Related papers: Adic curves: stable reduction, skeletons and metri…
We consider the space of embeddings of finitely many circles that bound disks in non-positively curved surfaces. We index the connected components of this space with finite rooted trees and show that the connected components are classifying…
Assur graphs are a tool originally developed by mechanical engineers to decompose mechanisms for simpler analysis and synthesis. Recent work has connected these graphs to strongly directed graphs, and decompositions of the pinned rigidity…
The aim of this paper is to classify reduction types of algebraic curves. Reduction types capture the discrete invariants of fibres in one-dimensional families of curves, and they have been described in genus 1, 2 and 3. For fixed genus…
A brief overview of dimensional reductions for diffeomorphism invariant theories is given. The distinction between the physical idea of compactification and the mathematical problem of a consistent truncation is discussed, and the typical…
We study the geometry of germs of definable (semialgebraic or subanalytic) sets over a $p$-adic field from the metric, differential and measure geometric point of view. We prove that the local density of such sets at each of their points…
Consider the semialgebraic structure over the real field. More generally, let an ominimal structure be over a real closed field. We show that a definable metric space X with a definable metric d is embedded into a Euclidean space so that…
Various methods have been used to construct rational points and rational curves on rationally connected algebraic varieties. We survey recent advances in two of them, the descent and the fibration method, in a number-theoretical context…
Let $K$ be a local field of residue characteristic $p$. Let $C$ be a curve over $K$ whose minimal proper regular model has totally degenerate semi-stable reduction. Under certain hypotheses, we compute the prime-to-$p$ rational torsion…
Proves that if a curve has totally split reduction and the corresponding skeleton (as a metric graph) is a chain of loops with generic edge lengths, then every divisor on the graph with imposed ramification at the rightmost vertex $p$ of…
Motivated by the problem of transverse deformation quantization of foliated manifolds, we describe a quantization of Dirac structures (more precisely, of those that are formal deformations of regular ones) to stacks of algebroids in the…
In this article, a new class of operators, termed Ad-contractions, is introduced to extend the framework of A-contractions to the setting of dislocated metric spaces. Fixed point results are established for single mappings, sequences of…
An adjoint-based procedure to determine weaknesses, or, more generally the material properties of structures is developed and tested. Given a series of force and deformation/strain measurements, the material properties are obtained by…
Given a family of nodal curves, a semistable modification of it is another family made up of curves obtained by inserting chains of rational curves of any given length at certain nodes of certain curves of the original family. We give…
In this paper, we propose new structured second-order methods and structured adaptive-gradient methods obtained by performing natural-gradient descent on structured parameter spaces. Natural-gradient descent is an attractive approach to…
Based on the simple and well understood concept of subfields in a finite field, the technique called `field reduction' has proved to be a very useful and powerful tool in finite geometry. In this paper we elaborate on this technique. Field…
We study algebraic (Artin) stacks over $\bar{\mathcal M}_g$ giving a functorial way of compactifying the relative degree $d$ Picard variety for families of stable curves. We also describe for every $d$ the locus of genus $g$ stable curves…
The bicategory of parameterized spectra has a remarkably rich structure. In particular, it is possible to take traces in this bicategory, which give classical invariants that count fixed points. We can also take equivariant traces, which…
Constructions and exploration of plane algebraic curves has received a new push with the development of automated methods, whose algorithms are continuously improved and implemented in various software packages. We use them to explore the…
On a manifold or a closed subset of a Euclidean vector space, a retraction enables to move in the direction of a tangent vector while staying on the set. Retractions are a versatile tool to perform computational tasks such as optimization,…
In this paper, we show that the affine, non-rigid structure-from-motion problem can be solved by rank-one, thus degenerate, basis shapes. It is a natural reformulation of the classic low-rank method by Bregler et al., where it was assumed…