论文标题
割线的品种和矩阵乘法的复杂性
Secant varieties and the complexity of matrix multiplication
论文作者
论文摘要
这是一项有关确定张量的边界等级的调查，尤其是与矩阵乘法复杂性研究相关的调查。一方面，这是一个主题，在理论计算机科学中具有重要意义，另一方面，这是一个涉及代数几何的许多美丽主题，例如经典和最新的雪橇品种方程式（例如，通过矢量束和代表性理论方法）以及零点的几何学和变形理论。
This is a survey primarily about determining the border rank of tensors, especially those relevant for the study of the complexity of matrix multiplication. This is a subject that on the one hand is of great significance in theoretical computer science, and on the other hand touches on many beautiful topics in algebraic geometry such as classical and recent results on equations for secant varieties (e.g., via vector bundle and representation-theoretic methods) and the geometry and deformation theory of zero dimensional schemes.
