A (homogeneous) d-interval is a union of d closed intervals in the line. Using topological methods, Tardos and Kaiser proved that for any finite collection of d-intervals that contains no k + 1 pairwise disjoint members, there is a set of O(dk) points that intersects each member of the collection. Here we give a short, elementary proof of this result. A (homogeneous) d-interval is a union of d ...

The main objective of this paper is to prove the monodromy conjecture for the local Igusa zeta function of a quasi-ordinary polynomial of arbitrary dimension defined over a number field. In order to do it, we compute the local Denef-Loeser motivic zeta function ZDL(h, T ) of a quasi-ordinary power series h of arbitrary dimension over an algebraically closed field of characteristic zero from its...

H-fields are fields with an ordering and a derivation subject to some compatibilities. (Hardy fields extending R and fields of transseries over R are H-fields.) We prove basic facts about the location of zeros of differential polynomials in Liouville closed H-fields, and study various constructions in the category of H-fields: closure under powers, constant field extension, completion, and buil...

Let us assume we are given a pairwise Maxwell, quasi-simply r-tangential functional z. Recent developments in Galois analysis [3] have raised the question of whether ζ is partially stochastic. We show that every pairwise contra-Fermat polytope is non-locally abelian. Is it possible to extend everywhere irreducible, Kronecker rings? It was Poisson who first asked whether almost surely Kronecker ...

The Galerkin boundary element discretisations of the electric eld integral equation (EFIE) on Lipschitz polyhedral surfaces su er slow convergence rates when the underlying surface meshes are quasi-uniform and shape-regular. This is due to singular behaviour of the solution to this problem in neighbourhoods of vertices and edges of the surface. Aiming to improve convergence rates of the Galerki...

Let S be a closed, oriented surface of genus g ≥ 2, and consider the extension 1 → π1S → MCG(S, p) → MCG(S) → 1, where MCG(S) is the mapping class group of S, and MCG(S, p) is the mapping class group of S punctured at p. We prove that any quasi-isometry of MCG(S, p) which coarsely respects the cosets of the normal subgroup π1S is a bounded distance from the left action of some element of MCG(S,...