N. Mavraki

activity

20132026

most citedImpossible intersections in a Weierstrass family of elliptic curves

3 citations · 11 across the 14 of their papers we have counts for

collaborators

17 papers

math.DS2026

Dynamical relations on $P^{1}$ , higher bifurcations, and arithmetic bigness

Laura DeMarco, Niki Myrto Mavraki

In this article, we study algebraic relations among rational maps on $P^{1}$ and among their preperiodic points. Working over $C$ , we characterize algebraic familie…

math.NT2025

A quantitative dynamical Zhang fundamental inequality and Bogomolov-type problems

Niki Myrto Mavraki, Jit Wu Yap

We prove a quantitative version of Zhang's fundamental inequality for heights attached to polarizable endomorphisms. As an application, we obtain a gap principle for the Néron-Tate…

math.DS2024

The geometry of preperiodic points in families of maps on $P^{N}$

Laura DeMarco, Niki Myrto Mavraki

We study the dynamics of algebraic families of maps on $P^{N}$ , over the field $C$ of complex numbers, and the geometry of their preperiodic points. The goal of thi…

math.DS2024

Bounded geometry for PCF-special subvarieties

Laura DeMarco, Niki Myrto Mavraki, Hexi Ye

For each integer $d \geq 2$ , let $M_{d}$ denote the moduli space of maps $f : P^{1} \to P^{1}$ of degree $d$ . We study the geometric configurations of subsets of postcriti…

math.DS2023★ 1 cited

Geometry of PCF parameters in spaces of quadratic polynomials

Laura DeMarco, Niki Myrto Mavraki

We study algebraic relations among postcritically finite (PCF) parameters in the family $f_{c} (z) = z^{2} + c$ . Ghioca, Krieger, Nguyen and Ye proved that an algebraic curve in $\mathb…

math.DS2022★ 1 cited

Dynamics on $P^{1}$ : preperiodic points and pairwise stability

Laura DeMarco, Niki Myrto Mavraki

In [DKY], it was conjectured that there is a uniform bound $B$ , depending only on the degree $d$ , so that any pair of holomorphic maps $f, g : P^{1} \to P^{1}$ with degr…

math.NT2022

Height coincidences in products of the projective line

Niki Myrto Mavraki, Harry Schmidt, Robert Wilms

We consider hypersurfaces in $(P^{1})^{n}$ that contain a generic sequence of small dynamical height with respect to a split map and project onto $n - 1$ coordinates. We show th…

math.NT2022

On the dynamical Bogomolov conjecture for families of split rational maps

Niki Myrto Mavraki, Harry Schmidt

We prove that Zhang's dynamical Bogomolov conjecture holds uniformly along $1$ -parameter families of rational split maps and curves. This provides dynamical analogues of recent res…

math.NT2021

Arithmetic dynamics of random polynomials

Pierre Le Boudec, Niki Myrto Mavraki

We investigate from a statistical perspective the arithmetic properties of the dynamics of polynomials of fixed degree and defined over the field of rational numbers. To start with…

math.NT2021

A dynamical Shafarevich theorem for endomorphisms of $P^{N}$

Jamie Juul, Holly Krieger, Nicole Looper +1

We prove a dynamical analogue of the Shafarevich conjecture for morphisms $f : P_{K}^{N} \to P_{K}^{N}$ of degree $d \geq 2$ , defined over a number field $K$ . This extends previ…

math.DS2021

Variation of Canonical Height for Fatou points on $P^{1}$

Laura DeMarco, Niki Myrto Mavraki

Let $f : P^{1} \to P^{1}$ be a map of degree $> 1$ defined over a function field $k = K (X)$ , where $K$ is a number field and $X$ is a projective curve over $K$ . For each…

math.NT2020★ 1 cited

Elliptic surfaces and intersections of adelic $R$ -divisors

Laura DeMarco, Niki Myrto Mavraki

Suppose $E \to B$ is a non-isotrivial elliptic surface defined over a number field, for smooth projective curve $B$ . Let $k$ denote the function field $\overline{\mathbb{…

math.NT2017

Variation of canonical height and equidistribution

Laura DeMarco, Niki Myrto Mavraki

Let $π : E \to B$ be an elliptic surface defined over a number field $K$ , where $B$ is a smooth projective curve, and let $P : B \to E$ be a section defined over $K$ with canonical he…

math.NT2015

Algebraic approximations to linear combinations of powers: an extension of results by Mahler and Corvaja-Zannier

Avinash Kulkarni, Niki Myrto Mavraki, Khoa D. Nguyen

For every complex number $x$ , let $∥ x ∥_{Z} := min {∣ x - m ∣ : m \in Z}$ . Let $K$ be a number field, let $k \in N$ , and let $α_{1}, \dots, α_{k}$ be non-zero…

math.NT2015★ 3 cited

Impossible intersections in a Weierstrass family of elliptic curves

Niki Myrto Mavraki

Consider the Weierstrass family of elliptic curves $E_{λ} : y^{2} = x^{3} + λ$ parametrized by nonzero $λ \in Q_{2}$ , and let $P_{λ} (x) = (x, x^{3} + λ) \in E_{λ}$ . In this article,…

math.DS2015★ 2 cited

Quasi-adelic measures and equidistribution on $P^{1}$

Niki Myrto Mavraki, Hexi Ye

Baker-Rumely and Favre-Rivera-Letelier independently proved an important arithmetic equidistribution theorem for points of small height on the Berkovich compactification of the pro…

math.NT2013★ 3 cited

Variation of the canonical height in a family of rational maps

Dragos Ghioca, Niki Myrto Mavraki

Let $d \geq 2$ be an integer, let $c (t)$ be any rational map, and let $f_{t} (z) := (z^{d} + t) / z$ be a family of rational maps indexed by t. For each algebraic number $t$ , we let $h_{f_t}(…

Dynamical relations on P1, higher bifurcations, and arithmetic bigness

A quantitative dynamical Zhang fundamental inequality and Bogomolov-type problems

The geometry of preperiodic points in families of maps on PN

Bounded geometry for PCF-special subvarieties

Geometry of PCF parameters in spaces of quadratic polynomials

Dynamics on P1: preperiodic points and pairwise stability

Height coincidences in products of the projective line

On the dynamical Bogomolov conjecture for families of split rational maps

Arithmetic dynamics of random polynomials

A dynamical Shafarevich theorem for endomorphisms of PN

Variation of Canonical Height for Fatou points on P1

Elliptic surfaces and intersections of adelic R-divisors

Variation of canonical height and equidistribution

Algebraic approximations to linear combinations of powers: an extension of results by Mahler and Corvaja-Zannier

Impossible intersections in a Weierstrass family of elliptic curves

Quasi-adelic measures and equidistribution on P1

Variation of the canonical height in a family of rational maps

Dynamical relations on $P^{1}$ , higher bifurcations, and arithmetic bigness

The geometry of preperiodic points in families of maps on $P^{N}$

Dynamics on $P^{1}$ : preperiodic points and pairwise stability

A dynamical Shafarevich theorem for endomorphisms of $P^{N}$

Variation of Canonical Height for Fatou points on $P^{1}$

Elliptic surfaces and intersections of adelic $R$ -divisors

Quasi-adelic measures and equidistribution on $P^{1}$