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

这个美国-斯洛文尼亚数学项目是由北山加州州立大学的B. A. Sethuraman和他的搭档，卢布尔雅那大学的Tomaz Kosir共同完成的，该项目研究了与矩阵交换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异体的一种推广的变异体，重点研究不变子空间的变异体和交换矩阵的变异体。这些是与矩阵的几何性质相关的基本问题，与图形相关。联合研究计划采用了经典代数几何、计算代数、组合交换代数和表示理论的混合。两所大学的初级研究人员将参与部分研究。这项合作建立在Sethuraman和Kosir关于矩阵交换三元组的初步工作的基础上，并利用了美国方面在代数方面的互补优势和斯洛文尼亚方面在矩阵和算子理论方面的专业知识。结果将导致在数值计算中使用线性代数的精细模型。该数学研究项目通过使美国和中欧的专家在共同感兴趣和能力强的领域结合互补的人才和共享研究资源，实现了推进科学知识的计划目标。

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.