Related papers: How to flatten a soccer ball

Consider the problem of minimizing a quadratic objective subject to quadratic equations. We study the semialgebraic region of objective functions for which this problem is solved by its semidefinite relaxation. For the Euclidean distance…

To study coisotropic reduction in the context of deformation quantization we introduce constraint manifolds and constraint algebras as the basic objects encoding the additional information needed to define a reduction. General properties of…

We investigate the quasisymmetric uniformization of a special class of metric surfaces known as paper surfaces, constructed as quotients of planar multipolygons via segment pairings, including infinite Type W identifications. These spaces,…

We study the orthogonal projections of symplectic balls in $\mathbb{R}^{2n}$ on complex subspaces. In particular we show that these projections are themselves symplectic balls under a certain complexity assumption. Our main result is a…

Matrix configurations coming from matrix models comprise many important aspects of modern physics. They represent special quantum spaces and are thus strongly related to noncommutative geometry. In order to establish a semiclassical limit…

In this exploration paper, we design algorithms for deforming and contracting a simply connected discrete closed manifold to a discrete sphere. Such a contraction is a kind of shrinking or reducing process. In our algorithms, we need to…

We consider Calderon's inverse problem with partial data in dimensions $n \geq 3$. If the inaccessible part of the boundary satisfies a (conformal) flatness condition in one direction, we show that this problem reduces to the invertibility…

We analyze a 1-parameter family of heart shape and a 3-parameter family obtained by gluing three footballs, both of which are examples of reducible spherical conical metrics. For these examples we verify the structure theorem given in [15]…

We follow a stream of the history of positive matrices and positive functionals, as applied to algebraic sums of squares decompositions, with emphasis on the interaction between classical moment problems, function theory of one or several…

Given a smooth simply connected planar domain, the area is bounded away from zero in terms of the maximal curvature alone. We show that in higher dimensions this is not true, and for a given maximal mean curvature we provide smooth…

Computational tools in numerical algebraic geometry can be used to numerically approximate solutions to a system of polynomial equations. If the system is well-constrained (i.e., square), Newton's method is locally quadratically convergent…

In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…

We study the set of lines that meet a fixed line and are tangent to two spheres and classify the configurations consisting of a single line and three spheres for which there are infinitely many lines tangent to the three spheres that also…

The presented paper is devoted to statistical modeling of Gaussian scalar real random fields inside a three-dimensional sphere (ball). We propose a statistical model describing the spatial heterogeneity in a unit ball and a numerical…

The algebraic method of singular reduction is applied for non regular group action on manifolds which provides singular symplectic spaces. The problem of deformation quantization of the singular surfaces is the focus. For some examples of…

The present paper suggests a new approach for geometric representation of 3D spatial models and provides a new compression algorithm for 3D meshes, which is based on mathematical theory of convex geometry. In our approach we represent a 3D…

We present a link between billiards in convex plane domains and Hofer's geometry, an area of symplectic topology. For smooth strictly convex billiard tables, we prove that the Hofer distance between the corresponding billiard ball maps…

The continuity, in a suitable topology, of algebraic and geometric operations on real analytic manifolds and vector bundles is proved. This is carried out using recently arrived at seminorms for the real analytic topology. A new…

The notion of hidden symmetry algebra used in the context of exactly solvable systems is re-examined from the purely algebraic way, analyzing subspaces of commuting polynomials that generate finite-dimensional quadratic algebras. By…

In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…