arXiv research

Paper derives closed-form solutions for CEV model using semiclassical approximation.

Match van Stockum dust to vacuum metrics with a single parameter.

Groupoids help define Riemann sums on manifolds.

Novel knot polynomials from Gaussian calculus show half vanish and determine Jones polynomials.

In this paper we continue our study of Groenewold-Van Hove obstructions to quantization. We show that there exists such an obstruction to quantizing the cylinder $T^*S^1.$ More precisely, we prove that there is no quantization of the Poisson algebra of $T^*S^1$ which is irreducible on a naturally defined $e(2) \times R…

New findings on embedding simplicial complexes, showing instability under joins.

The classical Van Est theory relates the smooth cohomology of Lie groups with the cohomology of the associated Lie algebra, or its relative versions. Some aspects of this theory generalize to Lie groupoids and their Lie algebroids. In this paper, continuing an idea from [18], we revisit the van Est theory using the Per…

The Van Est homomorphism for a Lie groupoid $G \rightrightarrows M$, as introduced by Weinstein-Xu, is a cochain map from the complex $C^\infty(BG)$ of groupoid cochains to the Chevalley-Eilenberg complex $C(A)$ of the Lie algebroid $A$ of $G$. It was generalized by Weinstein, Mehta, and Abad-Crainic to a morphism from…

New theorem shows embedding restrictions for manifold skeletons.

Analyses cohomology relations for moving frames and coframes.

We answer Question 6.12 in the paper "Monoids in the mapping class group" written by Etnyre and Van Horn-Morris.

The paper derives Gauss-Bonnet theorems for deformed connections in affine and rigid motions groups.

We exhibit relations between van Kampen-Flores, Conway-Gordon-Sachs and Radon theorems, by presenting direct proofs of some implications between them. The key idea is an interesting relation between the van Kampen and the Conway-Gordon-Sachs numbers for restrictions of a map of $(d+2)$-simplex to $\mathbb R^d$ to the $…

VB-groupoids define a special class of Lie groupoids which carry a compatible linear structure. In this paper, we show that their differentiable cohomology admits a refinement by considering the complex of cochains which are k-homogeneous on the linear fiber. Our main result is a Van Est theorem for such cochains. We a…

Graphs from van der Corput sequence embed into Chamanara surface.

We present the Variational Adaptive Newton (VAN) method which is a black-box optimization method especially suitable for explorative-learning tasks such as active learning and reinforcement learning. Similar to Bayesian methods, VAN estimates a distribution that can be used for exploration, but requires computations th…

Automatically learns summary features from time series data for likelihood-free inference.

Study finds multiple solutions for Van der Waals-Cahn-Hilliard equation on manifolds.

Generalizes van Est map to geometric stacks and homotopy theory.

Embeddability of simplicial complex $[3]*K$ linked to $K$'s embeddability.

A cubic identity for the Infeld-van der Waerden field is found and its application to verifying an explicit formula for the spinor components of the metric connection is demonstrated.

Maps Lie 2-groups to Weil algebras, showing cohomology isomorphisms.

New method uses quantum annealing and VAN for better statistical mechanics calculations.

We generalize C. Van Cott's results on the $τ$ and $s$-invariants of cabled knots to apply to general satellite knots. This paper uses no Heegaard-Floer homology, relying on more geometric techniques.

This paper belongs to a series devoted to the study of the cohomology of classifying spaces. Generalizing the Weil algebra of a Lie algebra and Kalkman's BRST model, here we introduce the Weil algebra $W(A)$ associated to any Lie algebroid $A$. We then show that this Weil algebra is related to the Bott-Shulman-Stasheff…

Study on Schouten solitons on Kenmotsu manifolds, focusing on torse-forming vector fields.

We study the Schouten-van Kampen connection associated to an almost contact or paracontact metric structure. With the help of such a connection, some classes of almost (para) contact metric manifolds are characterized. Certain curvature properties of this connection are found.

New connections defined for a specific geometric structure.

The paper calculates curvature limits and Gauss-Bonnet theorems in the Heisenberg group.

In this comment on "Solving Statistical Mechanics Using Variational Autoregressive Networks" by Wu et al., we propose a subtle yet powerful modification of their approach. We show that the inherent sampling error of their method can be corrected by using neural network-based MCMC or importance sampling which leads to a…

The computation of the fundamental group of the complement of an algebraic plane curve has been theoretically solved since Zariski-van Kampen, but actual computations are usually cumbersome. In this work, we describe the notion of Wirtinger presentation of such a group relying on the real picture of the curve and with …

Proves integrability of strict Lie 2-algebras using cohomological methods.

We give a self contained proof using Seiberg Witten invariants that for Kähler surfaces with non negative Kodaira dimension (including those with $p_g = 0$) the canonical class of the minimal model and the $(-1)$-curves, are oriented diffeomorphism invariants up to sign. This implies that the Kodaira dimension is deter…

In the first section we discuss Morita invariance of differentiable/algebroid cohomology. In the second section we present an extension of the van Est isomorphism to groupoids. This immediately implies a version of Haefliger's conjecture for differentiable cohomology. As a first application we clarify the connection be…

The van Est map is a map from Lie groupoid cohomology (with respect to a sheaf taking values in a representation) to Lie algebroid cohomology. We generalize the van Est map to allow for more general sheaves, namely to sheaves of sections taking values in a (smooth or holomorphic) $G$-module, where $G$-modules are struc…

We give multiplicity results for the solutions of a nonlinear elliptic equation, with an asymmetric double well potential of Van der Waals-Allen--Cahn--Hilliard type, satisfying a linear volume constraint, on a bounded Lipschitz domain $Ω\subset\mathds R^N$. The number of solutions is estimated in terms of topological …

We prove an upper bound for the evaluation of all classical SU(2) spin networks conjectured by Garoufalidis and van der Veen. This implies one half of the analogue of the volume conjecture which they proposed for classical spin networks. We are also able to obtain the other half, namely, an exact determination of the s…

Paper calculates homotopy types of non-compact surfaces using groupoids.

Shallow Art presents, implements, and tests the use of simple single-output classification and regression models for the purpose of art generation. Various machine learning algorithms are trained on collections of computer generated images, artworks from Vincent van Gogh, and artworks from Rembrandt van Rijn. These mod…

There are introduced and studied a pair of associated Schouten-van Kampen affine connections adapted to the contact distribution and an almost contact B-metric structure generated by the pair of associated B-metrics and their Levi-Civita connections. By means of the constructed non-symmetric connections, the basic clas…

Theory extends optimal learning rates without realizability assumption.

A map $\varphi:K\to R^2$ of a graph $K$ is approximable by embeddings, if for each $\varepsilon>0$ there is an $\varepsilon$-close to $\varphi$ embedding $f:K\to R^2$. Analogous notions were studied in computer science under the names of cluster planarity and weak simplicity. This short survey is intended not only for …

t-distributed Stochastic Neighborhood Embedding (t-SNE), a clustering and visualization method proposed by van der Maaten & Hinton in 2008, has rapidly become a standard tool in a number of natural sciences. Despite its overwhelming success, there is a distinct lack of mathematical foundations and the inner workings of…

Proves generic nondegeneracy for solutions under volume constraint in closed manifolds.

Study hypoelliptic operators on Carnot manifolds, extending index theory results.

We demonstrate the use of conditional autoregressive generative models (van den Oord et al., 2016a) over a discrete latent space (van den Oord et al., 2017b) for forward planning with MCTS. In order to test this method, we introduce a new environment featuring varying difficulty levels, along with moving goals and obst…

Geometrically solves differentiating simplicial manifolds.

We consider topological T-duality of torus bundles equipped with S^{1}-gerbes. We show how a geometry on the gerbe determines a reduction of its band to the subsheaf of S^{1}-valued functions which are constant along the torus fibres. We observe that such a reduction is exactly the additional datum needed for the const…