NSF/CBMS Regional Conference in the Mathematical Sciences: Wave Packets, Multilinear Operators and Carleson Theorems; May 23-28, 2004; Atlanta, GA

该主题领域是在该地区的多线性奇异积分，和一些相关的最大运营商，特别强调那些与一些不变性质的调制。 这是近十年来谐波分析的一个新的分支，其特点是使用波包技术，其根源可以追溯到L. Carleson和C. 40年前的一个农民。然而，直到1995年，这些技术的使用在傅立叶级数收敛的主题之外几乎没有感觉到。 就在那时，M。Lacey和C. Thiele利用相关的技术对A. Calderon关于双线性Hilbert变换。现在已经知道，通过相当数量的数学家的努力，这些技巧对于研究广泛的一类多线性奇异积分和极大算子是至关重要的。这些讲座的时机发生在已经有大量复杂结果的时候，从这些结果中可以看出一个美丽理论的迹象。 与其他数学领域的联系也在地平线上。Thiele教授将在一系列讲座中介绍这一最新发展，并将由该主题的主要研究人员进行一些额外的讲座。

The subject area is in the area of multilinear singular integrals, and some related maximal operators, with a particular emphasis on those with some invariance properties with respect to modulations. This is a new branch of Harmonic Analysis that has arisen within the last decade.A distinguishing feature of this area is the use of wave packet techniques which have roots going back to seminal work on convergence of Fourier series by L. Carleson, and C. Fefferman about 40 years ago. Yet the use of these techniques was hardly felt outside the subject of convergence of Fourier series until 1995. It was then that M. Lacey and C. Thiele used related techniques to a long standing conjecture of A. Calderon concerning the bilinear Hilbert transform.It is now understood, through the efforts of a sizable number of mathematicans, that these techniques are crucial to the study a wide class of multilinear singular integral and maximal operators. The timing of these lectures occurs when there is already a body of sophisticated results, from which are emerging signs of a beautiful theory. Connections to other fields of mathematics are at the horizon.Professor Thiele's will present this recent development in a series of lectures and there will be a few additional lectures by leading researchers in the subject.