2022年10月23日

报告人:张浩楠

报告题目: Quantum KKL, Talagrand and Friedgut's theorems

报告摘要:

The KKL theorem is a fundamental result in Boolean analysis,saying that any Boolean function has an influential variable.Two related results are Talagrand's inequality which implies the KKL theorem, and Friedgut's theorem on juntas. Montanaro and Osborne proposed a quantum extension of Boolean functions.In this context, some classical results have been extended to the quantum setting, such as Talagrand's inequality. However, this quantum Talagrand's inequality does not seem to derive a KKL theorem in the quantum setting. So a quantum version of the KKL theorem seems to be missing, as conjectured by Montanaro and Osborne. In this talk, I will present an alternative answer to this question. We prove that every balanced quantum Boolean function has a geometrically influentialvariable. This is based on a quantum analogue of a variant of Talagrand's inequality which we prove using recently studied hypercontractivity and gradient estimates. We also prove Friedgut's junta Theorem in the quantum setting that has applications in the learnability of quantum observables. This isbased on joint work with Cambyse Rouzé(TUM) and Melchior Wirth (IST Austria).

报告人简介:主要研究方向为非交换分析及其应用,相关学术成果发表于Comm. Math. Phys.,Adv. Math.等国际期刊.

报告人:刘双

题目：Isoperimetric inequality and functional inequalities on non-negatively curved graph

摘要：In this talk, I will present isoperimetric inequality on non-nonnegatively curved graphs. Moreover, I will discuss the equivalent between isoperimetric inequality, functional inequalities and heat kernel uniform upper bound on non-nonnegatively curved graphs. These functional inequalities include Sobolev inequality, Nash inequality, Faber–Krahn inequality and log- Sobolev inequality. This talk is based on the joint works with Prof. Yong Lin and Hongye Song.

报告人简介：刘双，博士毕业于中国人民大学，之后于清华大学丘成桐数学科学中心从事博士后工作，现任中国人民大学数学学院讲师。研究方向为图上的几何和分析，感兴趣的主题有图上的梯度估计、热核估计和泛函不等式，部分研究成果发表在Adv. Math.，J. Reine Angew. Math.和Calc. Var. Partial Differential Equations上。

报告人:孙龙发

报告题目:Stability properties of three classes non-linear mappings between Banach spaces

报告摘要:In this talk, we study the stability ofε-isometries、ε-norm-additive mappings andε-phase isometries between Banach spaces. We obtain a series of new stability results about the three classes mappings. For instance, we prove that every surjectiveε-norm-additive mapping between two Banach spaces can be approximated by a linear surjective isometry with the error no more than 3/2ε. The estimate is sharp.

报告人简介：孙龙发，博士，华北电力大学数理系硕士研究生导师。主要从事Banach空间理论以及扰动等距理论的研究。近年来，在Results Math.、J. Math. Anal. Appl.、Acta Math. Sin.(Engl. Ser.)等期刊发表论文20余篇。目前主持国家自然科学基金、河北省自然科学基金和中央高校科研业务费各一项。

报告人:程国正

报告题目: Cesaro Exponents of Mixed Norm Spaces

报告摘要: In 1934, G. H. Hardy and J. E. Littlewood calculated the optimal Cesaro exponent for Hardy spaces. But this exponent has never been determined for other spaces since then. In this talk we calculate it for mixed norm spaces, hence, including the Bergman spaces in particular.

报告人简介:程国正，大连理工大学数学科学学院教授，博士生导师，主要从事算子理论与算子代数研究。先后主持完成3项国家自然科学基金项目，在IMRN, J. Funct. Anal. Trans. Amer. Math.Soc.等数学刊物上发表论文十余篇。

报告人：赖旭东

报告题目: Fourier restriction estimates on quantum Euclidean spaces

报告摘要：In this talk, we willintroducethe Fourier restriction phenomena on quantum Euclidean spaces. In particular, we establish the analogues of the Stein-Tomas restriction theorem and the two-dimensional full restriction theorem. This isjoint work with G. Hong and L. Wang.

报告人简介:任教于哈尔滨工业大学 数学研究院.相关学术成果发表于Comm. Math. Phys., Trans. Amer. Math.Soc.等国际期刊.

报告人：夏润莲

报告题目: Fourier multipliers coming from group actions on

tree-like structures

报告摘要:

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报告人简介:主要研究方向为非交换调和分析,相关学术成果发表于Adv. Math.,JFA等国际期刊