Related papers: Projectively equivalent 2-dimensional superintegra…

We introduce a notion of parity for formal morphisms between invertible objects and use it to prove a corresponding coherence theorem. Parity is conceptually similar to the sign of underlying permutations, but not defined as such. To give…

Projective structures on curves appear naturally in many areas of mathematics, from extrinsic conformal geometry to analysis, where the main problem is to find qualitative information about the solutions of Hill equations. In this paper, we…

We study the duality of reconstruction systems, which are $g$-frames in a finite dimensional setting. These systems allow redundant linear encoding-decoding schemes implemented by the so-called dual reconstruction systems. We are…

Similarity notions between vertices in a graph, such as structural and regular equivalence, are one of the main ingredients in clustering tools in complex network science. We generalise structural and regular equivalences for undirected…

In this paper we give a brief account of the relations between non-projected supermanifolds and projectivity in supergeometry. Following the general results of arXiv:1706.01354, we study an explicit example of non-projected and…

In this paper we discuss maximal superintegrability of both classical and quantum St\"ackel systems. We prove a sufficient condition for a flat or constant curvature St\"ackel system to be maximally superintegrable. Further, we prove a…

We compute the integral homology and cohomology groups of configuration spaces of two distinct points on a given real projective space. The explicit answer is related to the (known multiplicative structure in the) integral cohomology---with…

We consider a geometric property of the closest-points projection to a geodesic in Teichm\"uller space: the projection is called contracting if arbitrarily large balls away from the geodesic project to sets of bounded diameter. (This…

The Separation of Variables theory for the Hamilton-Jacobi equation is 'by definition' related to the use of special kinds of coordinates, for example Jacobi coordinates on the ellipsoid or St\"ackel systems in the Euclidean space. However,…

Stationary black holes of massless supergravity theories are described by certain geodesic curves on the target space that is obtained after dimensional reduction over time. When the target space is a symmetric coset space we make use of…

This paper studies the Bondi-Metzner-Sachs group in homogeneous projective coordinates, because it is then possible to write all transformations of such a group in a manifestly linear way. The 2-sphere metric, Bondi-Metzner-Sachs metric,…

We construct the $\mathcal{N}=8$ supersymmetric mechanics with potential term whose configuration space is the special K\"ahler manifold of rigid type and show that it can be viewed as the K\"ahler counterpart of $\mathcal{N}=4$ mechanics…

We study smooth projective varieties with small dual variety using methods from symplectic topology. We prove the affine parts of such varieties are subcritical, and that the hyperplane class is invertible in their quantum cohomology. We…

Non-hermitian, $\mathcal{PT}$-symmetric Hamiltonians, experimentally realized in optical systems, accurately model the properties of open, bosonic systems with balanced, spatially separated gain and loss. We present a family of exactly…

We discuss an algorithm computing the push-forward to projective space of several classes associated to a (possibly singular, reducible, nonreduced) projective scheme. For example, the algorithm yields the topological Euler characteristic…

Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…

This paper studies the situation when two 4-dimensional Lorentz manifolds (that is, space-times) admit the same (unparametrised) geodesics, that is, when they are projectively related. A review of some known results is given and then the…

One-dimensional sigma-models with N supersymmetries are considered. For conventional supersymmetries there must be N-1 complex structures satisfying a Clifford algebra and the constraints on the target space geometry can be formulated in…

The concept of superintegrability in quantum mechanics is extended to the case of a particle with spin s=1/2 interacting with one of spin s=0. Non-trivial superintegrable systems with 8- and 9-dimensional Lie algebras of first-order…

This article presents an overview of the theory of integrable systems with symmetries, focusing on toric systems, semitoric systems, and their classifications via decorated polygons. We discuss certain one-parameter families of integrable…