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math.DS2025
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…
math.DS2018
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…
math.DS2018
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…