Steininger, Jakob Yurkevich, Sergey

A polyhedron $\textbf{P} \subset \mathbb{R}^3$ has Rupert's property if a hole can be cut into it, such that a copy of $\textbf{P}$ can pass through this hole. There are several works investigating this property for some specific polyhedra: for example, it is known that all 5 Platonic and 9 out of the 13 Archimedean solids admit Rupert's property. ...

Da Fontoura Costa, Luciano

Continuity and Connectedness constitute two central concepts in several theoretical and applied areas, including signal and image analysis, neuronal networks and deep learning, as well as scientific modeling in general. At the same time, several important theoretical concepts such as manifolds, which are extensively used in several applications, re...

Daviaud, Édouard

Recently, mass transference principles in metric number theory extended towards two direction. On one hand, the approximating sets can be taken of various shapes, balls, rectangles or even general open sets (one refers to some results of Rams and Koivusalo regarding this last example) when the ambient measure is Lebesgue, on the other hand, progres...

Coulon, Rémi Sela, Zlil

This article is a first step in the study of equations in periodic groups. As an application, we study the structure of periodic quotients of hyperbolic groups. We investigate for instance the Hopf and co-Hopf properties, the isomorphism problem, the existence of free splittings, etc. We also consider the automorphism group of such periodic groups....

Gutiérrez, Armando Walsh, Cormac

We introduce the notion of firm non-expansive mapping in weak metric spaces, extending previous work for Banach spaces and certain geodesic spaces. We prove that, for firm non-expansive mappings, the minimal displacement, the linear rate of escape, and the asymptotic step size are all equal. This generalises a theorem by Reich and Shafrir.

Haettel, Thomas

Philibert, Manon

Les sous-graphes isométriques d'hypercubes (dit cubes partiels) constituent une classe centrale de la théorie métrique des graphes. Ils englobent des familles de graphes importantes (arbres, graphes médians, graphes de topes de complexes de matroïdes orientés, etc.), provenant de différents domaines de recherche, tels que la géométrie discrète, la ...

Ancona, Michele Letendre, Thomas

We study the number of real roots of a Kostlan (or elliptic) random polynomial of degree d in one variable. More generally, we are interested in the distribution of the counting measure of the set of real roots of such a polynomial. We compute the asymptotics of the central moments of any order of these random variables, in the large degree limit. ...

Huang, Yi Ohshika, Ken'ichi Papadopoulos, Athanase

We undertake a systematic study of the infinitesimal geometry of the Thurston metric, showing that the topology, convex geometry and metric geometry of the tangent and cotangent spheres based at any marked hyperbolic surface representing a point in Teichmüller space can recover the marking and geometry of this marked surface. We then translate the ...

Saglam, Ismail Papadopoulos, Athanase

Consider a compact surface equipped with a fixed quadrangulation.One may identify each quadrangle on the surface by a Euclidean rectangle to obtain a singular flat metric on the surface with conical singularities. We call such a singular flat metric a rectangular structure. Westudy a metric on the space of unit area rectangular structures which isa...