arXiv research

Study on homeomorphism groups of telescoping 2-manifolds showing strong distortion.

We overview few results which use the construction described in our paper "Telescopic actions".

Telescope detects LLM generated text by measuring token repetition probability.

Modern detectors of cosmic gamma-rays are a special type of imaging telescopes (air Cherenkov telescopes) supplied with cameras with a relatively large number of photomultiplier-based pixels. For example, the camera of the TAIGA-IACT telescope has 560 pixels of hexagonal structure. Images in such cameras can be analyse…

A group action H on X is called "telescopic" if for any finitely presented group G, there exists a subgroup H' in H such that G is isomorphic to the fundamental group of X/H'. We construct examples of telescopic actions on some CAT[-1] spaces, in particular on 3 and 4-dimensional hyperbolic spaces. As applications we g…

We study topology of configuration spaces of planar linkages having one leg of variable length. Such telescopic legs are common in modern robotics where they are used for shock absorbtion and serve a variety of other purposes. Using a Morse theoretic technique, we compute explicitly, in terms of the metric data, the Be…

Algorithm finds Liouvillian solutions for planar rational vector fields.

Study classifies 2-manifolds with special homeomorphism groups.

A connected combinatorial 2-manifold is called degree-regular if each of its vertices have the same degree. A connected combinatorial 2-manifold is called weakly regular if it has a vertex-transitive automorphism group. Clearly, a weakly regular combinatorial 2-manifold is degree-regular and a degree-regular combinator…

We consider optimization problems in which the objective requires an inner loop with many steps or is the limit of a sequence of increasingly costly approximations. Meta-learning, training recurrent neural networks, and optimization of the solutions to differential equations are all examples of optimization problems wi…

Observations of astrophysical objects such as galaxies are limited by various sources of random and systematic noise from the sky background, the optical system of the telescope and the detector used to record the data. Conventional deconvolution techniques are limited in their ability to recover features in imaging da…

We introduce the notion of complex $G_2$ manifold $M_{\mathbb C}$, and complexification of a $G_2$ manifold $M\subset M_{\mathbb C}$. As an application we show the following: If $(Y,s)$ is a closed oriented $3$-manifold with a $Spin^{c}$ structure, and $(Y,s)\subset (M, \varphi)$ is an imbedding as an associative subma…

The study provides homological characterizations for $Q$-manifolds and $l_2$-manifolds.

A simple model explains deep learning phenomena like grokking and gradient boosting.

We define deformations of $RP^2$-manifolds.

We prove geometric superrigidity for actions of cocompact lattices in semisimple Lie groups of higher rank on infinite dimensional Riemannian manifolds of nonpositive curvature and finite telescopic dimension.

Game theory applied to splitting surfaces of compact 2-manifolds.

Conditions for Penrose-Ward transformation on specific manifolds.

The study explores homeomorphism groups of self-similar 2-manifolds, including the 2-sphere and Cantor set.

The vision systems of the eagle and the snake outperform everything that we can make in the laboratory, but snakes and eagles cannot build an eyeglass or a telescope or a microscope. (Judea Pearl)

This paper examines limits of Riemannian 2-manifolds with bounded curvature.

The paper constructs complex hyperbolic 2-manifolds with one cusp.

New methods model gamma-ray data to better understand Galactic emissions.

Formula derived for $G_2$-manifolds, showing moduli spaces are incomplete.

In this survey, we describe invariants that can be used to distinguish connected components of the moduli space of holonomy G_2 metrics on a closed 7-manifold, or to distinguish G_2-manifolds that are homeomorphic but not diffeomorphic. We also describe the twisted connected sum and extra-twisted connected sum construc…

New Roman pipeline detects astronomical transients.

We consider the minimum Yang-Mills energy on the complete $G_{2}$-manifolds and Calabi-Yau 3-folds,the connection $A$ is a stability Yang-Mills connection on the $G$-bundle $E$.We prove that the connection must be a $G_{2}$-instanton on $G_{2}$-manifold and the bundle is holomorphic on Calabi-Yau 3-fold with holonomy $…

TRE improves density-ratio estimation for highly dissimilar densities.

Classifies manifolds with dense conjugacy classes in their mapping class groups.

Study constructs associative submanifolds in $G_2$-manifolds from orbifolds.

We prove that the homeomorphism problem for 2-manifolds can be decided in logspace. The proof relies on Reingold's logspace solution to the undirected $s,t$-connectivity problem in graphs.

This is a very short and elementary introduction to G_2 manifolds. We stress the similarities and the differences with Kähler manifolds in general and with Calabi-Yau manifolds in particular.

On a projective complex manifold, the Abelian group of Divisors maps surjectively onto that of holomorphic line bundles (the Picard group). On a $G_2$-manifold we use coassociative submanifolds to define an analogue of the first, and a gauge theoretical equation for a connection on a gerbe to define an analogue of the …

Study of $U(1)$ gauge theories on $G_2$ manifolds, including instantons and Chern-Simons.

M-theory compactified on $G_2$-holonomy manifolds results in 4d $\mathcal{N}=1$ supersymmetric gauge theories coupled to gravity. In this paper we focus on the gauge sector of such compactifications by studying the Higgs bundle obtained from a partially twisted 7d super Yang-Mills theory on a supersymmetric three-cycle…

Study geometry on $G_2$-manifolds, focusing on $Spin(7)$ and $G_2$.

Study $G_2$-manifolds from symplectic $SU(3)$-manifolds with $T^2$-symmetry.

Computes a $ν$-invariant for Joyce's $G_2$-manifolds.

Article constructs coassociative submanifolds in Joyce's $G_2$-manifolds.

We obtained that any 2-form and any smooth function on 2-manifolds with boundary can be realized as the curvature form and the gaussian curvature function of some Riemmanian metric, respectively.

CNN identifies AGN host galaxies from Sloan Digital Sky Survey data.

The paper constructs diffeomorphisms on a $G_2$-manifold achieving entropy bounds.

In this paper we show that the topological closure of the holonomy group of a certain class of projectively flat Finsler 2-manifolds of constant curvature is maximal, that is isomorphic to the connected component of the diffeomorphism group of the circle. This class of 2-manifolds contains the standard Funk plane of co…

For an arbitrary nondegenerate curve in a pseudo-Riemann\-ian (including Riemannian) 2-manifold, we express the equi-affine curvature with the help of the Frenet (geodesic) curvature of this curve.

We show that any homomorphism from the homeomorphism group of a compact 2-manifold, with the compact-open topology, or equivalently, with the topology of uniform convergence, into a separable topological group is automatically continuous.

We discuss Witten's formulas for the symplectic volumes of moduli spaces of flat connections on 2-manifolds from the viewpoint of Hamiltonian cobordism as introduced by Ginzburg-Guillemin-Karshon.

The study constructs $G_2$-manifolds from K3 surfaces with a specific action.

We study supergravity solutions corresponding to fivebranes wrapped on a three-sphere inside a G_2 holonomy manifold. By changing a parameter the solutions interpolate between a G_2 manifold X_i \cong S^3 x R^4 with flux on a three-sphere and a distinct G_2 manifold X_j \cong S^3 x R^4 with branes on another three-sphe…