We review notions of small sets,-irreducibility, etc., and present a simple proof of asymptotic convergence of general state space Markov chains to their stationary distributions.

This is a survey of recent progress on the irreducibility Fermi varieties, rigidity results and embedded eigenvalue problems discrete periodic Schr\"odinger operators.

Given a commensurated subgroup $\Lambda$ of group $\Gamma$, we completely characterize when the inclusion $\Lambda\leq \Gamma$ is $C^*$-irreducible and provide new examples such inclusions. In particular, obtain that $\rm{PSL}(n,\mathbb{Z})\leq\rm{PGL}(n,\mathbb{Q})$ for any $n\in \mathbb{N}$, $C^*$-simple into its abstract commensurator $C^*$-irreducible. The main ingredient use fact action $\...

We consider Krammer’s representation of the pure braid group on three strings: P3 → GL 3, Z t±1, q±1 , where t and q are indeterminates. As it was done in the case of the braid group, B3, we specialize the indeterminates t and q to nonzero complex numbers. Then we present our main theorem that gives us a necessary and sufficient condition that guarantees the irreducibility of the complex specia...

This is a continuation of [7] in which we proved irreducibility of spaces of rational curves on a general hypersurface X d ⊂ P n of degree d < n+1 2. In this paper, we prove that if d 2 + d + 2 ≤ n and if d ≥ 3, then the spaces of rational curves are themselves rationally connected.

In this paper, we compare the moduli spaces of rank-3 vector bundles stable with respect to diierent ample divisors over rational ruled surfaces. We also discuss the irreducibility, unirationality, and rationality of these moduli spaces.