arXiv research

Defines state sum models with defects in 3-manifolds.

Refines knot defect measurement in 3D and 4D.

Study active nematic forces on curved surfaces, revealing new coupling mechanisms.

A modular tensor category $\mathcal{C}$ gives rise to a Reshetikhin-Turaev type topological quantum field theory which is defined on 3-dimensional bordisms with embedded $\mathcal{C}$-coloured ribbon graphs. We extend this construction to include bordisms with surface defects which in turn can meet along line defects. …

We introduce a Bayesian defect detector to facilitate the defect detection on the motion blurred images on rough texture surfaces. To enhance the accuracy of Bayesian detection on removing non-defect pixels, we develop a class of reflected non-local prior distributions, which is constructed by using the mode of a distr…

The angle defect, which is the standard way to measure curvature at the vertices of polyhedral surfaces, goes back at least as far as Descartes. Although the angle defect has been widely studied, there does not appear to be in the literature an axiomatic characterization of the angle defect. We give a characterization …

Simplified 3D Dijkgraaf-Witten theory with defects explained geometrically.

In this article, we propose some conditions on the modified defect relations of the Gauss map of a complete minimal surface $M$ to show that $M$ has finite total curvature.

Study of defects in gauge theories connects quantum field theory to classical integrability.

Given a distribution of defects on a structured surface, such as those represented by 2-dimensional crystalline materials, liquid crystalline surfaces, and thin sandwiched shells, what is the resulting stress field and the deformed shape? Motivated by this concern, we first classify, and quantify, the translational, ro…

Study of surface defects in gauge theories leads to duality and separation of variables.

Study on minimal surfaces and their Gauss maps intersecting a specific hypersurface.

We define the sigma-model action for world-sheets with embedded defect networks in the presence of a three-form field strength. We derive the defect gluing condition for the sigma-model fields and their derivatives, and use it to distinguish between conformal and topological defects. As an example, we treat the WZW mod…

Framework for efficient defect classification and inspection.

Authors show that genus defects of Hopf arborescent links are decidable.

Develops skein theory for 3-manifolds with defects, extending quantum character stacks.

New quantum integrals discovered for a spin chain model.

In this article, we study the modified defect relations of the Gauss map of complete minimal surfaces in $\mathbb R^3$ and $\mathbb R^4$ on annular ends. We obtain results which are similar to the ones obtained by Fujimoto~[J. Differential Geometry \textbf{29} (1989), 245-262] for (the whole) complete minimal surfaces…

Study magnetic Laplacians on hyperbolic surfaces, revealing three regimes of eigenfunction behavior.

The paper characterizes coverings over the projective plane with minimal defect.

Study of knotted defects in smectic liquid crystals using topological knot theory.

The paper improves the Gauss curvature estimation for harmonic surfaces and verifies a modified defect relation.

In this article, we give the non-integrated defect relations for the Gauss map of a complete minimal surface with finite total curvature in $\mathbb R^m.$ This is a continuation of previous work of Ha-Trao [J. Math. Anal. Appl., \textbf{430} (2015), 76-84.], which we extend here to targets of higher dimension.

Recognition of defects in concrete infrastructure, especially in bridges, is a costly and time consuming crucial first step in the assessment of the structural integrity. Large variation in appearance of the concrete material, changing illumination and weather conditions, a variety of possible surface markings as well …

We describe discrete symmetries of two-dimensional Yang-Mills theory with gauge group $G$ associated to outer automorphisms of $G$, and their corresponding defects. We show that the gauge theory partition function with defects can be computed as a path integral over the space of twisted $G$-bundles, and calculate it ex…

The paper improves defect relations for Gauss maps of minimal surfaces intersecting hypersurfaces in projective space.

In this paper, we provide a construction of a state-sum model for finite gauge-group Dijkgraaf-Witten theory on surfaces with codimension 1 defects. The construction requires not only that the triangulation be subordinate to the filtration, but flag-like: each simplex of the triangulation is either disjoint from the de…

Surface inspection systems are an important application domain for computer vision, as they are used for defect detection and classification in the manufacturing industry. Existing systems use hand-crafted features which require extensive domain knowledge to create. Even though Convolutional neural networks (CNNs) have…

For a null-homologous transverse link $\mathcal T$ in a general contact manifold with an open book, we explore strongly quasipositive braids and Bennequin surfaces. We define the defect $δ(\mathcal T)$ of the Bennequin-Eliashberg inequality. We study relations between $δ(\mathcal T)$ and minimal genus Bennequin surface…

The study analyzes group testing algorithms for identifying defective items with high confidence.

One of the primary concerns of product quality control in the automotive industry is an automated detection of defects of small sizes on specular car body surfaces. A new statistical learning approach is presented for surface finish defect detection based on spline smoothing method for feature extraction and $k$-neares…

In this work we study the decomposability property of branched coverings of degree $d$ odd, over the projective plane, where the covering surface has Euler characteristic $\leq 0$. The latter condition is equivalent to say that the defect of the covering is greater than $d$. We show that, given a datum $\mathscr{D}=\{D…

This research extends topological recursion to hyperbolic surfaces with tight boundaries and conical defects.

Improved defect detection in layered materials using signal separation methods.

Maps links in 3-manifolds to links in branched covers, relating quantum field theories.

Novel defects in hyperbolic sheets explain complex wrinkling patterns in nature.

Study on Gauss maps of minimal surfaces over projective hypersurfaces.

The paper proves surfaces close to spheres under specific conditions.

We introduce defects, with internal gauge symmetries, on a knot and Seifert surface to a knot into the combinatorial construction of finite gauge-group Dijkgraaf-Witten theory. The appropriate initial data for the construction are certain three object categories, with coefficients satisfying a partially degenerate cocy…

We study supersymmetric probe M5-branes in the AdS_4 solution that arises from M5-branes wrapped on a hyperbolic 3-manifold M_3. This amounts to introducing internal defects within the framework of the 3d-3d correspondence. The BPS condition for a probe M5-brane extending along all of AdS_4 requires it to wrap a surfac…

The study investigates how branch points affect the shape and mechanics of hyperbolic surfaces.

The study examines K-polystability on Fano 4-folds with specific Lefschetz defects.

Hermitian bundle gerbes with connection are geometric objects for which a notion of surface holonomy can be defined for closed oriented surfaces. We systematically introduce bundle gerbes by closing the pre-stack of trivial bundle gerbes under descent. Inspired by structures arising in a representation theoretic approa…

Polyhedra can mimic constant curvature surfaces, even with self-intersections.

In this paper, we survey recent results on index defects of elliptic operators on manifolds with boundary. Index defects are similar to the Hirzebruch signature defects in topology, where the defects appear as the correction terms to the signature formula on manifolds with boundary. For some natural classes of elliptic…

We study the topology of smectic defects in two and three dimensions. We give a topological classification of smectic point defects and disclination lines in three dimensions. In addition we describe the combination rules for smectic point defects in two and three dimensions, showing how the broken translational symmet…

Alexander polynomial degree correlates with knot defect, proving conjecture for defect zero.

Automates defect detection using autoencoders on normal images only.