We present sufficient conditions under which effective descent morphisms in a quasivariety of universal algebras are the same as regular epimorphisms and examples for which they are the same as regular epimorphisms satisfying projectivity. 1. Preliminaries A variety is a full subcategory of the category of structures for a first order (one sorted) language, closed under substructures, products ...

We prove that if G is a non-uniform lattice in a rank-one semisimple Lie group = Isom(H2 R ), then G is quasi-isometrically co-Hopf. This means that every quasi-isometric embedding G → G is coarsely surjective and thus is a quasi-isometry.

In this study, we investigate the further properties of quasi irresolute topological groups defined in [20]. We show that if a group homomorphism f between quasi irresolute topological groups is irresolute at $e_G$, then $f$ is irresolute on $G$. Later we prove that in a semi-connected quasi irresolute topological group $(G,*,tau )$, if $V$ is any symmetric semi-open neighborhood of $e_G$, then...

We prove that at large disorder, with large probability and for a set of Diophantine frequencies of large measure, Anderson localization in Z is stable under localized time-quasi-periodic perturbations by proving that the associated quasi-energy operator has pure point spectrum. The main tools are the Fröhlich-Spencer mechanism for the random component and the Bourgain-Goldstein-Schlag mechanis...

We establish braided tensor equivalences among module categories over the twisted quantum double of a finite group defined by an extension of a group G by an abelian group, with 3-cocycle inflated from a 3-cocycle on G. We also prove that the canonical ribbon structure of the module category of any twisted quantum double of a finite group is preserved by braided tensor equivalences. We give two...

In these lecture notes, we combine recent homological methods of Kevin Whyte with older dynamical methods developed by Benson Farb and myself, to obtain a new quasiisometric rigidity theorem for the mapping class group MCG(S g ) of a once punctured surface S g : if K is a finitely generated group quasi-isometric to MCG(S g ) then there is a homomorphism K → MCG(S g ) with finite kernel and fini...

If G is either a connected Lie group, or a finitely generated solvable group with exponential growth, we show that G contains a quasi-isometrically embedded free sub-semigroup on 2 generators.

In this note we will construct an example of a quasi-geodesic in the Te-ichm uller space of a surface with the following instability property: Theorem For any hyperbolic surface S whose Teichm uller space T (S) has dimension at least 4, there is a bi-innnite quasi-geodesic L in T (S) such that 1. L projects to a compact part of the moduli space M(S), but 2. L does not lie in a bounded neighborh...

Our research was motivated by the pure parsimony haplotyping problem: Given a set G of genotypes, the haplotyping problem consists in finding a set H of haplotypes that explains G. In the pure parsimony haplotyping problem (PPH) we are interested in finding a set H of smallest possible cardinality. The pure parsimony haplotyping problem can be described as a graph colouring problem as follows: ...

Given an epimorphism φ: Π → Π' between projective planes Π and Π', it is an open question how the groups of projectivities of Π and Π' (regarded as permutation groups on projective lines) are related. Within this note we will not answer this sophisticated and hard problem in full, but we will address the question to which extend the projectivities of Π induce permutations on the lines of Π ' wh...