Related papers: Weakly positive and directed Anosov representation…
In the first section of this senior thesis the author provides some new efficient algorithms for calculating with finite permutation groups. They cannot be found in the computer algebra system MAGMA, but they can be implemented there. For…
We study primitive stable representations of free groups into higher rank semisimple Lie groups and their properties. Let $\Sigma$ be a compact, connected, orientable surface (possibly with boundary) of negative Euler characteristic. We…
Let $\Gamma$ be a group and $r_n(\Gamma)$ the number of its $n$-dimensional irreducible complex representations. We define and study the associated representation zeta function $\calz_\Gamma(s) = \suml^\infty_{n=1} r_n(\Gamma)n^{-s}$. When…
Despite the invertible setting, Anosov endomorphisms may have infinitely many unstable directions. Here we prove, under transitivity assumption, that an Anosov endomorphism on a closed manifold $M,$ is either special (that is, every $x \in…
For $\alpha >0$, let $$\mathscr{A}=\{ a_1<a_2<a_3<\cdots\}$$ and $$\mathscr{L}=\{ \ell_1, \ell_2, \ell_3,\cdots\} \quad \text{(not~necessarily~different)}$$ be two sequences of positive integers with $\mathscr{A}(m)>(\log m)^\alpha $ for…
We construct a new family of linearizations of rational matrices $R(\lambda)$ written in the general form $R(\lambda)= D(\lambda)+C(\lambda)A(\lambda)^{-1}B(\lambda)$, where $D(\lambda)$, $C(\lambda)$, $B(\lambda)$ and $A(\lambda)$ are…
We introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called weakly maximal representations. They are defined in terms of invariants in bounded cohomology and extend considerably the…
On the twisted Fock spaces $ \mathcal{F}^\lambda(\C^{2n}) $ we consider a family of unitary operators $\rho_\lambda(a,b) $ indexed by $ (a,b) \in \C^n \times \C^n.$ The composition formula for $ \rho_\lambda(a,b) \circ…
The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the second in a series of papers in…
A weak homomorphism from a graph G to a graph H is a mapping f from V(G) to V(H), where either f(x) = f(y) or {f(x), f(y)} is an element of E(H), and this holds for all {x, y} in E(G). A rectangular grid graph is formed by taking the…
We investigate the notion of involutive weak globular $\omega$-categories via T.Leinster's approach: as algebras for the initial contracted globular operad in the bicategory of globular collections induced by the Cartesian monad of the free…
The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the first in a series of papers in…
Let $\mathcal G$ denote the space of finitely generated marked groups. For any finitely generated group $G$, we construct a continuous, injective map $f$ from the space of subgroups $Sub(G)$ to $\mathcal G$ that sends conjugate subgroups to…
We show that the cuspidal component of the stable trace formula of a special odd orthogonal group over a number field, satisfies a weak form of beyond endoscopic decomposition. We also study the $r$-stable trace formula, when $r$ is the…
The Gromov-Lawson-Rosenberg conjecture for a group G states that a compact spin manifold with fundamental group G admits a metric of positive scalar curvature if and only if a certain topological obstruction vanishes. It is known to be true…
Let $(K,\mathcal O,k)$ be a $p$-modular system and assume $k$ is algebraically closed. We show that if $\Lambda$ is an $\mathcal O$-order in a separable $K$-algebra, then $\textrm{Pic}_{\mathcal O}(\Lambda)$ carries the structure of an…
We introduce L-presentations: group presentations given by a generating set, a set of relations and a set of substitution rules on the generating set producing more relations. We first study in full generality the structure of finitely…
We present a unified approach to proving Ramsey-type theorems for graphs with a forbidden induced subgraph which can be used to extend and improve the earlier results of Rodl, Erdos-Hajnal, Promel-Rodl, Nikiforov, Chung-Graham, and…
Let $G$ be a commutative algebraic group embedded in projective space and $\Gamma$ a finitely generated subgroup of $G$. From these data we construct a chain of algebraic subgroups of $G$ which is intimately related to obstructions to…
There is a procedure, due to Dani and Levcovitz, for taking a finite simplicial graph (\Gamma) and a subgraph (\Lambda) of its complement, checking some conditions, and, if satisfied, producing a graph (\Delta) such that the right-angled…