arXiv research

We show existence of centrally symmetric maps on surfaces all of whose faces are quadrangles and pentagons for each orientable genus $g \geq 0$. We also show existence of centrally symmetric maps on surfaces all of whose faces are hexagons for each orientable genus $g = 2k-1$, $k\in \mathbb{N}$. We enumerate centrally …

Paper computes link determinants using Fourier-Hadamard transforms.

The article considers the problem of existence and uniqueness of centrally symmetrical convex body for which the projection curvature radius function coincides with a given flag function. A necessary and sufficient condition is found that ensures a positive answer. An algorithm for construction the body in question is …

Polyhedral surfaces can be broken down into parallelograms.

The paper studies billiards in symmetric tables and finds a measure bound for maximizing orbits.

The paper establishes a majorization result for symmetric matrices.

In his paper "Shapes of Polyhedra and Triangulations of the Sphere", Thurston found that the set of shapes of convex polyhedra with prescribed cone-deficits has a complex hyperbolic structure. Inspired by his work, this paper studies the set of shapes of centrally symmetric octahedra with prescribed cone-deficits. We s…

Makeev proved that among centrally symmetric four-dimensional polytopes, with more than twenty facets and circumscribed about the Euclidean ball of diameter one, there is no universal cover for the family of unit diameter sets. In this paper we examine the converse problem, and prove that each centrally symmetric polyt…

The conformal Laplacian's algebraic structure is explored in 2D, revealing a central charge.

New central elements found in a quantum algebra related to knot theory.

Proves Birkhoff-Poritsky conjecture for centrally-symmetric billiards.

New random walk results on rank one symmetric spaces.

Constructs minimal submanifolds in symmetric spaces using eigenfunctions.

We prove: If a complete connected smooth surface M in euclidean 3-space has general position, intersects some plane along a clean figure-8 (a loop with total curvature zero) and all compact intersections with planes have central symmetry, then M is a (geometric) cylinder over some central figure-8. On the way, we estab…

An algebra $A$ with identity $(a\circ b)\circ c-a\circ(b\circ c)=(a\circ c)\circ b-a\circ(c\circ b),$ is called right-symmetric. Cohomology and deformation theory for right-symmetric algebras are developed. Cohomologies of $gl_n$ and half-Witt algebras $W_n^{rsym}, p=0,$ $W_n^{rsym}({\bf m}), p>0,$ are calculated. In p…

Linearizes Virasoro symmetries for semisimple Frobenius manifolds.

We consider two types of $p$-centro affine flows on smooth, centrally symmetric, closed convex planar curves, $p$-contracting, respectively, $p$-expanding. Here $p$ is an arbitrary real number greater than 1. We show that, under any $p$-contracting flow, the evolving curves shrink to a point in finite time and the only…

Let G/H be a compact 4-symmetric space of inner type such that the dimension of the center Z(H) of H is at most one. In this paper we shall classify involutions of G preserving H for the case where dim Z(H)=0, or H is a centralizer of a toral subgroup of G.

Formula establishes determinant majorization for symmetric matrices.

The paper proves a convex polytope conjecture with specific symmetry conditions.

This paper studies the large time existence for the motion of closed hypersurfaces in a radially symmetric potential. In physical, this surface can be considered as an electrically charged membrane with a constant charge per area in a radially symmetric potential. The evolution of such surface has been investigated by …

Develops symmetric Cartan calculus linking to Patterson-Walker metric.

We describe complex twistor spaces over inner 3-symmetric spaces $G/H$, such that $H$ acts transitively on the fibre. Like in the symmetric case, these are flag manifolds $G/K$ where $K$ is the centralizer of a torus in $G$. Moreover, they carry an almost complex structure defined using the horizontal distribution of t…

A Minkowski class is a closed subset of the space of convex bodies in Euclidean space Rn which is closed under Minkowski addition and non-negative dilatations. A convex body in Rn is universal if the expansion of its support function in spherical harmonics contains non-zero harmonics of all orders. If K is universal, t…

The paper explores symmetric representations of links and conditions for amphichirality.

Cyclohedra are a well-known infinite familiy of finite-dimensional polytopes that can be constructed from centrally symmetric triangulations of even-sided polygons. In this article we introduce an infinite-dimensional analogue and prove that the group of symmetries of our construction is a semidirect product of a degre…

It is shown that the multiplicative monoids of Brauer's centralizer algebras generated out of the basis are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself, and where, moreover, a kind of symmetry involving the self-adjoint functor is satisfied. As in a previous paper, of …

The article explores causal structures in symmetric spaces and their relation to AQFT.

Extended current algebra on S^3 with new bilinear form and 2-cocycle.

Study shows a central limit theorem for random coverings of manifolds with nilpotent groups.

New findings on magnetic geodesic flows and periodic motions.

Study shows conjugacy of torsion in genus 2 surfaces.

We discuss the concept of the shadow boundary of a centrally symmetric convex ball $K$ (actually being the unit ball of a Minkowski normed space) with respect to a direction ${\bf x}$ of the Euclidean n-space $R^n$. We introduce the concept of general parameter spheres of $K$ corresponding to this direction and prove t…

Generalising previous results on classical braid groups by Artin and Lin, we determine the values of m, n $\in$ N for which there exists a surjection between the n-and m-string braid groups of an orientable surface without boundary. This result is essentially based on specific properties of their lower central series, …

Kähler-Einstein metrics on toric submanifolds cannot be induced by projective immersions.

Paper introduces a diagnostic for approximate inference methods.

We relate the distribution of eigenvalues of a random symmetric matrix in the Gaussian Orthogonal Ensemble to the distribution of critical values of a random linear combination of eigenfunctions of the Laplacian on a compact Riemann manifold. We then prove a central limit theorem describing what happens when the dimens…

The paper studies Stein-Weiss operators on symmetric tensors, extending previous work.

R. Schwartz's inequality provides an upper bound for the Schwarzian derivative of a parameterization of a circle in the complex plane and on the potential of Hill's equation with coexisting periodic solutions. We prove a discrete version of this inequality and obtain a version of the planar Blaschke-Santalo inequality …

The paper calculates the full asymptotics of analytic torsions for compact orbifolds.

Multiplicative bundle gerbes are gerbes over a Lie group which are compatible with the group structure. In this article connections on such bundle gerbes are introduced and studied. It is shown that multiplicative bundle gerbes with connection furnish geometrical constructions of the following objects: smooth central e…

We create a minimal triangulation of 5D real projective space.

We study the long time behavior of the volume preserving $p$-flow in $\mathbb{R}^{n+1}$ for $1\leq p<\frac{n+1}{n-1}$. By extending Andrews' technique for the flow along the affine normal, we prove that every centrally symmetric solution to the volume preserving $p$-flow converges sequentially to the unit ball in the $…

Framework for systemic risk modeling using jointly exchangeable arrays.

The paper analyzes variance reduction in stochastic gradient Langevin dynamics.

This paper addresses the problem of distributed detection in multi-agent networks. Agents receive private signals about an unknown state of the world. The underlying state is globally identifiable, yet informative signals may be dispersed throughout the network. Using an optimization-based framework, we develop an iter…

The paper resolves a counterexample showing convergence of expected utility in binomial models.

The Murphy operators in the Hecke algebra H_n of type A are explicit commuting elements, whose symmetric functions are central in H_n. In [Skein theory and the Murphy operators, J. Knot Theory Ramif. 11 (2002), 475-492] I defined geometrically a homomorphism from the Homfly skein C of the annulus to the centre of each …