报告题目：双随机(子)矩阵及其对称性 The convex polytope of doubly (sub)stochastic matrices and its symmetries
报告摘要：
The term stochastic matrix goes back at least to Romanovsky who provided a detailed discussion of stochastic matrices in 1935. Since then doubly stochastic matrices have been studied intensively due to its applications in Markov chains, majorizations and in the variety of modelling problems such as economics and operation research.
We first introduce three different ways to partition the polytope of doubly substochastic matrices into sub-polytopes via the prescribed row and column sums, the sum of all elements and the sub-defect respectively. Some applications of these three partitions are provided.
The second part of talk is regarding three symmetries: regular symmetry, Hankel-symmetry and centrosymmetry. We consider the sub-polytopes of symmetric doubly stochastic matrices, Hankel symmetric matrices and centrosymmetric matrices respectively. We characterize the extreme points of each sub-polytope.
报告人：曹雷，美国 Georgian Court University 数学系助理教授，美国数学学会（American Mathematical Society），美国数学协会（Mathematical Association of America）会员。从2014年开始从事有关双随机（子）矩阵的研究，至今已发表十余篇相关文章。
