Related papers: Krull dimension for limit groups I: Bounding stric…

In this second paper, I construct a limit space of a Cauchy sequence of globally hyperbolic spacetimes. In the second section, I work gradually towards a construction of the limit space. I prove the limit space is unique up to isometry. I…

Let $\mathbf{G}$ be a reductive group defined over $\mathbb{Q}$ and let $\mathfrak{S}$ be a Siegel set in $\mathbf{G}(\mathbb{R})$. The Siegel property tells us that there are only finitely many $\gamma \in \mathbf{G}(\mathbb{Q})$ of…

Minimal linear codes are in one-to-one correspondence with special types of blocking sets of projective spaces over a finite field, which are called strong or cutting blocking sets. In this paper we prove an upper bound on the minimal…

Recently, Stull [18], [17] resolved a long-standing open problem posed by Lutz, on whether the set of effective Hausdorff dimensions of points on a straight line in $\mathbb{R}^2$ -- the effective dimension spectrum of the line -- contains…

In the representation theory of real reductive Lie groups, many objects have finiteness properties. For example, the lengths of Verma modules and principal series representations are finite, and more precisely, they are bounded. In this…

In this paper, we prove that uniformly bounded simple Lie conformal algebra must be finitely generated. Furthermore, we give a completely classification of simple uniformly bounded Lie conformal algebras with upper bound one.

Simple upper and lower bounds are established for the integral $\int_0^x\mathrm{e}^{-\beta t}t^\nu \mathbf{L}_\nu(t)\,\mathrm{d}t$, where $x>0$, $\nu>-1$, $0<\beta<1$ and $\mathbf{L}_\nu(x)$ is the modified Struve function of the first…

We establish upper bounds for the distance to finite-dimensional subspaces in inner product spaces and improve some generalisations of Bessel's inequality obtained by Boas, Bellman and Bombieri. Refinements of the Hadamard inequality for…

We prove the existence of a limit shape and give its explicit description for certain probability distribution on signatures (or highest weights for unitary groups). The distributions have representation theoretic origin-they encode…

We obtain sharp lower and upper bounds for the number of maximal (under inclusion) independent sets in trees with fixed number of vertices and diameter. All extremal trees are described up to isomorphism.

In the paper we obtained some estimations of Krull dimension of modules over group rings of minimax abelian groups. We also consider relations between the condition of existing of small deviation for normal subgroups and some previously…

We establish character rigidity for all non-uniform higher-rank irreducible lattices in semisimple groups of characteristic other than 2. This implies stabilizer rigidity for probability measure preserving actions and rigidity of invariant…

We present an explicit formula for subregular characters (i.e, irreducible finite-dimensional complex characters of submaximal degree) of the unitriangular group over a finite field of sufficiently large characteristic.

We introduce a fractal dimension for a metric space defined in terms of the persistent homology of extremal subsets of that space. We exhibit hypotheses under which this dimension is comparable to the upper box dimension; in particular, the…

We prove that the set of limit groups is recursive, answering a question of Delzant. One ingredient of the proof is the observation that a finitely presented group with local retractions (a la Long and Reid) is coherent and, furthermore,…

We consider relative character varieties on $\mathbb{P}^1\backslash\{0,1,\infty\}$ with $G=GL(r), O(r)$, or $Sp(r)$. Using a diagrammatic method of Simpson's, we give an explicit linear upper bound $R(d)$ on the rank $r$ of an MC-minimal…

In 2007, Y. Shimoda, in connection with a long-standing question of J. Sally, asked whether a Noetherian local ring, such that all its prime ideals different from the maximal ideal are complete intersections, has Krull dimension at most…

In this paper we present a new bound obtained with the probabilistic method for the solution of the Set Covering problem with unit costs. The bound is valid for problems of fixed dimension, thus extending previous similar asymptotic…

We prove the first known nontrivial bounds on the sizes of the 2-torsion subgroups of the class groups of cubic and higher degree number fields $K$ (the trivial bound being $O_{\epsilon}(|{\rm Disc}(K)|^{1/2+\epsilon})$ by Brauer--Siegel).…

We prove a lower bound on the dimension of the set of maximal border subrank tensors. This is the first such bound of its type.