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3-Manifold Groups

- Matthias Aschenbrenner, Stefan Friedl, H. Wilton
- Mathematics
- 1 May 2012

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

- Matthias Aschenbrenner
- Mathematics
- 12 May 2003

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

- Matthias Aschenbrenner, R. Hemmecke
- Mathematics, Computer Science
- Found. Comput. Math.
- 3 February 2005

TLDR

Finite generation of symmetric ideals

- Matthias Aschenbrenner, C. Hillar
- Mathematics
- 23 November 2004

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, and… Expand

Vapnik-Chervonenkis Density in Some Theories without the Independence Property, II

- Matthias Aschenbrenner, Alfred Dolich, D. Haskell, D. Macpherson, S. Starchenko
- Mathematics, Computer Science
- Notre Dame J. Formal Log.
- 26 September 2011

TLDR

Orderings of monomial ideals

- Matthias Aschenbrenner, W. Pong
- Mathematics
- 27 May 2003

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 is… Expand

Asymptotic Differential Algebra and Model Theory of Transseries

- Matthias Aschenbrenner, L. Dries, J. V. D. Hoeven
- Mathematics
- 9 September 2015

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 the… Expand

3-manifold groups are virtually residually p

- Matthias Aschenbrenner, Stefan Friedl
- Mathematics
- 21 April 2010

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 index… Expand

Vapnik-Chervonenkis Density in some Theories without the Independence Property, II

- Matthias Aschenbrenner, Alfred Dolich, D. Haskell, D. Macpherson, S. Starchenko
- Mathematics
- 22 December 2015

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-rank… Expand

Definable versions of theorems by Kirszbraun and Helly

- Matthias Aschenbrenner, A. Fischer
- Mathematics
- 5 June 2009

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: every… Expand

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