A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Complete Calabi-Yau metrics on C^{N+1} are constructed.
Study shortest geodesics on flat cone spheres with conical singularities.
Natural volume forms defined for pseudo-Finslerian manifolds with specific metrics.
Geometrically reformulates Cosserat solid mechanics using differential geometry.
Ancient formula connects volume forms and infinitesimal square volumes in manifolds.
Defines state sum models with defects in 3-manifolds.
Two Morse-Bott volume forms are diffeomorphic if their cohomology classes are equal.
S. Donaldson introduced a metric on the space of volume forms, with fixed total volume on any compact Riemmanian manifold. With this metric, the space of volume forms formally has non-positive curvature. The geodesic equation is a fully nonlinear degenerate elliptic equation. We solve the geodesic equation and its pert…
The study examines K-polystability on Fano 4-folds with specific Lefschetz defects.
Study geodesic equation on mixed-volume forms on balanced manifolds, proving existence of solutions.
The paper defines unimodularity for coisotropic Poisson spaces and discusses invariant volume forms.
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…
Study of knotted defects in smectic liquid crystals using topological knot theory.
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…
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…
Study on Berwald-Weyl curvature with projective invariance and vanishing results.
Geodesically equivalent Finsler metrics share invariant volume forms and first integrals.
Alexander polynomial degree correlates with knot defect, proving conjecture for defect zero.
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…
For a knot K in S^3 we construct according to Casson--or more precisely taking into account Lin and Heusener's further works--a volume form on the SU(2)-representation space of the group of K. We prove that this volume form is a topological knot invariant and explore some of its properties.
Framework for efficient defect classification and inspection.
Graph-based ML improves defect prediction in software development.
Simplified 3D Dijkgraaf-Witten theory with defects explained geometrically.
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 …
Spin TFTs created by gauging line defects in 3D.
The paper explores the connection between Poisson-Lie structures and invariant volume forms in Hamiltonian dynamics.
Defect of knot polynomials remains invariant under certain braid substitutions.
Anomaly detection refers to the task of finding unusual instances that stand out from the normal data. In several applications, these outliers or anomalous instances are of greater interest compared to the normal ones. Specifically in the case of industrial optical inspection and infrastructure asset management, findin…
We study the asymptotic behavior of volume forms on a degenerating family of compact complex manifolds. Under rather general conditions, we prove that the volume forms converge in a natural sense to a Lebesgue-type measure on a certain simplicial complex. In particular, this provides a measure-theoretic version of a co…
Extends knotted defect classification to bounded domains using handlebodies.
New theorem disproves Angle Defect for super triangles.
Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with a configuration of a body in classical elasticity is the sum of local contributions …
A modular tensor category gives rise to a Reshetikhin-Turaev type topological quantum field theory which is defined on 3-dimensional bordisms with embedded -coloured ribbon graphs. We extend this construction to include bordisms with surface defects which in turn can meet along line defects. …
A topological defect separating a pair of two-dimensional CFTs is a codimension one interface along which all components of the stress-energy tensor glue continuously. We study topological defects of the bosonic, (0,1)- and (0,2)-supersymmetric sigma models in two dimensions. We find a geometric classification of such …
We present a homogenization theorem for isotropically-distributed point defects, by considering a sequence of manifolds with increasingly dense point defects. The loci of the defects are chosen randomly according to a weighted Poisson point process, making it a continuous version of the first passage percolation model.…
The paper derives formulas for symplectic volume forms on surface representation varieties.
In this paper, we are interested in flat metric structures with conical singularities on surfaces which are obtained by deforming translation surface structures. The moduli space of such flat metric structures can be viewed as some deformation of the moduli space of translation surfaces. Using geodesic triangulations, …
The paper improves the regularity and existence of pseudo Calabi flow.
Develops skein theory for 3-manifolds with defects, extending quantum character stacks.
We prove a stability result for volume forms on fiber bundles with compact base and noncompact fibers. This generalizes the classical results of Moser and Greene--Shiohama, and recent work by the authors.
We describe discrete symmetries of two-dimensional Yang-Mills theory with gauge group associated to outer automorphisms of , 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 -bundles, and calculate it ex…
We prove that on any compact complex manifold one can find Gauduchon metrics with prescribed volume form. This is equivalent to prescribing the Chern-Ricci curvature of the metrics, and thus solves a conjecture of Gauduchon from 1984.
A novel method classifies wafer defects using topological data analysis.
A new deep metric learning method for defect classification in threaded pipe connections.
The goal of this paper is twofold. First we prove a rigidity estimate, which generalises the theorem on geometric rigidity of Friesecke, James and Müller to 1-forms with non-vanishing exterior derivative. Second we use this estimate to prove a kind of spontaneous breaking of rotational symmetry for some models of cryst…
New conditions ensure points can be uniquely represented by combinations of variety elements.
We show that Bonnesen's isoperimetic defect has a systolic analog for Loewner's torus inequality. The isosystolic defect is expressed in terms of the probabilistic variance of the conformal factor of the metric g with respect to the flat metric of unit area in the conformal class of g.
Graph coloring is explained using a topological field theory with defects.