Related papers: Asymptotic link invariants for ergodic vector fiel…

The paper concerns the problem for the ultrahyperbolic equation in the Euclidean space with data on a characteristic hyperplane. Smoothness and asymptotics of the solution along characteristic lines transversal to the initial hyperplane are…

Starting from a three-dimensional description of an active nematic layer, we employ an asymptotic theory to derive a series of low-dimensional continuum models that capture the coupled dynamics of flat and curved films, including variations…

We consider Bratteli diagrams of finite rank (not necessarily simple) and ergodic invariant measures with respect to the cofinal equivalence relation on their path spaces. It is shown that every ergodic invariant measure (finite or…

We investigate the structure of branching asymptotics appearing in solutions to elliptic edge problems. The exponents in powers of the half-axis variable, logarithmic terms, and coefficients depend on the variables on the edge and may be…

We obtain asymptotic expressions for the Green kernels of certain non-translation invariant transition matrices using methods of semiclassical and microlocal analysis. Combined with a result by Bach and M{\o}ller this yields asymptotic…

Knots naturally appear in continuous dynamical systems as flow periodic trajectories. However, discrete dynamical systems are also closely connected with the theory of knots and links. For example, for Pixton diffeomorphisms, the…

We construct stable vector bundles on the space of symmetric forms of degree d in n+1 variables which are equivariant for the action of SL_{n+1}(C), and admit an equivariant free resolution of length 2. For n=1, we obtain new examples of…

We provide conditions guaranteeing that certain classes of robust heteroclinic networks are asymptotically stable. We study the asymptotic stability of ac-networks --- robust heteroclinic networks that exist in smooth ${\mathbb…

We prove that for compact, non-contractible, one dimensional geodesic spaces, a version of the marked length spectrum conjecture holds. For a compact one dimensional geodesic space X, we define a subspace Conv(X). When X is…

We provide obstructions to a link in $S^3$ arising as the cross section of any number of unlinked spheres in $S^4$. Our obstructions arise from the multivariable signature, the Blanchfield form and generalised Seifert matrices. We also…

We study a lattice point counting problem for a class of families of domains in a Euclidean space. This class consists of anisotropically expanding bounded domains, which remain unchanged along some fixed linear subspace and expand in…

We study relationships between the restricted unrolled quantum group $\overline{U}_q^H(\mathfrak{sl}_2)$ at $2r$-th root of unity $q=e^{\pi i/r}, r \geq 2$, and the singlet vertex operator algebra $\mathcal M(r)$. We use deformable families…

In this paper we consider the convex hull of a spherically symmetric sample in $R^d$. Our main contributions are some new asymptotic results for the expectation of the number of vertices, number of facets, area and the volume of the convex…

Let $D$ be an effective divisor on a smooth projective variety $X$ over an algebraically closed field $k$ of characteristic $0$. We show that there is a one-to-one correspondence between the class of orthogonal (respectively, symplectic)…

In this paper we study the asymptotic behavior of the analytic torsion for compact, oriented hyperbolic manifolds with respect to certain rays of representations obtained by restriction of irreducible representations of the group of…

Let G be a simple algebraic group. Labelled trivalent graphs called webs can be used to product invariants in tensor products of minuscule representations. For each web, we construct a configuration space of points in the affine…

We construct a link in the $3$-space that is not isotopic to any PL link (non-ambiently). In fact, there exist uncountably many $I$-equivalence classes of links. The paper also includes some observations on Cochran's invariants $\beta_i$.

This paper is concerned with investigating the asymptotic behavior of the gradients of solutions to a class of elliptic systems with general boundary data, especially covering the Lam\'{e} systems, in a narrow region. The novelty of this…

We introduce and study the notion of orthosymmetric spaces over an Archimedean vector lattice as a generalization of finite-dimentional Euclidean inner spaces. A special attention has been paid to linear operators on these spaces.

Einstein-Maxwell theory is not only covariant under diffeomorphisms but also is under $U(1)$ gauge transformations. We introduce a combined transformation constructed out of diffeomorphism and $U(1)$ gauge transformation. We show that…