Algebraic geometry and representation theory in the study of matrix multiplication complexity and other problems in theoretical computer science
Algebraic geometry and representation theory in the study of matrix multiplication complexity and other problems in theoretical computer science
复制标题
理论计算机科学中矩阵乘法复杂性及其他问题研究中的代数几何和表示论
DOI：
10.1016/j.difgeo.2022.101888
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发表时间：
2022
影响因子：
0.5
通讯作者：
Landsberg, J.M.
中科院分区：
文献类型：
--
作者：
Landsberg, J.M.
理论计算机科学中的许多基本问题自然而然地被表示为以下问题的特例：设G是复约群，V是G-模，v，w是V的元素。确定w是否在V的G轨道闭包中。我解释了计算机科学问题，它们引起的表示论和代数几何中的问题，以及根据这些问题而出现的旧领域的新观点，如不变论。我主要关注矩阵乘法的复杂性。
Many fundamental questions in theoretical computer science are naturally expressed as special cases of the following problem: Let G be a complex reductive group, let V be a G-module, and let v, w be elements of V. Determine if w is in the G-orbit closure of v. I explain the computer science problems, the questions in representation theory and algebraic geometry that they give rise to, and the new perspectives on old areas such as invariant theory that have arisen in light of these questions. I focus primarily on the complexity of matrix multiplication.