arXiv research

Survey of recent Kleinian representation convergence results.

The paper extends Hodge-de Rham and Lichnérowicz Laplacians to double forms and proves vanishing theorems.

Paper develops a duality approach for robust loss functions in infinite-dimensional RKHSs.

Heegaard Floer homology connects to polynomial representations of Hecke algebras.

We use the exterior product of double forms to reformulate celebrated classical results of linear algebra about matrices and bilinear forms namely the Cayley-Hamilton theorem, Laplace expansion of the determinant, Newton identities and Jacobi's formula for the determinant. This new formalism is then used to naturally g…

A conjecture of Riley about the relationship between real parabolic representations and signatures of two-bridge knots is verified for double twist knots.

The paper proves an infinite double bubble theorem in higher dimensions.

Liouville theorem for minimal graphs on manifolds with specific properties.

The paper proves that rational concordance of double twist knots is reciprocal.

Paper classifies compact symmetric triads using double Satake diagrams and canonical forms.

The most important examples of a double vector bundle are provided by iterated tangent and cotangent functors: TTM, TT^*M, T^*TM, and T^*T^*M. We introduce the notions of the dual double vector bundle and the dual double vector bundle morphism. Theorems on canonical isomorphisms are formulated and proved. Several examp…

Paper doubles Hessian estimates for special Lagrangian equation with constraints.

We show that double Lie algebroids, together with a chosen linear splitting, are equivalent to pairs of 2-term representations up to homotopy satisfying compatibility conditions which extend the notion of matched pair of Lie algebroids. We discuss in detail the tangent of a Lie algebroid.

Geodesic nets on flat spheres are studied using Gauss-Bonnet theorem.

In this paper we show that topological subgroupoids of Lie groupoids, under special circumstances are Lie subgroupoids. Giving an example, we indicate that having the same topological dimension is a necessary condition for topological subgroupoids to be Lie subgroupoids. Also, we provide some conditions for double subg…

Factorization of DE coefficients is violated in antiparallel triple pretzels, but described elegantly.

Classifies solvable symplectic Lie algebras via extensions and proves structural theorems.

Study of double complexes on Iwasawa manifold yields 3 isomorphism types.

We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of such representations in terms of finite group data. This allows us to establish va…

Study on double descent behavior in two-layer neural networks for binary classification.

The paper explores conic-line arrangements via Poncelet's theorem and finds families of reducible curves.

The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in $\mathbb{R}^N$ is the standard double bubble. We seek the optimal double bubble in $\mathbb{R}^N$ with density, which we assume to be strictly log-convex. For $N=1$ we show that the solution is sometime…

Research decouples Lie algebroids using bicocycle double cross product theory.

The branched virtual fibering theorem by Sakuma states that every closed orientable $3$-manifold with a Heegaard surface of genus $g$ has a branched double cover which is a genus $g$ surface bundle over the circle. It is proved by Brooks that such a surface bundle can be chosen to be hyperbolic. We prove that the minim…

Study on nonorientable 4-genus of double twist knots.

Paper analyzes double twist knots using adjoint hyperbolic torsion polynomial.

Factorization of the differential expansion coefficients for HOMFLY-PT polynomials of double braids, discovered in arXiv:1606.06015 in the case of rectangular representations $R$, is extended to the first non-rectangular representations $R=[2,1]$ and $R=[3,1]$. This increases chances that such factorization will take p…

Paper optimizes prediction in semi-functional linear models using kernel methods.

Paper tackles utility maximization with job-switching and retirement constraints.

This article gives matrix factorizations for the trivalent diagrams and double line appearing in $\mathfrak{sl}_n$ quantum link invariant. These matrix factorizations reconstruct Khovanov-Rozansky homology. And we show that the Euler characteristic of the matrix factorization for a double loop equals the quantum dimens…

We generalise theorems of Khodorovskiy and Park-Park-Shin, and give new topological proofs of those theorems, using embedded surfaces in the 4-ball and branched double covers. These theorems exhibit smooth codimension-zero embeddings of certain rational homology balls bounded by lens spaces.

Geometric arguments show simplicial arrangements with few double points can't have an irreducible cubic curve dual.

New minimal surface doublings of Clifford Torus improve bounds on minimal surfaces in S^3.

We construct a certain cross product of two copies of the braided dual $\tilde H$ of a quasitriangular Hopf algebra $H$, which we call the elliptic double $E_H$, and which we use to construct representations of the punctured elliptic braid group extending the well-known representations of the planar braid group attache…

We use a new approach that we call unification to prove that standard weighted double bubbles in $n$-dimensional Euclidean space minimize immiscible fluid surface energy, that is, surface area weighted by constants. The result is new for weighted area, and also gives the simplest known proof to date of the (unit weight…

Researchers found all embeddings of Kuratowski graphs on a double torus.

This paper studies covariant derivatives for Lie groupoids with representation-valued forms.

New theorem for generalized group sparsity improves consistency and convergence rates.

Constructs special Kähler structures on Lie groups.

Proves volume conjecture for double twist knots using complexified tetrahedrons.

Study shows label noise impacts neural representations' information content, revealing double descent behavior.

The paper sets genus bounds for twisted quantum invariants.

News might trigger jump arrivals in financial time series. The "bad" and "good" news seems to have distinct impact. In the research, a double exponential jump distribution is applied to model downward and upward jumps. Bayesian double exponential jump-diffusion model is proposed. Theorems stated in the paper enable est…

Develops support theorem for analytic transforms in tomography.

This paper describes an equivalence of the canonical category of $\mathbb N$-manifolds of degree $2$ with a category of involutive double vector bundles. More precisely, we show how involutive double vector bundles are in duality with double vector bundles endowed with a linear metric. We describe then how special sect…

Generalizes LD approach to create minimal surfaces and self-shrinkers.

A theorem of Furuta and Fintushel-Stern provides a criterion for a collection of Seifert fibred homology spheres to be independent in the homology cobordism group of oriented homology 3-spheres. In this article we use these results and some 4-dimensional constructions to produce infinite families of positive torus knot…

The paper constructs Anosov representations for specific types of groups.