腾讯会议695 900 385

2022年10月29日

报告人:尹晟

报告题目: RANK INEQUALITY DONE BY FREE PROBABILITY AND RANDOM MATRICES

报告摘要:

报告人简介:尹晟博士,目前在美国贝勒大学访问，主要从事自由概率及其应用相关研究,取得了丰富的研究成果.

报告人:汪旭敏

报告题目:Pointwise convergence of noncommutative Fourier series

报告摘要:I will talk about pointwise convergence of Fourier series for group von Neumann algebras and quantum groups. It is well-known that a number of approximation properties of groups can be interpreted as summation methods and mean convergence of the associated noncommutative Fourier series. Based on this framework, I will introduce the main theorem: a general criterion of maximal inequalities for approximate identities of noncommutative Fourier multipliers. By using this criterion, for any countable discrete amenable group, there exists a sequence of finitely supported positive definite functions tending to 1 pointwise, so that the associated Fourier multipliers on noncommutative Lp-spaces satisfy the pointwise convergence for all p > 1. In a similar fashion, I will show a large subclass of groups (as well as quantum groups) with the Haagerup property and the weak amenability. I will also talk about the Pointwise convergence of Fejér and Bochner-Riesz means in the noncommutative setting. Finally, I will mention a byproduct-- the dimension free bounds of the noncommutative Hardy-Littlewood maximal inequalities associated with convex bodies.

报告人简介:汪旭敏博士,主要从事非交换分析研究,相关成果发表于Journal of Noncommutative Geometry, Mem. Amer. Math. Soc.等.

报告人:熊枭

报告题目:拟微分算子的谱渐进估计

报告摘要:我将简要回顾一下经典的拟微分算子理论，主要提及符号计算和拟微分算子的正则性。在L2空间上，由正则性可知，负数阶（紧支撑）拟微分算子为紧算子。基于此，我将给出-1阶拟微分算子的谱渐进极限。最后，我会介绍这个谱渐进极限结果在非交换几何中的应用。

报告人简介:熊枭教授,哈尔滨工业大学,主要从事非交换分析与几何研究,相关成果发表于Comm. Math. Phys.,Mem. Amer. Math. Soc., Adv. Math.等.

报告人:王斯萌

报告题目:Noncommutative pointwise ergodic theorem for amenable groups

报告摘要:We prove a noncommutative analogue of Lindenstrauss' pointwise ergodic theorem for actions of amenable groups on von Neumann algebras. To do so, we establish the maximal ergodic inequality for averages of operator-valued functions on amenable groups. Our new arguments are based on a geometric construction of martingales based on the Ornstein-Weiss quasi-tilings, as well as a pure group-theoretic realization of harmonic analytic techniques from noncommutative Calderón-Zygmund theory.

报告人简介:王斯萌教授,哈尔滨工业大学,主要从事非交换分析与概率相关研究,相关成果发表于Duke Math. J., Comm. Math. Phys.,Probab. Theory Related Fields等.

报告人:黄景灏

报告题目:Isometries on noncommutative symmetric spaces

报告摘要:The study of the description of isometries on symmetric spaces was initiated by Banach, who obtained the general form of isometries between L_p spaces on a finite measure space. Representation of linear isometries between more general symmetric function spaces were later obtained by Lumer, Zaidenberg and Kalton, etc. In the 1950s, Kadison showed that a surjective linear isometry between two von Neumann algebras can be written as a Jordan *-isomorphism followed by a multiplication of a unitary operator. The complete description (for the semifinite case) of isometries on noncommutative L_p-spaces was obtained by Yeadon. However, for general separable noncommutative symmetric spaces E, the description of surjective isometries on E was obtained by Sourour (1981) and by Sukochev (1996) in some special settings. In our joint paper with Sukochev, we provide a complete description of all surjective linear isometries on separable noncommutative symmetric spaces affiliated with a semifinite von Neumann algebra, which answers a long-standing open question raised in the 1980s.

报告人简介:黄景灏研究员,哈尔滨工业大学,主要从事非交换分析与概率相关研究,相关成果发表于Adv. Math., Comm. Math. Phys.,JFA等.