标题： 凸几何与算法理论中的Brascamp-Lieb不等式 显示英文标题

标题： The Brascamp-Lieb inequality in Convex Geometry and in the Theory of Algorithms

摘要： 调和分析中的Brascamp-Lieb不等式由Brascamp和Lieb在1976年的一般秩一情形下证明，而Lieb在1990年完成了完整证明。它表明，在某个不等式中，可以通过检查中心高斯分布来确定最佳常数。大约在1990年，Keith M Ball的开创性工作使得该不等式在凸几何中有各种应用，甚至在离散几何中也有应用，比如Brazitikos关于Helly定理的定量分数版本。另一方面，确定Brascamp-Lieb不等式中的最佳常数以及可能的高斯极值点可以表述为正定矩阵问题，而这个问题与算法理论有着密切联系。 显示英文摘要

摘要： The Brascamp-Lieb inequality in harmonic analysis was proved by Brascamp and Lieb in the rank one case in 1976, and by Lieb in 1990. It says that in a certain inequality, the optimal constant can be determined by checking the inequality for centered Gaussian distributions. It was Keith M Ball's pioneering work around 1990 that led to various applications of the inequality in Convex Geometry, and even in Discrete Geometry, like Brazitikos' quantitative fractional version of the Helly Theorem. On the other hand, determining the optimal constant and possible Gaussian extremizers for the Brascamp-Lieb inequality can be formulated as a problem in terms of positive definite matrices, and this problem has intimate links to the Theory of Algorithms.