Related papers: On the GIT stratification of prehomogeneous vector…

In this paper, we complete the classification of transitive ovoids of finite Hermitian polar spaces.

Let $G$ be a Lie group, and let $(M,\omega)$ be a symplectic manifold. If $G$ admits a Hamiltonian action on $(M,\omega)$ with momentum map $\mu$, then $M$, the zero-level set of $\mu$, the orbit space, and the corresponding symplectic…

Geodesic orbit spaces (or g.o. spaces) are defined as those homogeneous Riemannian spaces $(M=G/H,g)$ whose geodesics are orbits of one-parameter subgroups of $G$. The corresponding metric $g$ is called a geodesic orbit metric. We study the…

Riemannian geodesic orbit spaces (G/H,g) are natural generalizations of symmetric spaces, defined by the property that their geodesics are orbits of one-parameter subgroups of G. We study the geodesic orbit spaces of the form (G/S,g), where…

In this paper, we classify the groups of semisimilarities of finite classical polar spaces with exactly two orbits on the singular or isotropic points. As a byproduct, we obtain many highly symmetric regular sets in the point graphs of…

For fields with more than $2$ elements, the classification of the vector spaces of matrices with rank at most $2$ is already known. In this work, we complete that classification for the field $\mathbb{F}_2$. We apply the results to obtain…

We prove that the orbit closure of the determinant is not normal. A similar result is obtained for the orbit closure of the permanent multiplied by a power of a linear form.

Within the generalized definition of coherent states as group orbits we study the orbit spaces and the orbit manifolds in the projective spaces constructed from linear representations. Invariant functions are suggested for arbitrary groups.…

In this paper we study the geometry of GIT configurations of $n$ ordered points on $\mathbb{P}^1$ both from the the birational and the biregular viewpoint. In particular, we prove that any extremal ray of the Mori cone of effective curves…

We associate a geometric space to an arbitrary convex polytope. Our construction parallels the construction by D. Cox of a toric variety as a GIT quotient. The spaces that we obtain are endowed with a natural stratification and perfectly…

The Hilbert manifold $\Sigma$ consisting of positive invertible (unitized) Hilbert-Schmidt operators has a rich structure and geometry. The geometry of unitary orbits $\Omega\subset \Sigma$ is studied from the topological and metric…

We complete the classification of isometric cohomogeneity-one actions on all symmetric spaces of noncompact type up to orbit equivalence.

A complete classification of two-dimensional algebras over algebraically closed fields is provided

This paper is a contribution to frame theory. Frames in a Hilbert space are generalizations of orthonormal bases. In particular, Gabor frames of $L^2(\mathbb{R})$, which are made of translations and modulations of one or more windows, are…

Let $\mathcal G_2$ denote the affine group $GL(2,\mathbb Z) \ltimes \mathbb Z^{2}$. For every point $x=(x_1,x_2) \in \R2$ let $\orb(x)=\{y\in\R2\mid y=\gamma(x)$ for some $\gamma \in \mathcal{G}_2 \}$. Let $G_{x}$ be the subgroup of the…

We study the relationship between many natural conditions that one can put on a diffeological vector space: being fine or projective, having enough smooth (or smooth linear) functionals to separate points, having a diffeology determined by…

We present a combination of tools which allows for investigation of the coupled orbital and rotational dynamics of two rigid bodies with nearly arbitrary shape and mass distribution, under the influence of their mutual gravitational…

Let $X=G/H$ be a spherical homogeneous variety for a complex reductive algebraic group $G$. We prove that the orbit space of $X$ under the action of a maximal compact subgroup $K\subset G$ is homeomorphic to the valuation cone of $X$. We…

We consider a class of inhomogeneous self-similar cosmological models in which the perfect fluid flow is tangential to the orbits of a three-parameter similarity group. We restrict the similarity group to possess both an Abelian $G_{2}$,…

We give a complete classification of equivariant vector bundles of rank two over smooth complete toric surfaces and construct moduli spaces of such bundles. This note is a direct continuation of an earlier note where we developed a general…