Quasi-isometric groups with no common model geometry

A simple surface amalgam is the union of a finite collection of surfaces with precisely one boundary component each and which have their boundary curves identified. We prove if two fundamental groups of simple surface amalgams act properly and cocompactly by isometries on the same proper geodesic metric space, then the groups are commensurable. Consequently, there are infinitely many fundamental groups of simple surface amalgams that are quasi-isometric, but which do not act properly and cocompactly on the same proper geodesic metric space.Comment: v2: 19 pages, 6 figures; minor changes. To appear in Journal of the London Mathematical Societ

Hyperbolic groups that are not commensurably coHopfian

Sela proved every torsion-free one-ended hyperbolic group is coHopfian. We prove that there exist torsion-free one-ended hyperbolic groups that are not commensurably coHopfian. In particular, we show that the fundamental group of every simple surface amalgam is not commensurably coHopfian.Comment: v3: 14 pages, 4 figures; minor changes. To appear in International Mathematics Research Notice

How to recognize opportunities: Heterarchical search in a Wall Street trading room

Our task in this paper is to analyze the organization of trading in the era of quantitative finance. To do so, we conduct an ethnography of arbitrage, the trading strategy that best exemplifies finance in the wake of the quantitative revolution. In contrast to value and momentum investing, we argue, arbitrage involves an art of association - the construction of equivalence (comparability) of properties across different assets. In place of essential or relationa l characteristics, the peculiar valuation that takes place in arbitrage is based on an operation that makes something the measure of something else - associating securities to each other. The process of recognizing opportunities and the practices of making novel associations are shaped by the specific socio-spatial and socio-technical configurations of the trading room. Calculation is distributed across persons and instruments as the trading room organizes interaction among diverse principles of valuation.Arbitrage, trading, heterarchy

Resolving identities: Successive crises in a trading room after 9/11

How do organizations cope with extreme uncertainty? The existing literature is divided on this issue: some argue that organizations deal best with uncertainty in the environment by reproducing it in the organization, whereas others contend that the orga nization should be protected from the environment. In this paper we study the case of a Wall Street investment bank that lost its entire office and trading technology in the terrorist attack of September 11 th. The traders survived, but were forced to relocate to a makeshift trading room in New Jersey. During the six months the traders spent outside New York City, they had to deal with fears and insecurities inside the company as well as outside it: anxiety about additional attacks, questions of professional identity, doubts about the future of the firm, and ambiguities about the future re-location of the trading room. The firm overcame these uncertainties by protecting the traders’ identities and their ability to engage in sensemaking. The organization held together through a leadership style that managed ambiguities and created the conditions for new solutions to emerge.Organizational responsiveness, uncertainty, september 11th

Effects of self-consistent rest-ultraviolet colours in semi-empirical galaxy formation models

Connecting the observed rest-ultraviolet (UV) luminosities of high-$z$ galaxies to their intrinsic luminosities (and thus star formation rates) requires correcting for the presence of dust. We bypass a common dust-correction approach that uses empirical relationships between infrared (IR) emission and UV colours, and instead augment a semi-empirical model for galaxy formation with a simple -- but self-consistent -- dust model and use it to jointly fit high-$z$ rest-UV luminosity functions (LFs) and colour-magnitude relations ($M_{\mathrm{UV}}$-$\beta$). In doing so, we find that UV colours evolve with redshift (at fixed UV magnitude), as suggested by observations, even in cases without underlying evolution in dust production, destruction, absorption, or geometry. The observed evolution in our model arises due to the reduction in the mean stellar age and rise in specific star formation rates with increasing $z$. The UV extinction, $A_{\mathrm{UV}}$, evolves similarly with redshift, though we find a systematically shallower relation between $A_{\mathrm{UV}}$ and $M_{\mathrm{UV}}$ than that predicted by IRX-$\beta$ relationships derived from $z \sim 3$ galaxy samples. Finally, assuming that high $1600 \r{A}$ transmission ($\gtrsim 0.6$) is a reliable LAE indicator, modest scatter in the effective dust surface density of galaxies can explain the evolution both in $M_{\mathrm{UV}}$-$\beta$ and LAE fractions. These predictions are readily testable by deep surveys with the James Webb Space Telescope.Comment: 14+4 pages, 11+5 figures, accepted for publication in MNRA

Keck Spectroscopy of Faint 3 < z < 7 Lyman Break Galaxies: III. The Mean Ultraviolet Spectrum at z=4

We present and discuss the mean rest-frame ultraviolet spectrum for a sample of 81 Lyman Break Galaxies (LBGs) selected to be B-band dropouts with a mean redshift of z=3.9 and apparent magnitudes z_AB<26. Most of the individual spectra are drawn from our ongoing survey in the GOODS fields with the Keck DEIMOS spectrograph, and we have augmented our sample with published data taken with FORS2 on the VLT. In general we find similar trends in the spectral diagnostics to those found in the earlier, more extensive survey of LBGs at z=3 undertaken by Shapley et al (2003). Specifically, we find low-ionization absorption lines which trace the presence of neutral outflowing gas are weaker in galaxies with stronger Lyman-alpha emission, bluer UV spectral slopes, lower stellar masses, lower UV luminosities and smaller half-light radii. This is consistent with a physical picture whereby star formation drives outflows of neutral gas which scatters Lyman-alpha and gives rise to strong low-ionization absorption lines, while increasing the stellar mass, size, metallicity, and dust content of galaxies. Typical galaxies are thus expected to have stronger Lyman-alpha emission and weaker low-ionization absorption at earlier times (higher redshifts). Indeed, our mean spectrum at z=4 shows somewhat weaker low-ionization absorption lines than at z=3 and available data at higher redshift indicates a rapid decrease in low-ionization absorption strength with redshift. We argue that the reduced low-ionization absorption is likely caused by a decrease in the covering fraction and/or velocity range of outflowing neutral gas at earlier epochs. Our continuing survey will enable us to extend these diagnostics more reliably to higher redshift and determine the implications for the escape fraction of ionizing photons which governs the role of early galaxies in cosmic reionization. [Abridged]Comment: 17 pages, 12 figures, submitted to ApJ. Comments welcom

Keck Spectroscopy of Faint 3<z<7 Lyman Break Galaxies:- II. A High Fraction of Line Emitters at Redshift Six

As Lyman-alpha photons are scattered by neutral hydrogen, a change with redshift in the Lyman-alpha equivalent width distribution of distant galaxies offers a promising probe of the degree of ionization in the intergalactic medium and hence when cosmic reionization ended. This simple test is complicated by the fact that Lyman-alpha emission can also be affected by the evolving astrophysical details of the host galaxies. In the first paper in this series, we demonstrated both a luminosity and redshift dependent trend in the fraction of Lyman-alpha emitters seen within color-selected Lyman-break galaxies (LBGs) over the range 3<z<6; lower luminosity galaxies and those at higher redshift show an increased likelihood of strong emission. Here we present the results from much deeper 12.5 hour exposures with the Keck DEIMOS spectrograph focused primarily on LBGs at z~6 which enable us to confirm the redshift dependence of line emission more robustly and to higher redshift than was hitherto possible. We find 54+/-11% of faint z~6 LBGs show strong (W_0>25 A) emission, an increase of 1.6x from a similar sample observed at z~4. With a total sample of 74 z~6 LBGs, we determine the luminosity-dependent Lyman-alpha equivalent width distribution. Assuming continuity in these trends to the new population of z~7 sources located with the Hubble WFC3/IR camera, we predict that unless the neutral fraction rises in the intervening 200 Myr, the success rate for spectroscopic confirmation using Lyman-alpha emission should be high.Comment: 6 pages, 3 figures, submitted to ApJ

The [OIII]++Hβ\beta Equivalent Width Distribution at z≃\simeq7: Implications for the Contribution of Galaxies to Reionization

We quantify the distribution of [OIII]+H$\beta$ line strengths at z$\simeq$7 using a sample of 20 bright (M$_{\mathrm{UV}}$ $\lesssim$ $-$21) galaxies. We select these systems over wide-area fields (2.3 deg$^2$ total) using a new colour-selection which precisely selects galaxies at z$\simeq$6.63$-$6.83, a redshift range where blue Spitzer/IRAC [3.6]$-$[4.5] colours unambiguously indicate strong [OIII]$+$H$\beta$ emission. These 20 galaxies suggest a log-normal [OIII]$+$H$\beta$ EW distribution with median EW = 759$^{+112}_{-113}$ $\mathrm{\mathring{A}}$ and standard deviation = 0.26$^{+0.06}_{-0.05}$ dex. We find no evidence for strong variation in this EW distribution with UV luminosity. The typical [OIII]+H$\beta$ EW at z$\simeq$7 implied by our sample is considerably larger than that in massive star forming galaxies at z$\simeq$2, consistent with a shift toward larger average sSFR (4.4 Gyr$^{-1}$) and lower metallicities (0.16 Z$_\odot$). We also find evidence for the emergence of a population with yet more extreme nebular emission ([OIII]+H$\beta$ EW$>$1200 $\mathrm{\mathring{A}}$) that is rarely seen at lower redshifts. These objects have extremely large sSFR ($>$30 Gyr$^{-1}$), as would be expected for systems undergoing a burst or upturn in star formation. While this may be a short-lived phase, our results suggest that 20% of the z$\simeq$7 population has such extreme nebular emission, implying that galaxies likely undergo intense star formation episodes regularly at z$>$6. We argue that this population may be among the most effective ionizing agents in the reionization era, both in terms of photon production efficiency and escape fraction. We furthermore suggest that galaxies passing through this large sSFR phase are likely to be very efficient in forming bound star clusters.Comment: 20 pages, 11 figures. Accepted in MNRAS with minor revision

High-redshift galaxies and black holes in the eyes of JWST: a population synthesis model from infrared to X-rays

The first billion years of the Universe is a pivotal time: stars, black holes (BHs) and galaxies form and assemble, sowing the seeds of galaxies as we know them today. Detecting, identifying and understand- ing the first galaxies and BHs is one of the current observational and theoretical challenges in galaxy formation. In this paper we present a population synthesis model aimed at galaxies, BHs and Active Galactic Nuclei (AGNs) at high redshift. The model builds a population based on empirical relations. Galaxies are characterized by a spectral energy distribution determined by age and metallicity, and AGNs by a spectral energy distribution determined by BH mass and accretion rate. We validate the model against observational constraints, and then predict properties of galaxies and AGN in other wavelength and/or luminosity ranges, estimating the contamination of stellar populations (normal stars and high-mass X-ray binaries) for AGN searches from the infrared to X-rays, and vice-versa for galaxy searches. For high-redshift galaxies, with stellar ages < 1 Gyr, we find that disentangling stellar and AGN emission is challenging at restframe UV/optical wavelengths, while high-mass X-ray binaries become more important sources of confusion in X-rays. We propose a color-color selection in JWST bands to separate AGN vs star-dominated galaxies in photometric observations. We also esti- mate the AGN contribution, with respect to massive, hot, metal-poor stars, at driving high ionization lines, such as C IV and He II. Finally, we test the influence of the minimum BH mass and occupa- tion fraction of BHs in low mass galaxies on the restframe UV/near-IR and X-ray AGN luminosity function.Comment: Accepted for publication in the Astrophysical Journa