Abstract:
Nucleic acid amplification tests are sensitive for identifying Mycobacterium tuberculosis in populations with positive sputum smears for acid-fast bacilli, but less sensitive in sputum-smear-negative populations. Few studies have evaluated the clinical impact of these tests in low-income countries with high burdens of TB and HIV.

Abstract:
We describe typical degenerations of quadratic differentials thus describing ``generic cusps'' of the moduli space of meromorphic quadratic differentials with at most simple poles. The part of the boundary of the moduli space which does not arise from ``generic'' degenerations is often negligible in problems involving information on compactification of the moduli space. However, even for a typical degeneration one may have several short loops on the Riemann surface which shrink simultaneously. We explain this phenomenon, describe all rigid configurations of short loops, present a detailed description of analogs of desingularized stable curves arising here, and show how one can reconstruct a Riemann surface endowed with a quadratic differential which is close to a ``cusp'' by the corresponding point at the principal boundary.

Abstract:
We construct an example of a quadratic differential whose vertical foliation is uniquely ergodic and such that the Teichmuller geodesic determined by the quadratic differential diverges in the moduli space of Riemann surfaces.

Abstract:
It is well-known that on any Veech surface, the dynamics in any minimal direction is uniquely ergodic. In this paper it is shown that for any genus 2 translation surface which is not a Veech surface there are uncountably many minimal but not uniquely ergodic directions.

Abstract:
We analyze the coarse geometry of the Weil-Petersson metric on Teichm\"uller space, focusing on applications to its synthetic geometry (in particular the behavior of geodesics). We settle the question of the strong relative hyperbolicity of the Weil-Petersson metric via consideration of its coarse quasi-isometric model, the "pants graph." We show that in dimension~3 the pants graph is strongly relatively hyperbolic with respect to naturally defined product regions and show any quasi-flat lies a bounded distance from a single product. For all higher dimensions there is no non-trivial collection of subsets with respect to which it strongly relatively hyperbolic; this extends a theorem of [BDM] in dimension 6 and higher into the intermediate range (it is hyperbolic if and only if the dimension is 1 or 2 [BF]). Stability and relative stability of quasi-geodesics in dimensions up through 3 provide for a strong understanding of the behavior of geodesics and a complete description of the CAT(0)-boundary of the Weil-Petersson metric via curve-hierarchies and their associated "boundary laminations."

Abstract:
We give a distance estimate for the metric on the disk complex and show that it is Gromov hyperbolic. As another application of our techniques, we find an algorithm which computes the Hempel distance of a Heegaard splitting, up to an error depending only on the genus.

Abstract:
We prove that every Weil-Petersson isometry of the Teichmuller space T(g,n) is induced by an element of the extended mapping class group; here 3g-3+n > 1 and (g,n) is not (1,2). Our method follows Ivanov's proof of the Royden's analogous theorem for the Teichmuller metric: we study the action of an isometry on the frontier of the metric completion of the Teichmuller space, and show that the isometry then induces an automorphism on the relevant complex of curves. Some synthetic geometry of the Weil-Petersson metric completes the proof.

Abstract:
Let $S$ be a closed, oriented surface with a finite (possibly empty) set of points removed. In this paper we relate two important but disparate topics in the study of the moduli space $\M(S)$ of Riemann surfaces: Teichm\"{u}ller geometry and the Deligne-Mumford compactification. We reconstruct the Deligne-Mumford compactification (as a metric stratified space) purely from the intrinsic metric geometry of $\M(S)$ endowed with the Teichm\"{u}ller metric. We do this by first classifying (globally) geodesic rays in $\M(S)$ and determining precisely how pairs of rays asymptote. We construct an "iterated EDM ray space" functor, which is defined on a quite general class of metric spaces. We then prove that this functor applied to $\M(S)$ produces the Deligne-Mumford compactification.

Abstract:
We study the asymptotic geometry of Teichmueller geodesic rays. We show that when the transverse measures to the vertical foliations of the quadratic differentials determining two different rays are topologically equivalent, but are not absolutely continuous with respect to each other, then the rays diverge in Teichmueller space.