报告摘要：It is well-known that the doubly stochastic orbit of a self-adjoint n×n matrix A coincides with the Hardy-Littlewood-Polya orbit of A. Moreover, the set of all extreme points of the doubly stochastic orbit of A coincides with the set of all matrices which are unitarily equivalent to A.In 1982, Alberti and Uhlmann asked how to formulate a variant of these results in the setting of von Neumann algebras. In 1987, Hiai obtained that the doubly stochastic orbit coincides with the Hardy-Littlewood-Polya orbit in the setting of a finite von Neumann algebra equipped with a finite faithful normal trace, and he conjectured that the assumption that the trace is finite is sharp.

In this talk, we present an answer to the problem by Alberti and Uhlmann in the setting of general semifinite von Neumann algebras. In particular, we confirm Hiai's conjecture, and completely resolve a problem raised by Luxemburg in 1967 on the description of extreme points of the Hardy-Littlewood-Polya orbit of an integrable function on a finite measure space.

报告人简介：黄景灏，哈尔滨工业大学研究员。2013年本科毕业于中山大学数学学院，2019年在澳大利亚新南威尔士大学英国威廉希尔公司官网获得博士学位。主要从事非交换分析理论的研究，解决了该领域中若干公开问题，包括彻底解决了荷兰院士Luxemburg于1967年提出的轨道极端点问题，回答了德国院士Uhlmann于1982年提出的von Neumann代数中自伴算子的双随机轨道问题并证明了日本数学家Hiai的一个猜测，解决了澳大利亚院士Sukochev于30多年前提出的关于非对称空间上的保距映射的著名问题，证明了Kaftal-Weiss导子定理对任意C*代数成立等。目前，在 《Advance Mathematics》，《Journal of Functional Analysis》等国际顶级数学期刊上发表论文20多篇，被同行引用200余次。