Related papers: On first order rigidity for linear groups

Differential Galois theory has played important roles in the theory of integrability of linear differential equation. In this paper we will extend the theory to nonlinear case and study the integrability of the first order nonlinear…

We present simple graph-theoretic characterizations of Cayley graphs for monoids, semigroups and groups. We extend these characterizations to commutative monoids, semilattices, and abelian groups.

We use algebraic geometry to study matrix rigidity, and more generally, the complexity of computing a matrix-vector product, continuing a study initiated by Kumar, et. al. We (i) exhibit many non-obvious equations testing for (border)…

We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier free definability of types over stable sets, introduce an…

Observations on rational Chow groups and cycle class maps in equivariant contexts.

This is a survey of some problems in geometric group theory which I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some…

The area of research called \textquotedblleft Lineability\textquotedblright% \ looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general settings;…

This paper extends our earlier results to higher dimensions using a different approach, based on the rigidity of complex structures on certain domains.

In this paper I present some open problems on Coxeter groups and unimodality, together with the main partial results, and computational evidence, that are known about them.

This is a survey on (lack of) stable rationality over arbitrary fields (including algebraically closed fields). Topics addressed include: Rationality and unirationality, R-equivalence on rational points, Chow groups of zero-cycles, Galois…

After introducing the concept of commutativity for continuous-time linear time-varying systems, the related literature and the results obtained so far are presented. For a simple introduction of the commutativity of discrete-time linear…

We compute the kernel of the stabilization map for $K_1$-functors modeled on split Chevalley groups of types $B_l, C_l, E_l$ one step below the stable range. For the groups of type $B_l$ this implies early injective stability for $K_1(B_l,…

In this paper, we study the relationship between the McKay quivers of a finite subgroups $G$ of special linear groups general linear groups, via some natural extension and embedding. We show that the McKay quiver of certain extension of a…

We describe our recent results concerning the rigidity/unlockability properties of clusters of rigid bodies sliding over the unit sphere.

We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.

We show that the weak monadic second order theory of the structure $({\mathbb Q}, <)$ is first order interpretable in its automorphism group.

For every compact, connected manifold $M$, we prove the existence of a sentence $\phi_M$ in the language of groups such that the homeomorphism group of another compact manifold $N$ satisfies $\phi_M$ if and only if $N$ is homeomorphic to…

In this paper homology stability for unitary groups over a ring with finite unitary stable rank is established. Homology stability of symplectic groups and orthogonal groups appears as a special case of our results.

Linear programming is the seminal optimization problem that has spawned and grown into today's rich and diverse optimization modeling and algorithmic landscape. This article provides an overview of the recent development of first-order…

We make available some results about model theory cyclically ordered groups. We start with a classification of complete theories of divisible abelian cyclically ordered groups. Then we look at the cyclically ordered groups where the only…