Related papers: 2D problems in groups

We show that Wall's D(2) problem, the Realization problem and the Relation Gap problem could all be solved if it could be shown that the deficiency of a certain group is, as intuition would suggest, less than -1. Note the paper has been…

In this paper we discuss a conjecture on intermediate subfactors which is a generalization of Wall's conjecture from the theory of finite groups. We explore special cases of this conjecture and present supporting evidence. In particular we…

We discuss some new results concerning Gap Conjecture on group growth and present a reduction of it (and its *-version) to several special classes of groups. Namely we show that its validity for the classes of simple groups and residually…

We examine second bounded cohomology and mod p homology in finite index subgroups of 1-relator groups and groups with a presentation of deficiency at least one. We use this to determine exactly which 1-relator groups are boundedly…

If a finite p-group G acts continuously on a compact topological manifold M then, with some bound C depending on M alone, G has a subgroup H of index at most C such that the H-action on M has at most C stabilizer subgroups. This result…

This paper continues the studies of symbolic integration by focusing on the stability problems on D-finite functions. We introduce the notion of stability index in order to investigate the order growth of the differential operators…

For each subgroup of GL_2(F_p) or order divisible by p, generated by (pseudo-)reflections, we compute the ideals of stable and generalized invariants. These groups and these ideals are related to the cohomology of compact Lie groups,…

We explore the stability of domain wall and bubble solutions in theories with compact extra dimensions. The energy density stored inside of the wall can destabilize the volume modulus of a compactification, leading to solutions containing…

In this paper we address the global stability problem for double-bubbles in the plane. This is accomplished by combining the "improved convergence theorem" for planar clusters developed in arXiv:1409.6652 with an ad hoc analysis of the…

We give a structural description of the normal subgroups of subgroups of finite index in branch groups in terms of rigid stabilizers. This gives further insight into the structure lattices of branch groups introduced by the second author.…

We study a doubly nonlinear parabolic problem arising in the modeling of gas transport in pipelines. Using convexity arguments and relative entropy estimates we show uniform bounds and exponential stability of discrete approximations…

We investigate an analogue of the Grothendieck $p$-curvature conjecture, where the vanishing of the $p$-curvature is replaced by the stronger condition, that the module with connection mod $p$ underlies a $\mathcal{D}_X$-module structure.…

This article is a survey of conjectures and results on reductive algebraic groups having good reduction at a suitable set of discrete valuations of the base field. Until recently, this subject has received relatively little attention, but…

Recently, sub-indices and sub-factors of groups with connections to number theory, additive combinatorics, and factorization of groups have been introduced and studied. Since all group subsets are considered in the theory and there are many…

We propose an algorithm to numerically determined whether a second-order linear PDE problem satisfying a Garding inequality is well-posed. This algorithm further provides a lower bound to the inf-sup constant of the weak formulation, which…

Extending the thoroughly studied theory of group stability, we study Ulam stability type problems for associative and Lie algebras; namely, we investigate obstacles to rank-approximation of almost solutions by exact solutions for systems of…

This article contains a self-contained proof of the stability under convolution of the space of resurgent functions associated with a closed discrete subset of the complex plane (the set of possible singularities), under the assumption that…

We consider the problem of closeness of solutions of an exact and an averaged difference equations on an infinite interval. Appropriate assertions are derived from one special theorem on the stability under constantly acting perturbations.

This paper presents finite-time and fixed-time stabilization results for inhomogeneous abstract evolution problems, extending existing theories. We prove well-posedness for strong and weak solutions, and estimate upper bounds for settling…

In this paper we prove a stability theorem for block diffeomorphisms of 2d-dimensional manifolds that are connected sums of S^d x S^d. Combining this with a recent theorem of S. Galatius and O. Randal-Williams and Morlet's lemma of…