Combinatorial Algebraic Geometry

这个项目涉及由代数几何、交换代数和符号计算引起的组合问题。这个项目的一个重要部分是培养研究生和博士后，特别是在以下三个领域：单项式理想和晶格理想的细胞分辨率，正则完整d模的Grobner变形，以及多维超几何函数（由Gel'fand-Kapranov-Zelevinsky定义）。作为该项目的一部分，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。该项目的另一个关键因素是与Eduardo Cattani和Alicia Dickenstein共同研究理性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的学科。它起源于19世纪大卫·希尔伯特（David Hilbert）的研究，并在物理学和数据安全等领域有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.