Related papers: Galois/monodromy groups for decomposing minimal pr…

Visual navigation and three-dimensional (3D) scene reconstruction are essential for robotics to interact with the surrounding environment. Large-scale scenes and critical camera motions are great challenges facing the research community to…

A lot of work has gone into computing images of Galois representations coming from elliptic curves. This article presents an algorithm to determine the image of the mod-$3$ Galois representation associated to a principally polarized abelian…

In this paper, we aim to recover the 3D human pose from 2D body joints of a single image. The major challenge in this task is the depth ambiguity since different 3D poses may produce similar 2D poses. Although many recent advances in this…

Estimating metric relative camera pose from a pair of images is of great importance for 3D reconstruction and localisation. However, conventional two-view pose estimation methods are not metric, with camera translation known only up to a…

This article is the first part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. In this first part, we determine the smallest field over which the…

Let $X$ be a smooth, separated, geometrically connected scheme defined over a number field $K$ and $\{\rho_\lambda\}_\lambda$ a system of n-dimensional semisimple $\lambda$-adic representations of the \'etale fundamental group of $X$ such…

This paper introduces a novel approach to understanding Galois theory, one of the foundational areas of algebra, through the lens of machine learning. By analyzing polynomial equations with machine learning techniques, we aim to streamline…

I discuss a seemingly unlikely confluence of topics in algebra, numerical computation, and computer vision. The motivating problem is that of solving multiples instances of a parametric family of systems of algebraic (polynomial or rational…

We present a geometric setting for the differential Galois theory of $G$-invariant connections with parameters. As an application of some classical results on differential algebraic groups and Lie algebra bundles, we see that the Galois…

We present a Galois theory of parameterized linear differential equations where the Galois groups are linear differential algebraic groups, that is, groups of matrices whose entries are functions of the parameters and satisfy a set of…

Multi-camera systems offer rich observation capabilities for visual navigation and 3D scene reconstruction; however, the resulting feature redundancy often compromises computational efficiency. This challenge is particularly pronounced…

Estimating relative camera poses from consecutive frames is a fundamental problem in visual odometry (VO) and simultaneous localization and mapping (SLAM), where classic methods consisting of hand-crafted features and sampling-based outlier…

Suppose $\rho_1, \rho_2$ are two $\ell$-adic Galois representations of the absolute Galois group of a number field, such that the algebraic monodromy group of one of the representations is connected and the representations are locally…

We introduce a new family of minimal problems for reconstruction from multiple views. Our primary focus is a novel approach to autocalibration, a long-standing problem in computer vision. Traditional approaches to this problem, such as…

In this work we present a unified method of relative camera pose estimation from points and lines correspondences. Given a set of 2D points and lines correspondences in three views, of which two are known, a method has been developed for…

The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…

We describe algorithms to compute fixed fields, splitting fields and towers of radical extensions without using polynomial factorisation in towers or constructing any field containing the splitting field, instead extending Galois group…

Let $k/\mathbb F_p$ denote a finite field. For any split connected reductive group $G/W(k)$ and certain CM number fields $F$, we deform certain Galois representations $\overline\rho:Gal(\overline F/F) \to G(k)$ to continuous families…

To a "stable homotopy theory" (a presentable, symmetric monoidal stable $\infty$-category), we naturally associate a category of finite \'etale algebra objects and, using Grothendieck's categorical machine, a profinite group that we call…

3D pose estimation from sparse multi-views is a critical task for numerous applications, including action recognition, sports analysis, and human-robot interaction. Optimization-based methods typically follow a two-stage pipeline, first…