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A new norm related to the Gowers U^3 norm

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If you have a question about this talk, please contact Anton Evseev.

The uniformity norms (or U^d norms, for d>1 a positive integer) were introduced about ten years ago by Gowers in his effective proof of Szemer├ędi’s theorem, and have played an important role in arithmetic combinatorics ever since. The U^2 norm is naturally related to Fourier analysis, and a very active trend in current research aims to develop an analogue of Fourier analysis for each U^d norm with d>2. The body of results of this research for d=3 is known as quadratic Fourier analysis. After an introduction to this area we will consider a new norm related to the U^3 norm, and discuss some of its applications in quadratic Fourier analysis, including a strengthening of a central theorem of Green and Tao (the inverse theorem for the U^3 norm), and how this stronger version of the theorem can be used to give a new proof of a recent decomposition-theorem of Gowers and Wolf.

This talk is part of the Junior Algebra and Number Theory seminar series.

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