We classify an action of the n-strand braid group on the free group of rank n, which is similar to the Artin representation in the sense that the ith generator σi of Bn acts so that it fixes all free generators xj except j = i, i + 1.We determine all such representations and discuss knot invariants coming from such representations.

We prove a large sieve inequality with moduli of general polynomial form. The version with moduli being the product of l many kth powers has an application to counting l-tuples of consecutive integers with high index of composition, a problem related to the abc-conjecture.

We investigate the consequences of natural conjectures of Montgomery type on the non-vanishing of Dirichlet L-functions at the central point. We first justify these conjectures using probabilistic arguments. We then show using a result of Bombieri, Friedlander and Iwaniec, and a result of the author that they imply that almost all Dirichlet L-functions do not vanish at the central point. We al…

In this note, we prove a generalization of the ‘strange formula’ of Freudenthal and de-Vries for compact homogeneous spaces with positive Euler characteristic. As a corollary, we obtain a new proof of the original formula. We also apply our results to computing a topological invariant used to study hyper-Kähler structures.

We consider the homotopy category of complexes of projective modules over a Noetherian ring. Truncation at degree zero induces a fully faithful triangle functor from the totally acyclic complexes to the singularity category.We show that if the ring is either Artin or commutative Noetherian local, then the functor is dense if and only if the ring is Gorenstein. Motivated by this, we define the G…

We study the homological finiteness properties FPm of wreath products  = H X G. We show that, when H has infinite abelianization,  is of type FPm if and only if both G and H have type FPm and G acts (diagonally) on Xi with stabilizers of type FPm−i and with finitely many orbits for all 1 ≤ i ≤ m. If furthermore H is torsion-free, we give a criterion for  to be Bredon-FPm …

For c > 1, c / ∈ Z and χ a primitive character (mod q), we estimate the sum  x

We describe the bifurcation diagrams of plane-to-plane map-germs of corank 2 up to Aecodimension 4, and draw some new pictures. Two applications are presented: First, we study the affine differential geometry of crosscaps in 3-space by means of analyzing singularities of projections of the singular surface to the plane. Secondly, we give some new examples of generic two-dimensional bifurcation…

In general, observations are normally considered to refer to an epoch in time, however, observations take time. During this time span temporal variations of the observable alias the measurement. Similar phenomenon can be defined in the space domain as well: data treated to refer to a geographical location often contains integrated information of the surroundings. In each case the appropriate si…

The measure of non-compactness of operators between complex interpolation spaces is studied. An estimate of this measure, under the Calderón approximation condition, is proved. Examples of Banach couples satisfying the mentioned condition are provided. An estimate of the essential spectral radius of an operator under complex interpolation is also given.