### Higher order Fourier analysis of multiplicative functions and applications

, 2014

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### Uniformity of multiplicative functions and partition regularity of some quadratic equations

, 2013

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### A POINT OF VIEW ON GOWERS UNIFORMITY NORMS

, 2012

"... Abstract. Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and deducing properties of the function. Instead of focusing on the norms themselves, we study associated du ..."

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Abstract. Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and deducing properties of the function. Instead of focusing on the norms themselves, we study associated dual norms and dual functions. Combining this study with a variant of the Szemerédi Regularity Lemma, we give a decomposition theorem for dual functions, linking the dual norms to classical norms and indicating that the dual norm is easier to understand than the norm itself. Using the dual functions, we introduce higher order algebras that are analogs of the classical Fourier algebra, which in turn can be used to further characterize the dual functions. 1.

### unknown title

"... A point of view on Gowers uniformity norms Bernard Host and Bryna Kra Abstract. Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and deducing properties of the functio ..."

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A point of view on Gowers uniformity norms Bernard Host and Bryna Kra Abstract. Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and deducing properties of the function. Instead of focusing on the norms themselves, we study associated dual norms and dual functions. Combining this study with a variant of the Szemerédi Regularity Lemma, we give a decomposition theorem for dual functions, linking the dual norms to classical norms and indicating that the dual norm is easier to understand than the norm itself. Using the dual functions, we introduce higher order algebras that are analogs of the classical Fourier algebra, which in turn

### unknown title

"... A point of view on Gowers uniformity norms Bernard Host and Bryna Kra Abstract. Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and deducing properties of the functio ..."

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A point of view on Gowers uniformity norms Bernard Host and Bryna Kra Abstract. Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and deducing properties of the function. Instead of focusing on the norms themselves, we study associated dual norms and dual functions. Combining this study with a variant of the Szemerédi Regularity Lemma, we give a decomposition theorem for dual functions, linking the dual norms to classical norms and indicating that the dual norm is easier to understand than the norm itself. Using the dual functions, we introduce higher order algebras that are analogs of the classical Fourier algebra, which in turn