Related papers: Determination Problems for Orbit Closures and Matr…

The Profinite Isomorphism Problem for a class of groups \mathcal{C} asks for an algorithm that decides for any two groups in \mathcal{C} whether they have isomorphic profinite completions. We present the positive solution to this problem…

We consider the conjugation-action of an arbitrary upper-block parabolic subgroup of the general linear group on the variety of nilpotent matrices in its Lie algebra. Lie-theoretically, it is natural to wonder about the number of orbits of…

We exhibit an explicit formula for the cardinality of solutions to a class of quadratic matrix equations over finite fields. We prove that the orbits of these solutions under the natural conjugation action of the general linear groups can…

We deal with the orbit determination problem for hyperbolic maps. The problem consists in determining the initial conditions of an orbit and, eventually, other parameters of the model from some observations. We study the behaviour of the…

The main goal of the paper is the discussion of a deeper interaction between matrix theory over polynomial rings over a field and typical methods of commutative algebra and related algebraic geometry. This is intended in the sense of…

We give a necessary and sufficient condition on a matrix for its centralizer in $\sf{GL}(n,\mathbb{Z})$ to be polycyclic, or equivalently in this case, not to contain a non-abelian free subgroup. We give a simple condition on the matrix…

Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special linear two dimensional representations of the…

This paper exploits adjacencies between the orbits of an ordered set P and a consequence of the classification of finite simple groups to, in many cases, exponentially bound the number of automorphisms. Results clearly identify the…

In this paper we study the Grassmannian of submodules of a given dimension inside a finitely generated projective module $P$ for a finite dimensional algebra $\Lambda$ over an algebraically closed field. The orbit of such a submodule $C$…

Results of number of geometric operations (often used in technical practise, as e.g. the operation of blending) are in many cases surfaces described implicitly. Then it is a challenging task to recognize the type of the obtained surface,…

The restricted $S$-matrix of $V^G$ is determined for any regular vertex operator algebra $V$ and finite automorphism group $G$ of $V.$ As an application, the $S$-matrices for cyclic permutation orbifolds of prime orders are computed.

We define a class of stochastic processes based on evolutions and measurements of quantum systems, and consider the complexity of predicting their long-term behavior. It is shown that a very general class of decision problems regarding…

Arithmetic groups are groups of matrices with integral entries. We shall first discuss their origin in number theory (Gauss, Minkowski) and their role in the "reduction theory of quadratic forms". Then we shall describe these groups by…

The group of 2-by-2 matrices with integer entries and determinant $\pm > 1$ can be identified either with the group of outer automorphisms of a rank two free group or with the group of isotopy classes of homeomorphisms of a 2-dimensional…

In this paper we investigate the orbit closures for the class of representations of simple algebraic groups associated to various gradings on a simple Lie algebras of type $E_6$, $F_4$ and $G_2$. The methods for classifying the orbits for…

In [Tohoku Math. J. 62 (2010), 45--53] the second author showed that, except for a few cases, the order $N$ of a cyclic group of self-homeomorphisms of a closed orientable topological surface $S_g$ of genus $g \geq 2$ determines the group…

For For a given PDE system, or an exterior differential system possessing a Lie group of internal symmetries the orbit reduction procedure is introduced. It is proved that the solutions of the reduced exterior differential system are in…

Motivated by a historical combinatorial problem that resembles the well-known Josephus problem, we investigate circular partition algorithms and formulate problems in deterministic finite automata with practical algorithms. The historical…

We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…

A positive definite completion problem pertains to determining whether the unspecified positions of a partial (or incomplete) matrix can be completed in a desired subclass of positive definite matrices. In this paper we study an important…