10 citations · 26 across the 18 of their papers we have counts for
18 papers · 1 filter
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 sets with missing differences in compact abelian groups
Pablo Candela, Fernando Chamizo, Antonio Córdoba
A much-studied problem posed by Motzkin asks to determine, given a finite set of integers, the so-called Motzkin density for , i.e., the supremum of upper densities of sets…
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…
Coloring graphs by translates in the circle
Pablo Candela, Carlos Catala, Robert Hancock +4
The fractional and circular chromatic numbers are the two most studied non-integral refinements of the chromatic number of a graph. Starting from the definition of a coloring base…
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}…
Regularity and inverse theorems for uniformity norms on compact abelian groups and nilmanifolds
Pablo Candela, Balázs Szegedy
We prove a general form of the regularity theorem for uniformity norms, and deduce an inverse theorem for these norms which holds for a class of compact nilspaces including all com…
A step beyond Freiman's theorem for set addition modulo a prime
Pablo Candela, Oriol Serra, Christoph Spiegel
Freiman's 2.4-Theorem states that any set satisfying and can be covered by an arithmetic progression of length at most…
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…
On sets with small sumset in the circle
Pablo Candela, Anne de Roton
We prove results on the structure of a subset of the circle group having positive inner Haar measure and doubling constant close to the minimum. These results go toward a continuou…
Notes on nilspaces: algebraic aspects
Pablo Candela
These notes constitute the first part of a detailed exposition of the theory of nilspaces developed by Camarena and Szegedy. We treat what can be called the algebraic part of the t…
A continuous model for systems of complexity 2 on simple abelian groups
Pablo Candela, Balázs Szegedy
It is known that if is a sufficiently large prime then for every function there exists a continuous function on the circle su…
On linear configurations in subsets of compact abelian groups, and invariant measurable hypergraphs
Pablo Candela, Balázs Szegedy, Lluís Vena
We prove an arithmetic removal result for all compact abelian groups, generalizing a finitary removal result of Král', Serra and the third author. To this end, we consider infinite…
On the dimension of additive sets
P. Candela, H. A. Helfgott
We study the relations between several notions of dimension for an additive set, some of which are well-known and some of which are more recent, appearing for instance in work of S…
Convergence results for systems of linear forms on cyclic groups, and periodic nilsequences
Pablo Candela, Olof Sisask
Given a positive integer and real number , let denote the minimum, over all sets of size at least , of the normalize…
A removal lemma for linear configurations in subsets of the circle
Pablo Candela, Olof Sisask
We obtain a removal lemma for systems of linear equations over the circle group, using a similar result for finite fields due to Král, Serra and Vena, and we discuss some applicati…
On the asymptotic maximal density of a set avoiding solutions to linear equations modulo a prime
Pablo Candela, Olof Sisask
Given a finite family F of linear forms with integer coefficients, and a compact abelian group G, an F-free set in G is a measurable set which does not contain solutions to any equ…