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

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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.