Related papers: The Hyperbolic Ax-Lindemann-Weierstrass conjecture

In order to better understand the structure of classical rings of invariants for binary forms, Dixmier proposed, as a conjectural homogeneous system of parameters, an explicit collection of invariants previously studied by Hilbert. We…

We formulate and prove a combinatorial criterion to decide if an A-hypergeometric system of differential equations has a full set of algebraic solutions or not. This criterion generalises the so-called interlacing criterion in the case of…

Let $X$ be a $n$-dimensional smooth projective variety and $L$ be an ample Cartier divisor on $X$. We conjecture that a very general element of the linear system $|K_X+(3n+1)L|$ is a hyperbolic algebraic variety. This conjecture holds for…

This paper gives a self-contained introduction to the Hilbert projective metric $\mathcal{H}$ and its fundamental properties, with a particular focus on the space of probability measures. We start by defining the Hilbert pseudo-metric on…

We show the existence of hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants, addressing a conjecture of Claude LeBrun. This is achieved by showing, using results in geometric and arithmetic group theory, that certain hyperbolic…

A birationally liftable Galois section s of a hyperbolic curve X/k over a number field k yields an adelic point x(s) in the smooth completion of X. We show that x(s) is X-integral outside a set of places of Dirichlet density 0, or s is…

The K-theoretic analog of Spanier-Whitehead duality for noncommutative C*-algebras is shown to hold for the Ruelle algebras associated to irreducible Smale spaces. This had previously been proved only for shifts of finite type. Implications…

In this article we introduce a hyperbolic metric on the (normalized) space of stability conditions on projective K3 surfaces $X$ with Picard rank $\rho (X) =1$. And we show that all walls are geodesic in the normalized space with respect to…

We extend Lang's conjectures to the setting of intermediate hyperbolicity and prove two new results motivated by these conjectures. More precisely, we first extend the notion of algebraic hyperbolicity (originally introduced by Demailly) to…

In this paper, we prove the Khavinson conjecture for hyperbolic harmonic functions on the unit ball. This conjecture was partially solved in \cite{JKM2020}.

We prove the Invariant Subspace Conjecture for separable Hilbert spaces.

Using the concepts of Hyperbolic Classification of Natural Numbers, Essential Regions and Goldbach Conjecture Function we prove that the existence of a proof of the Goldbach Conjecture in First-Order Arithmetic would imply the existence of…

We prove the Baum-Connes conjecture for hyperbolic groups and their subgroups.

We prove the log-Brunn-Minkowski conjecture for convex bodies with symmetries to $n$ independent hyperplanes, and discuss the equality case and the uniqueness of the solution of the related case of the logarithmic Minkowski problem. We also…

We present a topological proof of the existence of a normally hyperbolic invariant manifold for maps. In our approach we do not require that the map is a perturbation of some other map for which we already have an invariant manifold. But a…

We construct Zollfrei Lorentzian metrics on every nontrivial orientable circle bundle over a orientable closed surface. Further we prove a weaker version of Guillemin's conjecture assuming global hyperbolicity of the universal cover.

Given isometric actions by a group G on finitely many \delta-hyperbolic metric spaces, we provide a sufficient condition that guarantees the existence of a single element in G that is hyperbolic for each action. As an application we prove a…

In this article we study a coarse version of the K-theoretic Farrell-Jones conjecture we call coarse or bounded isomorphism conjecture. With techniques that have already been used to prove the Farrell-Jones conjecture for hyperbolic groups…

Grothendieck gave two forms of his "main conjecture of anabelian geometry", i.e. the section conjecture and the hom conjecture. He stated that these two forms are equivalent and that if they hold for hyperbolic curves then they hold for…

Demailly's conjecture, which is a consequence of the Green-Griffiths-Lang conjecture on varieties of general type, states that an algebraically hyperbolic complex projective variety is Kobayashi hyperbolic. Our aim is to provide evidence…