是对研究生和博士后的培训，特别是在以下三个领域：单项理想和格子理想的元胞分解，正则完整D-模的Grobner变形，以及多维超几何函数(由Gel‘fand-Kapranov-Zlevinsky定义)。作为这个项目的一部分，Sturmfels将与MutSumi Saito和Nobuki Takayama共同撰写一本关于超几何微分方程的Grobner变形的书。这个项目的另一个关键部分是与Eduardo Cattani和Alicia Dickenstein共同研究有理超几何函数及其与多维残数的关系。代数几何是研究由多项式方程定义的几何对象。它起源于19世纪对大卫·希尔伯特的研究，并在物理学和数据安全等领域得到了越来越多的现代应用。

STRUMFELS9970254This project concerns combinatorial problems arising from algebraic geometry, commutative algebra and symbolic computation. An essential part of this project is the training of graduate students and postdocs, specifically in the following three areas: cellular resolutions of monomial ideals and lattice ideals, Grobner deformations of regular holonomic D-modules, and multidimensional hypergeometric functions (as defined by Gel'fand-Kapranov-Zelevinsky). As part of this project, Sturmfels will write a book on ``Grobner deformations of hypergeometric differentialequations'' jointly with Mutsumi Saito and Nobuki Takayama. Anotherkey ingredient in this project is the study, jointly with Eduardo Cattani and Alicia Dickenstein of rational hypergeometric functions and its relations to multidimensional residues.Algebraic geometry is the study of geometric objects defined by polynomial equations. It has its roots in the 19th century investigations of David Hilbert, and has increasing modern applications to fields like physics and data security.