Freddie Manners

activity

20132026

most citedAdditive triples of bijections, or the toroidal semiqueens problem

25 citations · 88 across the 11 of their papers we have counts for

collaborators

18 papers

math.AG2026

The motivic class of the space of genus $0$ maps to the flag variety

Jim Bryan, Balázs Elek, Freddie Manners +2

Let $k$ be a field, let $Fl_{n + 1}$ be the variety of complete flags in $A_{k}^{n + 1}$ , and let $Ω_{β}^{2} (Fl_{n + 1})$ be the sp…

math.NT2024

Marton's Conjecture in abelian groups with bounded torsion

W. T. Gowers, Ben Green, Freddie Manners +1

We prove a Freiman--Ruzsa-type theorem with polynomial bounds in arbitrary abelian groups with bounded torsion, thereby proving (in full generality) a conjecture of Marton. Specifi…

math.NT2023

On a conjecture of Marton

W. T. Gowers, Ben Green, Freddie Manners +1

We prove a conjecture of K. Marton, widely known as the polynomial Freiman--Ruzsa conjecture, in characteristic $2$ . The argument extends to odd characteristic, with details to fol…

math.NT2023★ 12 cited

Sumsets and entropy revisited

Ben Green, Freddie Manners, Terence Tao

The entropic doubling $σ_{ent} [X]$ of a random variable $X$ taking values in an abelian group $G$ is a variant of the notion of the doubling constant $σ [A]$ of a fin…

math.CO2022★ 4 cited

Transversals in quasirandom latin squares

Sean Eberhard, Freddie Manners, Rudi Mrazović

A transversal in an $n \times n$ latin square is a collection of $n$ entries not repeating any row, column, or symbol. Kwan showed that almost every $n \times n$ latin square has $…

math.NT2021★ 2 cited

True complexity and iterated Cauchy--Schwarz

Freddie Manners

We prove a polynomial bound in the "true complexity" problem of Gowers and Wolf. The proof uses only repeated applications of the Cauchy--Schwarz inequality, answering negatively a…

math.CO2021★ 8 cited

The apparent structure of dense Sidon sets

Sean Eberhard, Freddie Manners

The correspondence between perfect difference sets and transitive projective planes is well-known. We observe that all known dense (i.e., close to square-root size) Sidon subsets o…

math.CO2020★ 11 cited

An asymptotic for the Hall--Paige conjecture

Sean Eberhard, Freddie Manners, Rudi Mrazović

Hall and Paige conjectured in 1955 that a finite group $G$ has a complete mapping if and only if its Sylow $2$ -subgroups are trivial or noncyclic. This conjecture was proved in 200…

math.CO2017

A proof of Tomescu's graph coloring conjecture

Jacob Fox, Xiaoyu He, Freddie Manners

In 1971, Tomescu conjectured that every connected graph $G$ on $n$ vertices with chromatic number $k \geq 4$ has at most $k! (k - 1)^{n - k}$ proper $k$ -colorings. Recently, Knox and Moha…

math.NT2017

Formulations of the PFR Conjecture over $Z$

Freddie Manners

The polynomial Fre\uıman--Ruzsa conjecture is a fundamental open question in additive combinatorics. However, over the integers (or more generally $R^{d}$ or $Z^{d}$ )…

math.NT2017★ 3 cited

Good Bounds in Certain Systems of True Complexity One

Freddie Manners

Let $Φ = (ϕ_{1}, \dots, ϕ_{6})$ be a system of $6$ linear forms in $3$ variables, i.e. $ϕ_{i} : Z^{3} \to Z$ for each $i$ . Suppose also that $Φ$ has Cauchy--Schwarz com…

math.DS2016

The structure theory of Nilspaces III: Inverse limit representations and topological dynamics

Yonatan Gutman, Freddie Manners, Péter P. Varjú

This paper forms the third part of a series by the authors [GMV1,GMV2] concerning the structure theory of nilspaces. A nilspace is a compact space $X$ together with closed collecti…

math.DS2016

The structure theory of Nilspaces II: Representation as nilmanifolds

Yonatan Gutman, Freddie Manners, Péter P. Varjú

This paper forms the second part of a series by the authors [GMV1,GMV3] concerning the structure theory of nilspaces of Antolín Camarena and Szegedy. A nilspace is a compact space…

math.DS2016

The structure theory of Nilspaces I

Yonatan Gutman, Freddie Manners, Péter P. Varjú

This paper forms the first part of a series by the authors [GMV2,GMV3] concerning the structure theory of nilspaces of Antolín Camarena and Szegedy. A nilspace is a compact space $…

math.CO2015

Finding a low-dimensional piece of a set of integers

Freddie Manners

We show that a finite set of integers $A \subseteq Z$ with $∣ A + A ∣ \leq K ∣ A ∣$ contains a large piece $X \subseteq A$ with Freĭman dimension $O (lo g K)$ , where large means $…

math.CO2015★ 25 cited

Additive triples of bijections, or the toroidal semiqueens problem

Sean Eberhard, Freddie Manners, Rudi Mrazović

We prove an asymptotic for the number of additive triples of bijections ${1, \dots, n} \to Z / n Z$ , that is, the number of pairs of bijections $π_1,π_2\colon \{1,\dot…

math.CO2013★ 2 cited

A solution to the Pyjama Problem

Freddie Manners

The "pyjama stripe" is the subset of $R^{2}$ consisting of a vertical strip of width $2 ε$ around every integer $x$ -coordinate. The "pyjama problem" asks whether f…

math.CO2013★ 21 cited

Sets of integers with no large sum-free subset

Sean Eberhard, Ben Green, Freddie Manners

Answering a question of P. Erdos from 1965, we show that for every eps>0 there is a set A of n integers with the following property: every subset A' of A with at least (1/3 + eps)n…

The motivic class of the space of genus 0 maps to the flag variety

Marton's Conjecture in abelian groups with bounded torsion

On a conjecture of Marton

Sumsets and entropy revisited

Transversals in quasirandom latin squares

True complexity and iterated Cauchy--Schwarz

The apparent structure of dense Sidon sets

An asymptotic for the Hall--Paige conjecture

A proof of Tomescu's graph coloring conjecture

Formulations of the PFR Conjecture over Z

Good Bounds in Certain Systems of True Complexity One

The structure theory of Nilspaces III: Inverse limit representations and topological dynamics

The structure theory of Nilspaces II: Representation as nilmanifolds

The structure theory of Nilspaces I

Finding a low-dimensional piece of a set of integers

Additive triples of bijections, or the toroidal semiqueens problem

A solution to the Pyjama Problem

Sets of integers with no large sum-free subset

The motivic class of the space of genus $0$ maps to the flag variety

Formulations of the PFR Conjecture over $Z$