Related papers: Rigidity in automorphic representations and local …

Rigid, hard and soft problems and results in arithmetic geometry are presented. "Soft" and "hard" in our paper are limited to the framework of solutions of quadratic forms over rings of integers of local and global fields, the…

We study automorphism groups of formal matrix algebras. We also consider automorphisms of ordinary matrix algebras (in particular, triangular matrix algebras).

We prove automorphy lifting results for geometric representations $\rho:G_F \rightarrow GL_2(\mathcal{O})$, with $F$ a totally real field, and $\mathcal{O}$ the ring of integers of a finite extension of $\mathbb{Q}_p$ with $p$ an odd prime,…

We compute the universal deformations of cuspidal representations $\pi$ of $\GL_2(F)$ over an algebraically closed field of characteristic $l$, where $F$ is a local field of residue characteristic $p$ not equal to $l$. When $\pi$ is…

This paper is devoted to a study of the automorphism groups of three series of finite dimensional special odd Hamiltonian superalgebras $\mathfrak{g}$ over a field of prime characteristic. Our aim is to characterize the connections between…

We obtain a set of generalized eigenvectors that provides a generalized spectral decomposition for a given unitary representation of a commutative, locally compact topological group. These generalized eigenvectors are functionals belonging…

A framework (a straight-line embedding of a graph into a normed space allowing edges to cross) is globally rigid if any other framework with the same edge lengths with respect to the chosen norm is an isometric copy. We investigate global…

We prove rigidity of various types of holomorphic parabolic geometry on smooth complex projective varieties.

We study the local Killing Lie algebra of meromorphic almost rigid geometric structures on complex manifolds. This leads to classification results for compact complex manifolds bearing holomorphic rigid geometric structures.

We discuss progress towards the classification of irreducible admissible representations of reductive groups over non-archimedean local fields and the local Langlands correspondence. We also state some (partly conjectural) compatibility…

Combinatorial rigidity theory seeks to describe the rigidity or flexibility of bar-joint frameworks in R^d in terms of the structure of the underlying graph G. The goal of this article is to broaden the foundations of combinatorial rigidity…

We study the automorphism group of graphons (graph limits). We prove that after an appropriate "standardization" of the graphon, the automorphism group is compact. Furthermore, we characterize the orbits of the automorphism group on…

This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…

For plane frameworks with reflection or rotational symmetries, where the group action is not necessarily free on the vertex set, we introduce a phase-symmetric orbit rigidity matrix for each irreducible representation of the group. We then…

The Hamiltonian formulation for the mechanical systems with reparametrization-invariant Lagrangians, depending on the worldline external curvatures is given, which is based on the use of moving frame. A complete sets of constraints are…

We introduce the concept of strongly independent matrices over any field, and prove the existence of such matrices for certain fields and the non-existence for algebraically closed fields. Then we apply strongly independent matrices over…

In earlier work of the author rigid irregular connections with differential Galois group $G_2$ and whose slopes have numerator $1$ were classified and new rigid connections were constructed. The same construction can be carried out for…

We show that if $K$ is an arbitrary field and $G$ is a finite group then there exists a curve over $K$ with automorphism group $G$. We also give a positive solution to the weak inverse Galois problem for function fields over an arbitrary…

Let $R$ be a ring with unity, $\sigma$ an endomorphism of $R$ and $M_R$ a right $R$-module. In this paper, we continue studding $\sigma$-rigid modules that were introduced by Gunner et al. \cite{generalized/rigid}. We give some results on…

This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…