205 citations · 615 across the 51 of their papers we have counts for
6 papers · 1 filter
An inverse theorem for all finite abelian groups via nilmanifolds
Pablo Candela, Diego González-Sánchez, Balázs Szegedy
We prove a first inverse theorem for Gowers norms on all finite abelian groups that uses only nilmanifolds (rather than possibly more general nilspaces). This makes progress toward…
On measure-preserving -systems of order
Pablo Candela, Diego González-Sánchez, Balázs Szegedy
Building on previous work in the nilspace-theoretic approach to the study of Host-Kra factors of measure-preserving systems, we prove that every ergodic -system of…
On higher-order Fourier analysis in characteristic
Pablo Candela, Diego González-Sánchez, Balázs Szegedy
In this paper, the nilspace approach to higher-order Fourier analysis is developed in the setting of vector spaces over a prime field , with applications mainly in er…
On nilspace systems and their morphisms
Pablo Candela, Diego González-Sánchez, Balázs Szegedy
A nilspace system is a generalization of a nilsystem, consisting of a compact nilspace X equipped with a group of nilspace translations acting on X. Nilspace systems appear in diff…
Nilspace factors for general uniformity seminorms, cubic exchangeability and limits
Pablo Candela, Balázs Szegedy
We study a class of measure-theoretic objects that we call cubic couplings, on which there is a common generalization of the Gowers norms and the Host-Kra seminorms. Our main resul…
Nilspaces, nilmanifolds and their morphisms
Omar Antolin Camarena, Balazs Szegedy
Recent developments in ergodic theory, additive combinatorics, higher order Fourier analysis and number theory give a central role to a class of algebraic structures called nilmani…