Related papers: Combinatorial higher dimensional isoperimetry and …
We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which…
Our goal is to convince the readers that the theory of complex normal surface singularities can be a powerful tool in the study of numerical semigroups, and, in the same time, a very rich source of interesting affine and numerical…
This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…
We find boundaries of Borel-Serre compactifications of locally symmetric spaces, for which any filling is incompressible. We prove this result by showing that these boundaries have small singular models and using these models to obstruct…
This survey paper concerns mainly with some asymptotic topological properties of finitely presented discrete groups: quasi-simple filtration (QSF), geometric simple connectivity (GSC), topological inverse-representations, and the notion of…
In this paper, two sequences of minimal isoparametric hypersurfaces are constructed via representations of Clifford algebras. Based on these, we give estimates on eigenvalues of the Laplacian of the focal submanifolds of isoparametric…
Let $X = G/\Gamma$, where $G$ is a Lie group and $\Gamma$ is a lattice in $G$, and let $U$ be a subset of $X$ whose complement is compact. We use the exponential mixing results for diagonalizable flows on $X$ to give upper estimates for the…
Two groups have a common model geometry if they act properly and cocompactly by isometries on the same proper geodesic metric space. The Milnor-Schwarz lemma implies that groups with a common model geometry are quasi-isometric; however, the…
Given a finite set $A\subset\mathbb{R}^d$, let Cov$_{r,k}$ denote the set of all points within distance $r$ to at least $k$ points of $A$. Allowing $r$ and $k$ to vary, we obtain a 2-parameter family of spaces that grow larger when $r$…
It is conjectured that there exist finitely many isomorphism classes of simple endomorphism algebras of abelian varieties of GL_2-type over \Q of bounded dimension. We explore this conjecture when particularized to quaternion endomorphism…
We describe a procedure to construct infinite sets of pairwise smoothly inequivalent 2-spheres in simply connected 4-manifolds, which are topologically isotopic and whose complement has a prescribed fundamental group that satisfies some…
In this paper we construct families of homology spheres which bound 4-manifolds with intersection forms isomorphic to $-E_8$. We show that these families have arbitrary large correction terms. This result says that among homology spheres,…
We analyze the classification problem for finitely generated orderable groups from the viewpoint of descriptive set theory. We analyze the standard Borel space of finitely generated left-orderable groups, and the subspace of finitely…
We find sharp upper bounds on the order of the automorphism group of a hypersurface in complex projective space in every dimension and degree. In each case, we prove that the hypersurface realizing the upper bound is unique up to…
A subcomplex $X\leq \mathcal{C}$ of a simplicial complex is strongly rigid if every locally injective, simplicial map $X\to\mathcal{C}$ is the restriction of a unique automorphism of $\mathcal{C}$. Aramayona and the second author proved…
We uncover a combinatorial structure governing the differential equations satisfied by wavefunction coefficients of scalar fields with generic masses in de Sitter space. Using an integral representation of the massive mode functions, we…
We are generalizing to higher dimensions the Bavard-Ghys construction of the hyperbolic metric on the space of polygons with fixed directions of edges. The space of convex d-dimensional polyhedra with fixed directions of facet normals has a…
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…
In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the…
In this paper, we continue with the results in \cite{Pg} and compute the group of quasi-isometries for a subclass of split solvable unimodular Lie groups. Consequently, we show that any finitely generated group quasi-isometric to a member…