Related papers: La structure des courbes analytiques
We define and study the overconvergent site of an algebraic variety, the sheaf of overconvergent functions on this site and show that the modules of finite presentations correspond to Berthelot's overconvergent isocrystals. We work with…
This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…
This talk gives an introduction into the subject of Seiberg-Witten curves and their relation to integrable systems. We discuss some motivations and origins of this relation and consider explicit construction of various families of…
In this paper, we survey recent developments concerning the stability of naturally defined bundles on curves that play a central role in the deformation theory of the curve.
The direct correlation function and the (static) structure factor for a seven-dimensional hard-sphere fluid are considered. Analytical results for these quantities are derived within the Percus-Yevick theory
Many real-world networks are theorized to have core-periphery structure consisting of a densely-connected core and a loosely-connected periphery. While this phenomenon has been extensively studied in a range of scientific disciplines, it…
These are expanded lecture notes for the summer school on Berkovich spaces that took place at the Institut de Math\'ematiques de Jussieu, Paris in 2010. They serve to illustrate some techniques and results from the dynamics on…
We survey our works on the locally analytic vectors of completed cohomology of modular curves.
The existence of instabilities, for example in the form of adversarial examples, has given rise to a highly active area of research concerning itself with understanding and enhancing the stability of neural networks. We focus on a popular…
The stability analysis of possibly time varying positive semigroups on non necessarily compact state spaces, including Neumann and Dirichlet boundary conditions is a notoriously difficult subject. These crucial questions arise in a variety…
A branch of generalizations of the Banach Fixed Point Theorem replaces contractivity by a weaker but still effective property. The aim of the present note is to extend the contraction principle in this spirit for such complete semimetric…
The main results in this note concern the characterization of the length of continua 1 (Theorems 2.5) and the parametrization of continua with finite length (Theorem 4.4). Using these results we give two independent and relatively…
The aim of this note is to give a gentle introduction to algebras of partial triangulations of marked surfaces, following the structure of a talk given during the 49th symposium on ring theory and representation theory, held in Osaka. This…
Over the past few years there has been considerable progress in the structural understanding of special Colombeau algebras. We present some of the main trends in this development: non-smooth differential geometry, locally convex theory of…
The purpose of this paper is to present projective geometry in a synthetic, visual and intuitive style through the central notion of harmonicity which leads to harmonic curves. This presentation includes new results, unpublished proofs of…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
In this research a new algebraic semantics of rough set theory including additional meta aspects is proposed. The semantics is based on enhancing the standard rough set theory with notions of 'relative ability of subsets of approximation…
We introduce three representative topics in semi-classical analysis. Starting from the correspondence between classical and quantum mechanics, basic semi-classical analysis tools and results are presented. The three topics are investigated…
This article proposes a unified analytical approach leading to a partial resolution of the Erdos-Straus, Sierpinski conjectures, and their generalization. We introduce an equivalent reformulation of these conjectures while constructing two…
A long-standing controversy in studies of spiral structure has concerned the lifetimes of individual spiral patterns. Much theoretical work has sought quasi-stationary spiral modes while N-body simulations have consistently displayed…