The augmented marking complex of a surface

We build an augmentation of the Masur-Minsky marking complex by Groves-Manning combinatorial horoballs to obtain a graph we call the augmented marking complex, $\mathcal{AM}(S)$. Adapting work of Masur-Minsky, we prove that $\mathcal{AM}(S)$ is quasiisometric to Teichm\"uller space with the Teichm\"uller metric. A similar construction was independently discovered by Eskin-Masur-Rafi. We also completely integrate the Masur-Minsky hierarchy machinery to $\mathcal{AM}(S)$ to build flexible families of uniform quasigeodesics in Teichm\"uller space. As an application, we give a new proof of Rafi's distance formula for the Teichm\"uller metric.Comment: 30 pages; significantly rewritten to strengthen main construction

Convex cocompactness and stability in mapping class groups

We introduce a strong notion of quasiconvexity in finitely generated groups, which we call stability. Stability agrees with quasiconvexity in hyperbolic groups and is preserved under quasi-isometry for finitely generated groups. We show that the stable subgroups of mapping class groups are precisely the convex cocompact subgroups. This generalizes a well-known result of Behrstock and is related to questions asked by Farb-Mosher and Farb.Comment: 15 pages, 1 figur

Recent PHENIX Results on Open Heavy Flavor

Throughout the history of the RHIC physics program, questions concerning the dynamics of heavy quarks have generated much experimental and theoretical investigation. A major focus of the PHENIX experiment is the measurement of these quarks through their semi-leptonic decay channels at mid and forward rapidity. Heavy quark measurements in $p+p$ collisions give information on the production of heavy flavor, without complications from medium effects. New measurements in $d+$Au and Cu+Cu indicate surprising cold nuclear matter effects on these quarks at midrapidity, and provide a new baseline for interpretation of the observed suppression in Au+Au collisions. When considered all together, these measurements present a detailed study of nuclear matter across a wide range of system size and temperature. Here we present preliminary PHENIX measurements of non-photonic electron spectra and their centrality dependence in $d$+Au and Cu+Cu, and discuss their implications on the current understanding of parton energy loss in the nuclear medium.Comment: 4 pages, 3 figures, to appear in the proceedings of Quark Matter 201