A new case of Shelah’s eventual categoricity conjecture is established: Theorem 1. LetK be an AEC with amalgamation. WriteH2 := i2i(2LS(K))+ + . Assume that K is H2-tame and K≥H2 has primes over sets of the form M∪{a}. If K is categorical in some λ > H2, then K is categorical in all λ′ ≥ H2. The result had previously been established when the stronger locality assumptions of full tameness an...

The main theorem of this paper states that if M is a closed orientable hyperbolic 3-manifold such that the rank of H1(M ;Z/2Z) is at least 11, then VolM > 3.08. The theorem depends on a purely topological result which can be viewed as an analogue of Dehn’s lemma for π1-injective singular surfaces of genus 2. The proof of the main theorem combines this topological result with several deep geomet...

In this talk I will describe the non-abelian Hodge theory of a non-compact curve. This was worked out by Simpson in the paper Harmonic Bundles on Non-Compact Curves, and as such almost everything I say here can be found in that paper in more detail. Let X be a smooth non-compact curve, with smooth completion j : X ↪→ X, and S = X \X a finite set of punctures. For simplicity, I’ll assume we have...

An extension of the idea of state tameness is presented in a dynamic framework. The proposed model for financial markets is rich enough to provide analytical tools that are mostly obtained in models that arise as the solution of SDEs with deterministic coefficients. In the presented model the augmentation by a shadow stock of the price evolution has a Markovian character. As in a previous paper...

T T T T T T T T T T T T T T T Abstract In this paper we continue an earlier study of ends non-compact manifolds. The over-arching goal is to investigate and obtain generalizations of Siebenmann's famous collaring theorem that may be applied to manifolds having non-stable fundamental group systems at infinity. In this paper we show that, for mani-folds with compact boundary, the condition of inw...

We show that any finitely generated metabelian group can be embedded in a metabelian group of type F3. The proof builds upon work of G. Baumslag [4], who independently with V. R. Remeslennikov [10] proved that any finitely generated metabelian group can be embedded in a finitely presented one. We also rely essentially on the Sigma theory of R. Bieri and R. Strebel [7], who introduced this geome...

Yak domestication represents an important episode in the early human occupation of the high-altitude Qinghai-Tibet Plateau (QTP). The precise timing of domestication is debated and little is known about the underlying genetic changes that occurred during the process. Here we investigate genome variation of wild and domestic yaks. We detect signals of selection in 209 genes of domestic yaks, sev...

Grossberg and VanDieren have started a program to develop a stability theory for tame classes (see [GrVa1]). We name some variants of tameness (Definitions 1.4 and 1.7) and prove the following. Theorem 0.1. Let K be an AEC with Löwenheim-Skolem number ≤ κ. Assume that K satisfies the amalgamation property and is κ-weakly tame and Galois-stable in κ. Then, K is Galois-stable in κ for all n < ω. ...

We introduce the notion of analytically and subanalytically tame measures. These are measures which behave well in the globally subanalytic context; they preserve tameness: integrals of globally subanalytic functions with parameters resp. analytic functions with parameters restricted to globally subanalytic compact sets are definable in an o-minimal structure. We consider the harmonic measure f...