Related papers: Notes on Thin Matrix Groups

We develop the theory of Diophantine approximation for systems of simultaneously small linear forms, which coefficients are drawn from any given analytic non-degenerate manifolds. This setup originates from a problem of Sprind\v{z}uk from…

We generalize one part of Thurston's hyperbolic Dehn filling theorem to arbitrary-rank semisimple Lie groups by showing that certain deformations of extended geometrically finite subgroups of a semisimple Lie group are still extended…

We investigate the existence problem of group invariant matrices using algebraic approaches. We extend the usual concept of multipliers to group rings with cyclotomic integers as coefficients. This concept is combined with the field descent…

In this paper we initiate a new approach to studying approximations by rational points to points on smooth submanifolds of $\mathbb{R}^n$. Our main result is a convergence Khintchine type theorem for arbitrary nondegenerate submanifolds of…

Motivated by recent results on diffeomorphisms of 4-manifolds, this paper investigates fundamental groups of spaces of embeddings of $S^1\times D^3$ in 4-manifolds. The majority of work goes into the case of framed immersed circles.

We introduce the notion of a diagram category and discuss its application to the invariant theory of classical groups and super groups, with some indications concerning extensions to quantum groups and quantum super groups. Tensor functors…

In this monograph we lay the foundation for a theory of coarse groups and coarse actions. Coarse groups are group objects in the category of coarse spaces, and can be thought of as sets with operations that satisfy the group axioms "up to…

This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first order theory of finite groups. The focus is on concepts from stability theory…

Our focus is on the set of lower-triangular, infinite matrices that have natural operations like addition, multiplication by a number, and matrix multiplication. With respect to addition this set forms and abelian group while with respect…

The construction and classification of super-modular categories is an ongoing project, of interest in algebra, topology and physics. In a recent paper, Cho, Kim, Seo and You produced two mysterious families of super-modular data, with no…

In Diophantine approximation, inhomogeneous problems are linked with homogeneous ones by means of the so-called Transference Theorems. We revisit this classical topic by introducing new exponents of Diophantine approximation. We prove that…

This thesis is devoted to algorithmic aspects of the implementation of Cartan's moving frame method to the problem of the equivalence of submanifolds under a Lie group action. We adopt a general definition of a moving frame as an…

A new pair of asymptotic invariants for finitely presented groups, called intrinsic and extrinsic tame filling functions, are introduced. These filling functions are quasi-isometry invariants that strengthen the notions of intrinsic and…

The representation problem of finite-dimensional Markov matrices in Markov semigroups is revisited, with emphasis on concrete criteria for matrix subclasses of theoretical or practical relevance, such as equal-input, circulant, symmetric or…

We construct analogues of FI-modules where the role of the symmetric group is played by the general linear groups and the symplectic groups over finite rings and prove basic structural properties such as Noetherianity. Applications include…

This paper is devoted to the study of a problem of Cassels in multiplicative Diophantine approximation which involves minimising values of a product of affine linear forms computed at integral points. It was previously known that values of…

This is an introduction to topology of complement to plane curves and hypersurfaces in the projective space and is based on the lectures given in Lumini in February and in ICTP (Trieste) in August of 2005. We discuss key problems concerning…

Given a projective surface and a generic projection to the plane, the braid monodromy factorization (and thus, the braid monodromy type) of the complement of its branch curve is one of the most important topological invariants, stable on…

I extend the framework of rigid analytic geometry to the setting of algebraic geometry relative to monoids, and study the associated notions of separated, proper, and overconvergent morphisms. The category of affine manifolds embeds as a…

Double coverings of the orthogonal groups of the real and complex spaces are considered. The relation between discrete transformations of these spaces and fundamental automorphisms of Clifford algebras is established, where an isomorphism…