U.S.-Slovenia Mathematics Research on Some Varieties Defined by Matrices

加州州立大学北岭分校的B·A·塞图拉曼和他的合作伙伴卢布尔雅那大学的托马兹·科西尔之间的这项美国-斯洛文尼亚数学项目，研究了与交换矩阵集有关的具体和计算问题。他们打算共同研究作为行列式变体的推广的簇，重点研究不变子空间的行列式簇和交换矩阵的簇。这些都是与图形相关的矩阵的几何性质相关的基本问题。联合研究计划结合了经典代数几何、计算代数、组合交换代数和表示理论。来自两所大学的初级研究人员将参与部分研究。这一合作建立在Sthuraman和Kosel关于交换矩阵三元组的初步工作的基础上，并利用了美方在代数方面的互补优势以及斯洛文尼亚在矩阵和算子理论方面的专业知识。结果应该导致在数值计算中使用线性代数的精细化模型。这一数学研究项目通过使美国和中欧的专家能够结合互补的人才，并在共同感兴趣和能力强的领域共享研究资源，实现了促进科学知识发展的计划目标。

This US-Slovenian mathematics project between B. A. Sethuraman of the California State University, Northridge, and his partner, Tomaz Kosir of the University of Ljubljana, examines concrete and computational problems concerned with commuting sets of matrices. Together they intend to study varieties that are a generalization of determinantal varieties with some emphasis on determinantal varieties of invariant subspaces and varieties of commuting matrices. These are fundamental questions associated with geometric properties of matrices that have relevance to graphing.The joint research plan employs a mix of classical algebraic geometry, computational algebra, combinatorial commutative algebra and representations theory. Junior researchers from both universities will participate in portions of the research. This collaboration builds upon initial work by Sethuraman and Kosir on commuting triples of matrices and utilizes complementary strengths of the U.S. side in algebra and Slovenian expertise in matrix and operator theory. Results should lead to refined models for using linear algebra in numerical computations. This mathematics research project fulfills the program objective of advancing scientific knowledge by enabling experts in the United States and Central Europe to combine complementary talents and share research resources in areas of strong mutual interest and competence.