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Spectral algorithms in higher-order Fourier analysis
Pablo Candela, Diego González-Sánchez, Balázs Szegedy
Our goal is to provide simple and practical algorithms in higher-order Fourier analysis which are based on spectral decompositions of operators. We propose a general framework for…
On the inverse theorem for Gowers norms in abelian groups of bounded torsion
Pablo Candela, Diego González-Sánchez, Balázs Szegedy
In recent work, Jamneshan, Shalom and Tao proved an inverse theorem for the Gowers -norm on finite abelian groups of fixed torsion , where the final correlating harmoni…
Free nilspaces, double-coset nilspaces, and Gowers norms
Pablo Candela, Diego González-Sánchez, Balázs Szegedy
Compact finite-rank nilspaces have become central in the nilspace approach to higher-order Fourier analysis, notably through their role in a general form of the inverse theorem for…
A refinement of Cauchy-Schwarz complexity
Pablo Candela, Diego González-Sánchez, Balázs Szegedy
We introduce a notion of complexity for systems of linear forms, called sequential Cauchy-Schwarz complexity, which is parametrized by two positive integers and refines th…
On sets with small sumset and m-sum-free sets in Z/pZ
Pablo Candela, Diego González-Sánchez, David J. Grynkiewicz
The conjecture in groups for prime states that if is a nonempty subset of satisfying $2A\neq \mathbb{Z}/p\mathbb{Z}…
A Plünnecke-Ruzsa inequality in compact abelian groups
Pablo Candela, Diego González-Sánchez, Anne de Roton
The Plünnecke-Ruzsa inequality is a fundamental tool to control the growth of finite subsets of abelian groups under repeated addition and subtraction. Other tools to handle sumset…