Related papers: Orbit Computation for Atomically Generated Subgrou…
Integration By Parts (IBP) is an important method for computing Feynman integrals. This work describes a formulation of the theory involving a set of differential equations in parameter space, and especially the definition and study of an…
Orbit-finite models of computation generalise the standard models of computation, to allow computation over infinite objects that are finite up to symmetries on atoms, denoted by $\mathbb{A}$. Set theory with atoms is used to reason about…
We show that for every countable group, any sequence of approximate homomorphisms with values in permutations can be realized as the restriction of a sofic approximation of an orbit equivalence relation. Moreover, this orbit equivalence…
We study probability-measure preserving (p.m.p.) actions of finitely generated groups via the graphings they define. We introduce and study the notion of isometric orbit equivalence for p.m.p. actions: two p.m.p. actions are isometric orbit…
We study a class of orbit recovery problems in which we observe independent copies of an unknown element of $\mathbb{R}^p$, each linearly acted upon by a random element of some group (such as $\mathbb{Z}/p$ or $\mathrm{SO}(3)$) and then…
We solve Dehn's isomorphism problem for virtually torsion-free relatively hyperbolic groups with nilpotent parabolic subgroups. We do so by reducing the isomorphism problem to three algorithmic problems in the parabolic subgroups, namely…
We prove that the isomorphism problem for separable nuclear C*-algebras is complete in the class of orbit equivalence relations. In fact, already the isomorphism of simple, separable AI C*-algebras is a complete orbit equivalence relation.…
Cohomology operations (including the cohomology ring) of a geometric object are finer algebraic invariants than the homology of it. In the literature, there exist various algorithms for computing the homology groups of simplicial complexes…
Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…
We present a simple approach to questions of topological orbit equivalence for actions of countable groups on topological and smooth manifolds. For example, for any action of a countable group $\Gamma$ on a topological manifold where the…
The concept of programmable matter envisions a very large number of tiny and simple robot particles forming a smart material. Even though the particles are restricted to local communication, local movement, and simple computation, their…
The classification of the unitary irreducible representations of symmetry groups is a cornerstone of modern quantum physics, as it provides the fundamental building blocks for constructing the Hilbert spaces of theories admitting these…
We introduce a Sinkhorn-type algorithm for producing quantum permutation matrices encoding symmetries of graphs. Our algorithm generates square matrices whose entries are orthogonal projections onto one-dimensional subspaces satisfying a…
It is known that an isometric action of a Lie group on a compact symmetric space gives rise to a proper Fredholm action of a path group on a path space via the gauge transformations. In this paper, supposing that the isometric action is a…
Orbits of coadjoint representations of classical compact Lie groups have a lot of applications. They appear in representation theory, geometrical quantization, theory of magnetism, quantum optics etc. As geometric objects the orbits were…
We give a solution to Dehn's isomorphism problem for the class of all hyperbolic groups, possibly with torsion. We also prove a relative version for groups with peripheral structures. As a corollary, we give a uniform solution to…
The article demonstrates the procedure how to compute the Zariski closure of an orbit by an algebraic action of finitely generated group on the affine plane. First half of the algorithm is about deciding whether given finitely generated…
We study the distribution of non-discrete orbits of geometrically finite groups in $\operatorname{SO}(n,1)$ acting on $\mathbb{R}^{n+1}$, and more generally on the quotient of $\operatorname{SO}(n,1)$ by a horospherical subgroup. Using…
The purpose of this note is twofold. In the first part we observe that two finitely generated non-amenable groups are quasi-isometric if and only if they admit topologically orbit equivalent Cantor minimal actions. In particular, free…
When a group acts on a set, it naturally partitions it into orbits, giving rise to orbit problems. These are natural algorithmic problems, as symmetries are central in numerous questions and structures in physics, mathematics, computer…