• Publications
  • Influence
3-Manifold Groups
We summarize properties of 3-manifold groups, with a particular focus on the consequences of the recent results of Ian Agol, Jeremy Kahn, Vladimir Markovic and Dani Wise.
Ideal membership in polynomial rings over the integers
We will reproduce a proof, using Hermann's classical method, in Section 3 below. Note that the computable character of this bound reduces the question of whether fo G (fi,..., fn) for given fj G F[X]Expand
Finiteness Theorems in Stochastic Integer Programming
We study Graver test sets for families of linear multistage stochastic integer programs with a varying number of scenarios. Expand
Finite generation of symmetric ideals
Let be a commutative Noetherian ring, and let be the polynomial ring in an infinite collection of indeterminates over . Let be the group of permutations of . The group acts on in a natural way, andExpand
Vapnik-Chervonenkis Density in Some Theories without the Independence Property, II
We recast the problem of calculating Vapnik-Chervonenkis (VC) density into one of counting types, and thereby calculate bounds (often optimal) on the VC density for some weakly o-minimal, weakly quasi-o-Minimal, and $P$-minality theories. Expand
Orderings of monomial ideals
We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of monomial ideals isExpand
Asymptotic Differential Algebra and Model Theory of Transseries
We develop here the algebra of the differential field of transseries and of related valued differential fields. This book contains in particular our recently obtained decisive positive results on theExpand
3-manifold groups are virtually residually p
Given a prime $p$, a group is called residually $p$ if the intersection of its $p$-power index normal subgroups is trivial. A group is called virtually residually $p$ if it has a finite indexExpand
Vapnik-Chervonenkis Density in some Theories without the Independence Property, II
We study the Vapnik-Chervonenkis (VC) density of denable families in certain stable rst-order theories. In particular we obtain uniform bounds on VC density of denable families in nite U-rankExpand
Definable versions of theorems by Kirszbraun and Helly
Kirszbraun's Theorem states that every Lipschitz map S ! R n , where S R m , has an extension to a Lipschitz map R m ! R n with the same Lipschitz constant. Its proof relies on Helly's Theorem: everyExpand