非交换调和分析专题讲习班

This project devotes to the noncommutative harmonic analysis. It includes two parts. One is about the basic concept and professional knowledge for Lie groups, such as the Fourier transform on the Heisenberg group, noncommutative Lp spaces, function spaces on quantum tori. Another part is about the frontier topics in noncommutative analysis, such as the multilinear spectral multipliers, Fourier multipliers on quantum tori, pointwise convergence of the Fourier series for group von Neumann algebras. New methods and progress in these fields will be discussed . This project will help young students and researches to know the hot and advanced research fields, the main methods and the popular tools in noncommutative harmonic analysis, thereby promoting the development of noncommutative harmonic analysis in China.

本项目是关于非交换调和分析中的重要基础及前沿研究领域的一个专题讲习班..主要内容分为两个方面：基础部分主要讲授海森堡群上Fourier变换及谱乘子理论、非交换Lp空间、量子环面上的函数空间等。专题部分，主要是结合专家们最新的重要研究成果，针对国际前沿的问题进行专题讲授，多线性谱乘子方面的研究问题,量子环面上的Fourier乘子,群代数上的Fourier级数点态收敛的重大进展及成果等。并对发展趋势、研究方法进行讲解及讨论。我们希望通过这个讲习班的学习，青年学者们能够较快地了解相关领域的国际前沿问题及发展趋势，为未来的科研工作开辟的新的研究方向。从而带动国内非交换调和分析的发展。