Related papers: Grassmannian spines, projection closure operators,…

We investigate special points on the Grassmannian which correspond to friezes with coefficients in the case of rank two. Using representations of arithmetic matroids we obtain a theorem on subpolygons of specializations of the coordinate…

In the elastic shape analysis approach to shape matching and object classification, plane curves are represented as points in an infinite-dimensional Riemannian manifold, wherein shape dissimilarity is measured by geodesic distance. A…

It is well-known that the coset spaces G(k((z)))/G(k[[z]]), for a reductive group G over a field k, carry the geometric structure of an inductive limit of projective k-schemes. This k-ind-scheme is known as the affine Grassmannian for G.…

We investigate the problem of finding inner ap-proximations of positive semidefinite (PSD) cones. We developa novel decomposition framework of the PSD cone by meansof conical combinations of smaller dimensional sub-cones. Weshow that many…

The Hilbert scheme $\mathbf{Hilb}_{p(t)}^{n}$ parametrizes closed subschemes and families of closed subschemes in the projective space $\mathbb{P}^n$ with a fixed Hilbert polynomial $p(t)$. It is classically realized as a closed subscheme…

We describe the fundamental group and second homotopy group of ordered $k-$point sets in $Gr(k,n)$ generating a subspace of fixed dimension.

It is known that the antipodal set of a Riemannian symmetric space of compact type $G / K$ consists of a union of $K$-orbits. We determine the dimensions of these $K$-orbits of most irreducible symmetric spaces of compact type. The…

We investigate the rudiments of Riemannian geometry on orbit spaces $M/G$ for isometric proper actions of Lie groups on Riemannian manifolds. Minimal geodesic arcs are length minimising curves in the metric space $M/G$ and they can hit…

In the recent past, nested structures in Riemannian manifolds has been studied in the context of dimensionality reduction as an alternative to the popular principal geodesic analysis (PGA) technique, for example, the principal nested…

Let D be a bounded pseudoconvex domain in $C^n, n\geq 2, 0\leq p\leq n,$ and $1\leq q\leq n-1.$ We show that compactness of the dbar-Neumann operator, $N_{p,q+1},$ on square integrable (p,q+1)-forms is equivalent to compactness of the…

We establish a structure theorem for minimizing sequences for the isoperimetric problem on noncompact $\mathsf{RCD}(K,N)$ spaces $(X,\mathsf{d},\mathcal{H}^N)$. Under the sole (necessary) assumption that the measure of unit balls is…

In the recent paper [arXiv:1612.06893] P. B\"urgisser and A. Lerario introduced a geometric framework for a probabilistic study of real Schubert Problems. They denoted by $\delta_{k,n}$ the average number of projective $k$-planes in…

Given a finite collection $\mathbf{V}:=(V_1,\dots,V_N)$ of closed linear subspaces of a real Hilbert space $H$, let $P_i$ denote the orthogonal projection operator onto $V_i$ and $P_{i,\lambda}:= (1-\lambda)I + \lambda P_i$ denote its…

The finite Grassmannian $\mathcal{G}_{q}(k,n)$ is defined as the set of all $k$-dimensional subspaces of the ambient space $\mathbb{F}_{q}^{n}$. Subsets of the finite Grassmannian are called constant dimension codes and have recently found…

Gaudin hamiltonians form families of r-dimensional abelian Lie subalgebras of the holonomy Lie algebra of the arrangement of reflection hyperplanes of a Coxeter group of rank r. We consider the set of principal Gaudin subalgebras, which is…

In a previous paper, we showed how certain orientations of the edges of a graph G embedded in a closed oriented surface S can be understood as discrete spin structures on S. We then used this correspondence to give a geometric proof of the…

Motivated by the recent approach of Milman, Shabelman, and Yehudayoff \cite{MilmanShabelmanYehudayoff2025}, we establish, for $p\geq 1$, a complete characterization of the fixed points of the composition of the $L_p$-centroid operator and…

Let $\mathcal{G}$ be a countably infinite group of unitary operators on a complex separable Hilbert space $H$. Let $X = \{x_{1},...,x_{r}\}$ and $Y = \{y_{1},...,y_{s}\}$ be finite subsets of $H$, $r < s$, $V_{0} = \bar{span}…

Given a densely defined and closed operator $A$ acting on a complex Hilbert space $\mathcal{H}$, we establish a one-to-one correspondence between its closed extensions and subspaces $\mathfrak{M}\subset\mathcal{D}(A^*)$, that are closed…

We are able to perform the duality transformation of the spin system which was found before as a lattice realization of the string with linear action. In four and higher dimensions this spin system can be described in terms of a…