Related papers: 2D problems in groups

We develop practical techniques to compute with arithmetic groups $H\leq \mathrm{SL}(n,\mathbb{Q})$ for $n>2$. Our approach relies on constructing a principal congruence subgroup in $H$. Problems solved include testing membership in $H$,…

We study Galois descent of K_1 of group algebras with coefficients in certain subrings of the ring of integers of C_p, the completion of an algebraic closure of Q_p.

We study some approximation problems on a strict subset of the circle by analytic functions of the Hardy space H2 of the unit disk (in C), whose modulus satisfy a pointwise constraint on the complentary part of the circle. Existence and…

Topological point defects on orientationally ordered spheres, and on deformable fluid vesicles have been partly motivated by their potential applications in creating super-atoms with directional bonds through functionalization of the…

We study the nature of the instability of the homogeneous steady states of the subcritical Ginzburg-Landau equation in the presence of group velocity. The shift of the absolute instability threshold of the trivial steady state, induced by…

One of the central problems in the study of parametrized constraint satisfaction problems is the Dichotomy Conjecture by T. Feder and M. Vardi stating that the constraint satisfaction problem (CSP) over a fixed, finite constraint language…

We introduce two-dimensional tensor network representations of finite groups carrying a 4-cocycle index. We characterize the associated gapped (2+1)D phases that emerge when these anomalous symmetries act on tensor network ground states. We…

A preliminary result on Subhomogeneous Cooperative Time-delay Systems, subject to revision.

This paper is concerned with the problem of robust stabilization for a class of uncertain 2D discrete switched systems with state delays represented by a model of Roesser type, where the switching instants of the controller experience…

We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…

We formulate problems of tight closure theory in terms of projective bundles and subbundles. This provides a geometric interpretation of such problems and allows us to apply intersection theory to them. This yields new results concerning…

We consider a combinatorial problem occurring naturally in a group theoretical setting and provide a constructive solution in a special case. More precisely, in 1999 the author established a logarithmic bound for the derived length of the…

This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the…

Let (W,S) be a Coxeter system of finite rank (ie |S| is finite) and let A be the associated Coxeter (or Davis) complex. We study chains of pairwise parallel walls in A using Tits' bilinear form associated to the standard root system of…

This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…

One of the most elusive challenges within the area of topological data analysis is understanding the distribution of persistence diagrams. Despite much effort, this is still largely an open problem. In this paper, we present a series of…

We consider vertices, a notion originating in local representation theory of finite groups, for the category $\mathcal{O}$ of a rational Cherednik algebra and prove the analogue of the Dipper-Du Conjecture for Hecke algebras of symmetric…

Finite $p$-groups with a unique $\mathcal{A}_2$-subgroup are classified up to isomorphism. A problem proposed by Berkovich and Janko is solved.

We suggest a tight inequality for norms in $d$-dimensional space $l_p $ which has simple formulation but appears hard to prove. We give a proof for $d=3$ and provide a detailed numerical check for $d\leq 200$ confirming the conjecture. We…

We classify graphs and, more generally, finite relational structures that are identified by C2, that is, two-variable first-order logic with counting. Using this classification, we show that it can be decided in almost linear time whether a…