相关论文: Computing Triangulations of Mapping Tori of Surfac…

In this article, gentle algebras are realised as tiling algebras, which are associated to partial triangulations of unpunctured surfaces with marked points on the boundary. This notion of tiling algebras generalise the notion of Jacobian…

Image matting aims to predict alpha values of elaborate uncertainty areas of natural images, like hairs, smoke, and spider web. However, existing methods perform poorly when faced with highly transparent foreground objects due to the large…

We give a method of counting the number of curves with a given type of singularity in a suitably ample linear series on a smooth surface using punctual Hilbert schemes. The types of singulaties for which our methods suffice include the…

In this technical report, we compare multiple reformulation techniques and solvers that can be used with the Julia package BilevelJuMP. We focus on the special case of Hyperparameter Tuning for Support Vector Regression. We describe a…

Geometric torsions are torsions of acyclic complexes of vector spaces which consist of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a…

Let $\mathbf{\Sigma}=(\Sigma,M,O)$ be a surface with marked points and order-2 orbifold points which is either unpunctured or once-punctured closed, and $\omega:O\rightarrow\{1,4\}$ a function. For each triangulation $\tau$ of…

We study trisections of 4-manifolds obtained by spinning and twist-spinning 3-manifolds, and we show that, given a (suitable) Heegaard diagram for the 3-manifold, one can perform simple local modifications to obtain a trisection diagram for…

In this paper, we survey recent works on the structure of the mapping class groups of surfaces mainly from the point of view of topology. We then discuss several possible directions for future research. These include the relation between…

Manifolds occur naturally as configuration spaces of robotic systems. They provide global descriptions of local coordinate systems that are common tools in expressing positions of robots. The purpose of this survey is threefold. Firstly, we…

This paper presents a systematic approach for computing local solutions to motion planning problems in non-convex environments using numerical optimal control techniques. It extends the range of use of state-of-the-art numerical optimal…

We introduce {\tt JuliBootS}, a package for numerical conformal bootstrap computations coded in {\tt Julia}. The centre-piece of {\tt JuliBootS} is an implementation of Dantzig's simplex method capable of handling arbitrary precision linear…

Recently, Ian Agol introduced a class of "veering" ideal triangulations for mapping tori of pseudo-Anosov homeomorphisms of surfaces punctured along the singular points. These triangulations have very special combinatorial properties, and…

We investigate zigzags in triangulations of connected closed $2$-dimensional surfaces and show that there is a one-to-one correspondence between triangulations with homogeneous zigzags and closed $2$-cell embeddings of directed Eulerian…

We explore geometric and topological properties of 3d surfaces swept by Poncelet triangles, as well as tangles formed by associated points.

Translation averaging aims to recover camera locations from pairwise relative translation directions and is a fundamental component of global Structure-from-Motion pipelines. The problem is challenging because direction measurements contain…

Normal surface theory is a central tool in algorithmic three-dimensional topology, and the enumeration of vertex normal surfaces is the computational bottleneck in many important algorithms. However, it is not well understood how the number…

Multiplexed imaging data are revolutionizing our understanding of the composition and organization of tissues and tumors. A critical aspect of such tissue profiling is quantifying the spatial relationship relationships among cells at…

Scanning probe microscopy (SPM) is a powerful technique for mapping nanoscale surface properties through tip-sample interactions. Thermal scanning-probe lithography (tSPL) is an advanced SPM variant that uses a silicon tip on a heated…

In this article, we compute the topological expansion of all possible mixed-traces in a hermitian two matrix model. In other words we give a recipe to compute the number of discrete surfaces of given genus, carrying an Ising model, and with…

We give a list of statements on the geometry of elliptic threefolds phrased only in the language of topology and homological algebra. Using only notions from topology and homological algebra, we recover existing results and prove new…