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We prove that a closed negatively curved analytic Riemannian manifold that contains infinitely many totally geodesic hypersurfaces is isometric to an arithmetic hyperbolic manifold. Equivalently, any closed analytic Riemannian manifold with negative sectional curvature has only finitely many totally geodesic hypersurfaces, unless it has constant curvature., Comment: 30 pages, minor revisions

We discuss many surprising implications of a positive answer to a question raised in some cases by Greenberg in the $`70$s and more generally by Shalom in the early $2000$s. We refer to this positive answer as the Greenberg-Shalom hypothesis. This hypothesis then says that any infinite discrete subgroup of a semisimple Lie group with dense commensurator is a lattice in a product of some factors. For some applications it is natural to extend the hypothesis to cover semisimple algebraic groups over other fields as well.

We establish a Tukia-type theorem for uniform quasiconformal groups of a Carnot group. More generally we establish a fiber bundle version (or foliated version) of Tukia theorem for uniform quasiconformal groups of a nilpotent Lie group whose Lie algebra admits a diagonalizable derivation with positive eigenvalues. These results have applications to quasi-isometric rigidity of solvable groups [DFX]., Comment: 26 pages

In this paper we study uniform quasiconformal groups of Carnot-by-Carnot groups. We show that they can be conjugated into conformal groups provided the induced action on the space of distinct pairs is cocompact. Following the approach of Eskin-Fisher-Whyte these results have applications to quasi-isometric rigidity of certain solvable groups., Comment: 60 pages

Individual participant data (IPD) meta-analyses of randomised trials are considered a reliable way to assess participant-level treatment effect modifiers but may not make the best use of the available data. Traditionally, effect modifiers are explored one covariate at a time, which gives rise to the possibility that evidence of treatment-covariate interaction may be due to confounding from a different, related covariate. We aimed to evaluate current practice when estimating treatment-covariate interactions in IPD meta-analysis, specifically focusing on involvement of additional covariates in the models. We reviewed 100 IPD meta-analyses of randomised trials, published between 2015 and 2020, that assessed at least one treatment-covariate interaction. We identified four approaches to handling additional covariates: (1) Single interaction model (unadjusted): No additional covariates included (57/100 studies); (2) Single interaction model (adjusted): Adjustment for the main effect of at least one additional covariate (35/100); (3) Multiple interactions model: Adjustment for at least one two-way interaction between treatment and an additional covariate (3/100); and (4) Three-way interaction model: Three-way interaction formed between treatment, the additional covariate and the potential effect modifier (5/100). IPD is not being utilised to its fullest extent. In an exemplar dataset, we demonstrate how these approaches can lead to different conclusions. Researchers should adjust for additional covariates when estimating interactions in IPD meta-analysis providing they adjust their main effects, which is already widely recommended. Further, they should consider whether more complex approaches could provide better information on who might benefit most from treatments, improving patient choice and treatment policy and practice., Comment: 23 pages, 3 figures, 4 tables

The main result is a classification of smooth actions of $SL(n,{\bf R})$, $n \geq 3$, or connected groups locally isomorphic to it, on closed $n$-manifolds, extending a theorem of Uchida. We construct new exotic actions of $SL(n,{\bf Z})$ on the $n$-torus and connected sums of $n$-tori, and we formulate a conjectural classification of actions of lattices in $SL(n,{\bf R})$ on closed $n$-manifolds. We prove some results about invariant rigid geometric structures for $SL(n,{\bf R})$-actions., Comment: 29 pp.; In memory of Fuichi Uchida (1938--2021). Minor changes in second version

We give a new proof of the finiteness of maximal arithmetic reflection groups. Our proof is novel in that it makes no use of trace formulas or other tools from the theory of automorphic forms and instead relies on the arithmetic Margulis lemma of Fraczyk, Hurtado and Raimbault.

We study a question of Greenberg-Shalom concerning arithmeticity of discrete subgroups of semisimple Lie groups with dense commensurators. We answer this question positively for normal subgroups of lattices. This generalizes a result of the second author and T. Koberda for certain normal subgroups of arithmetic lattices in SO(n,1) and SU(n,1).

This article discusses two recent works by the author, one with Brown and Hurtado on Zimmer's conjecture and one with Bader, Miller and Stover on totally geodesic submanifolds of real and complex hyperbolic manifolds. The main purpose of juxtaposing these two very disparate sets of results in one article is to emphasize a common aspect: that the study of invariant and partially invariant measures outside the homogeneous setting is important to questions about rigidity in geometry and dynamics. I will also discuss some open questions including some that seem particularly compelling in light of this juxtaposition., Comment: Contribution to Proceedings of the ICM 2022

The Hadwiger-Nelson problem asks for the minimum number of colors, so that each point of the plane can be assigned a single color with the property that no two points unit-distance apart are identically colored. It is now known that the answer is $5$, $6$, or $7$, Here we consider the problem in the context of Minkowski planes, where the unit circle is a regular polygon with $8$, $10$, or $12$ vertices. We prove that in each of these cases, one also needs at least five colors., Comment: 19 pages, 14 figures

We establish finiteness of low-dimensional actions of lattices in higher-rank semisimple Lie groups and establish Zimmer's conjecture for many such groups. This builds on previous work of the authors handling the case of actions by cocompact lattices and of actions by $\Sl(n,\Z)$. While the results are not sharp in all cases, they do dramatically improve all known results. The key difficulty overcome in this paper concerns escape of mass when taking limits of sequences of measures. Due to a need to control Lyapunov exponents for unbounded cocycles when taking such limits, quantitative controls on the concentration of mass at infinity are need and novel techniques are introduced to avoid ``escape of Lyapunov exponent.", Comment: Only expository changes to emphasize novetly relative to our prior work on Zimmer's conjecture

For $n \ge 2$, we prove that a finite volume complex hyperbolic $n$-manifold containing infinitely many maximal properly immersed totally geodesic submanifolds of dimension at least two is arithmetic, paralleling our previous work for real hyperbolic manifolds. As in the real hyperbolic case, our primary result is a superrigidity theorem for certain representations of complex hyperbolic lattices. The proof requires developing new general tools not needed in the real hyperbolic case. Our main results also have a number of other applications. For example, we prove nonexistence of certain maps between complex hyperbolic manifolds, which is related to a question of Siu, that certain hyperbolic $3$-manifolds cannot be totally geodesic submanifolds of complex hyperbolic manifolds, and that arithmeticity of complex hyperbolic manifolds is detected purely by the topology of the underlying complex variety, which is related to a question of Margulis. Our results also provide some evidence for a conjecture of Klingler that is a broad generalization of the Zilber--Pink conjecture., Comment: 49 pages, 1 figure. Final version, to appear Inventiones

This essay points to many of the interesting ramifications of Margulis' arithmeticity theorem, the superrigidity theorem, and normal subgroup theorem. We provide some history and background, but the main goal is to point to interesting open questions that stem directly or indirectly from Margulis' work and it's antecedents., Comment: Survey article. Comments welcome

Let $\Gamma$ be a lattice in $\mathrm{SO}_0(n, 1)$. We prove that if the associated locally symmetric space contains infinitely many maximal totally geodesic subspaces of dimension at least $2$, then $\Gamma$ is arithmetic. This answers a question of Reid for hyperbolic $n$-manifolds and, independently, McMullen for hyperbolic $3$-manifolds. We prove these results by proving a superrigidity theorem for certain representations of such lattices. The proof of our superrigidity theorem uses results on equidistribution from homogeneous dynamics and our main result also admits a formulation in that language., Comment: Corrected proof of folklore Proposition 3.1 and filled in minor omission in the proof of Lemma 3.4

We present the relation between stellar specific angular momentum $j_*$, stellar mass $M_*$, and bulge-to-total light ratio $\beta$ for THINGS, CALIFA and Romanowsky \& Fall datasets, exploring the existence of a fundamental plane between these parameters as first suggested by Obreschkow \& Glazebrook. Our best-fit $M_*-j_*$ relation yields a slope of $\alpha = 1.03 \pm 0.11$ with a trivariate fit including $\beta$. When ignoring the effect of $\beta$, the exponent $\alpha = 0.56 \pm 0.06$ is consistent with $\alpha = 2/3$ predicted for dark matter halos. There is a linear $\beta - j_*/M_*$ relation for $\beta \lesssim 0.4$, exhibiting a general trend of increasing $\beta$ with decreasing $j_*/M_*$. Galaxies with $\beta \gtrsim 0.4$ have higher $j_*$ than predicted by the relation. Pseudobulge galaxies have preferentially lower $\beta$ for a given $j_*/M_*$ than galaxies that contain classical bulges. Pseudobulge galaxies follow a well-defined track in $\beta - j_*/M_*$ space, consistent with Obreschkow \& Glazebrook, while galaxies with classical bulges do not. These results are consistent with the hypothesis that while growth in either bulge type is linked to a decrease in $j_*/M_*$, the mechanisms that build pseudobulges seem to be less efficient at increasing bulge mass per decrease in specific angular momentum than those that build classical bulges., Comment: Accepted to ApJ. 10 pages, 3 figures, 2 tables

Behavioural differences may arise in the absence of genetic or environmental variation. Chaotic dynamics may influence behavioural development, and so this among-individual variation. We discuss methods and experimental designs to test this idea. Ultimately, nonlinear and chaotic behavioural development may explain much of natural variation., Comment: Version of manuscript following initial rejection and invitation to resubmit from journal. Further revised version now published, see: https://www.sciencedirect.com/science/article/pii/S0003347218300654

Deriving circular velocities of galaxies from stellar kinematics can provide an estimate of their total dynamical mass, provided a contribution from the velocity dispersion of the stars is taken into account. Molecular gas (e.g., CO) on the other hand, is a dynamically cold tracer and hence acts as an independent circular velocity estimate without needing such a correction. In this paper we test the underlying assumptions of three commonly used dynamical models, deriving circular velocities from stellar kinematics of 54 galaxies (S0-Sd) that have observations of both stellar kinematics from the CALIFA survey, and CO kinematics from the EDGE survey. We test the Asymmetric Drift Correction (ADC) method, as well as Jeans, and Schwarzschild models. The three methods each reproduce the CO circular velocity at 1Re to within 10%. All three methods show larger scatter (up to 20%) in the inner regions (R < 0.4Re) which may be due to an increasingly spherical mass distribution (which is not captured by the thin disk assumption in ADC), or non-constant stellar M/L ratios (for both the JAM and Schwarzschild models). This homogeneous analysis of stellar and gaseous kinematics validates that all three models can recover Mdyn at 1Re to better than 20%, but users should be mindful of scatter in the inner regions where some assumptions may break down., Comment: 22 pages, 18 figures, Accepted for publication in MNRAS

We show that large classes of non-arithmetic hyperbolic $n$-manifolds, including the hybrids introduced by Gromov and Piatetski-Shapiro and many of their generalizations, have only finitely many finite-volume immersed totally geodesic hypersurfaces. In higher codimension, we prove finiteness for geodesic submanifolds of dimension at least $2$ that are maximal, i.e., not properly contained in a proper geodesic submanifold of the ambient $n$-manifold. The proof is a mix of structure theory for arithmetic groups, dynamics, and geometry in negative curvature., Comment: v2. Improved writing, improved Theorem 1.3, other results unchanged. 31 pages, 9 figures. v1. 28 pages, 9 figures

Stars form in molecular complexes that are visible as giant clouds ($\sim 10^{5-6} \mathrm{M}_\odot$) in nearby galaxies and as giant clumps ($\sim 10^{8-9}\mathrm{M}_\odot$) in galaxies at redshifts $z\approx1$$-$$3$. Theoretical inferences on the origin and evolution of these complexes often require robust measurements of their characteristic size, which is hard to measure at limited resolution and often ill-defined due to overlap and quasi-fractal substructure. We show that maximum and luminosity-weighted sizes of clumps seen in star formation maps (e.g.\ H$\alpha$) can be recovered statistically using the two-point correlation function (2PCF), if an approximate stellar surface density map is taken as the normalizing random field. After clarifying the link between Gaussian clumps and the 2PCF analytically, we design a method for measuring the diameters of Gaussian clumps with realistic quasi-fractal substructure. This method is tested using mock images of clumpy disk galaxies at different spatial resolutions and perturbed by Gaussian white noise. We find that the 2PCF can recover the input clump scale at $\sim20\%$ accuracy, as long as this scale is larger than the spatial resolution. We apply this method to the local spiral galaxy NGC 5194, as well as to three clumpy turbulent galaxies from the DYNAMO-HST sample. In both cases, our statistical H$\alpha$-clump size measurements agree with previous measurements and with the estimated Jeans lengths. However, the new measurements are free from subjective choices when fitting individual clumps., Comment: Published in ApJ on 2017 August 9. 13 pages, 8 figures

This paper can be viewed as a sequel to the author's long survey on the Zimmer program \cite{F11} published in 2011. The sequel focuses on recent rapid progress on certain aspects of the program particularly concerning rigidity of Anosov actions and Zimmer's conjecture that there are no actions in low dimensions. Some emphasis is put on the surprising connections between these two different sets of developments and also on the key connections and ideas for future research that arise from these works taken together., Comment: This is an expository article that will appear in Bob Zimmer's selected papers. Version to appear. I may eventually update this further for more recent developments

We report an integral-field spectroscopic (IFS) observation of a gravitationally lensed spiral galaxy A1689B11 at redshift $z=2.54$. It is the most ancient spiral galaxy discovered to date and the second kinematically confirmed spiral at $z\gtrsim2$. Thanks to gravitational lensing, this is also by far the deepest IFS observation with the highest spatial resolution ($\sim$ 400 pc) on a spiral galaxy at a cosmic time when the Hubble sequence is about to emerge. After correcting for a lensing magnification of 7.2 $\pm$ 0.8, this primitive spiral disk has an intrinsic star formation rate of 22 $\pm$ 2 $M_{\odot}$ yr$^{-1}$, a stellar mass of 10$^{9.8 \pm 0.3}$$M_{\odot}$ and a half-light radius of $r_{1/2}=2.6 \pm 0.7$ kpc, typical of a main-sequence star-forming (SF) galaxy at $z\sim2$. However, the H\alpha\ kinematics show a surprisingly tranquil velocity field with an ordered rotation ($V_{\rm c}$ = 200 $\pm$ 12 km/s) and uniformly small velocity dispersions ($V_{\rm \sigma, mean}$ = 23 $\pm$ 4 km/s and $V_{\rm \sigma, outer-disk}$ = 15 $\pm$ 2 km/s). The low gas velocity dispersion is similar to local spiral galaxies and is consistent with the classic density wave theory where spiral arms form in dynamically cold and thin disks. We speculate that A1689B11 belongs to a population of rare spiral galaxies at $z\gtrsim2$ that mark the formation epoch of thin disks. Future observations with JWST will greatly increase the sample of these rare galaxies and unveil the earliest onset of spiral arms., Comment: 18 pages, 13 figures, 1 table; accepted for publication in ApJ

We study the geometry of warped cones over free, minimal isometric group actions and related constructions of expander graphs. We prove a rigidity theorem for the coarse geometry of such warped cones: Namely, if a group has no abelian factors, then two such warped cones are quasi-isometric if and only if the actions are finite covers of conjugate actions. As a consequence, we produce continuous families of non-quasi-isometric expanders and superexpanders. The proof relies on the use of coarse topology for warped cones, such as a computation of their coarse fundamental groups., Comment: 48 pages, 3 figures

We prove Zimmer's conjecture for $C^2$ actions by finite-index subgroups of $\mathrm{SL}(m,\mathbb{Z})$ provided $m>3$. The method utilizes many ingredients from our earlier proof of the conjecture for actions by cocompact lattices in $\mathrm{SL}(m,\mathbb{R})$ but new ideas are needed to overcome the lack of compactness of the space $(G \times M)/\Gamma$ (admitting the induced $G$-action). Non-compactness allows both measures and Lyapunov exponents to escape to infinity under averaging and a number of algebraic, geometric, and dynamical tools are used control this escape. New ideas are provided by the work of Lubotzky, Mozes, and Raghunathan on the structure of nonuniform lattices and, in particular, of $\mathrm{SL}(m,\mathbb{Z})$ providing a geometric decomposition of the cusp into rank one directions, whose geometry is more easily controlled. The proof also makes use of a precise quantitative form of non-divergence of unipotent orbits by Kleinbock and Margulis, and an extension by de la Salle of strong property (T) to representations of nonuniform lattices., Comment: v3: Final version, to appear Inventiones. v2: Minor revision. One reference added. Submitted version

We present molecular gas mass estimates for a sample of 13 local galaxies whose kinematic and star forming properties closely resemble those observed in $z\approx 1.5$ main-sequence galaxies. Plateau de Bure observations of the CO[1-0] emission line and Herschel Space Observatory observations of the dust emission both suggest molecular gas mass fractions of ~20%. Moreover, dust emission modeling finds $T_{dust}<$30K, suggesting a cold dust distribution compared to their high infrared luminosity. The gas mass estimates argue that $z\sim$0.1 DYNAMO galaxies not only share similar kinematic properties with high-z disks, but they are also similarly rich in molecular material. Pairing the gas mass fractions with existing kinematics reveals a linear relationship between $f_{gas}$ and $\sigma$/$v_{c}$, consistent with predictions from stability theory of a self-gravitating disk. It thus follows that high gas velocity dispersions are a natural consequence of large gas fractions. We also find that the systems with lowest depletion times ($\sim$0.5 Gyr) have the highest ratios of $\sigma$/$v_{c}$ and more pronounced clumps, even at the same high molecular gas fraction., Comment: 10 pages, 6 figures. Accepted to ApJ

We use the ZFIRE survey (http://zfire.swinburne.edu.au) to investigate the high mass slope of the initial mass function (IMF) for a mass-complete (log10(M$_*$/M$_\odot$)~9.3) sample of 102 star-forming galaxies at z~2 using their H$\alpha$ equivalent widths (H$\alpha$-EW) and rest-frame optical colours. We compare dust-corrected H$\alpha$-EW distributions with predictions of star-formation histories (SFH) from PEGASE.2 and Starburst99 synthetic stellar population models. We find an excess of high H$\alpha$-EW galaxies that are up to 0.3--0.5 dex above the model-predicted Salpeter IMF locus and the H$\alpha$-EW distribution is much broader (10--500 \AA) than can easily be explained by a simple monotonic SFH with a standard Salpeter-slope IMF. Though this discrepancy is somewhat alleviated when it is assumed that there is no relative attenuation difference between stars and nebular lines, the result is robust against observational biases, and no single IMF (i.e. non-Salpeter slope) can reproduce the data. We show using both spectral stacking and Monte Carlo simulations that starbursts cannot explain the EW distribution. We investigate other physical mechanisms including models with variations in stellar rotation, binary star evolution, metallicity, and the IMF upper-mass cutoff. IMF variations and/or highly rotating extreme metal poor stars (Z~0.1Z$_\odot$) with binary interactions are the most plausible explanations for our data. If the IMF varies, then the highest H$\alpha$-EWs would require very shallow slopes ($\Gamma$>-1.0) with no one slope able to reproduce the data. Thus, the IMF would have to vary stochastically. We conclude that the stellar populations at z~2 show distinct differences from local populations and there is no simple physical model to explain the large variation in H$\alpha$-EWs at z~2., Comment: Accepted to MNRAS. 43 pages, 27 Figures. Survey website: http://zfire.swinburne.edu.au/

In this letter we study the mean sizes of Halpha clumps in turbulent disk galaxies relative to kinematics, gas fractions, and Toomre Q. We use 100~pc resolution HST images, IFU kinematics, and gas fractions of a sample of rare, nearby turbulent disks with properties closely matched to z~1.5-2 main-sequence galaxies (the DYNAMO sample). We find linear correlations of normalized mean clump sizes with both the gas fraction and the velocity dispersion-to-rotation velocity ratio of the host galaxy. We show that these correlations are consistent with predictions derived from a model of instabilities in a self-gravitating disk (the so-called "violent disk instability model"). We also observe, using a two-fluid model for Q, a correlation between the size of clumps and self-gravity driven unstable regions. These results are most consistent with the hypothesis that massive star forming clumps in turbulent disks are the result of instabilities in self-gravitating gas-rich disks, and therefore provide a direct connection between resolved clump sizes and this in situ mechanism., Comment: Accepted to Apj Letters

Networks describe a range of social, biological and technical phenomena. An important property of a network is its degree correlation or assortativity, describing how nodes in the network associate based on their number of connections. Social networks are typically thought to be distinct from other networks in being assortative (possessing positive degree correlations); well-connected individuals associate with other well-connected individuals, and poorly-connected individuals associate with each other. We review the evidence for this in the literature and find that, while social networks are more assortative than non-social networks, only when they are built using group-based methods do they tend to be positively assortative. Non-social networks tend to be disassortative. We go on to show that connecting individuals due to shared membership of a group, a commonly used method, biases towards assortativity unless a large enough number of censuses of the network are taken. We present a number of solutions to overcoming this bias by drawing on advances in sociological and biological fields. Adoption of these methods across all fields can greatly enhance our understanding of social networks and networks in general., Comment: 27 pages, including two figures, a table and references

Dust attenuation in galaxies has been extensively studied nearby, however, there are still many unknowns regarding attenuation in distant galaxies. We contribute to this effort using observations of star-forming galaxies in the redshift range z = 0.05-0.15 from the DYNAMO survey. Highly star-forming DYNAMO galaxies share many similar attributes to clumpy, star-forming galaxies at high redshift. Considering integrated Sloan Digital Sky Survey observations, trends between attenuation and other galaxy properties for DYNAMO galaxies are well matched to star-forming galaxies at high redshift. Integrated gas attenuations of DYNAMO galaxies are 0.2-2.0 mags in the V-band, and the ratio of stellar E(B-V) and gas E(B-V) is 0.78-0.08 (compared to 0.44 at low redshift). Four highly star-forming DYNAMO galaxies were observed at H-alpha using the Hubble Space Telescope and at Pa-alpha using integral field spectroscopy at Keck. The latter achieve similar resolution (~0.8-1 kpc) to our HST imaging using adaptive optics, providing resolved observations of gas attenuations of these galaxies on sub-kpc scales. We find < 1.0 mag of variation in attenuation (at H-alpha) from clump to clump, with no evidence of highly attenuated star formation. Attenuations are in the range 0.3-2.2 mags in the V band, consistent with attenuations of low redshift star-forming galaxies. The small spatial variation on attenuation suggests that a majority of the star-formation activity in these four galaxies occurs in relatively unobscured regions and, thus, star-formation is well characterised by our H-alpha observations., Comment: 16 pages, 16 figures, accepted for publication in MNRAS

The gas accretion and star-formation histories of galaxies like the Milky Way remain an outstanding problem in astrophysics. Observations show that 8 billion years ago, the progenitors to Milky Way-mass galaxies were forming stars 30 times faster than today and predicted to be rich in molecular gas, in contrast with low present-day gas fractions ($<$10%). Here we show detections of molecular gas from the CO(J=3-2) emission (rest-frame 345.8 GHz) in galaxies at redshifts z=1.2-1.3, selected to have the stellar mass and star-formation rate of the progenitors of today's Milky Way-mass galaxies. The CO emission reveals large molecular gas masses, comparable to or exceeding the galaxy stellar masses, and implying most of the baryons are in cold gas, not stars. The galaxies' total luminosities from star formation and CO luminosities yield long gas-consumption timescales. Compared to local spiral galaxies, the star-formation efficiency, estimated from the ratio of total IR luminosity to CO emission,} has remained nearly constant since redshift z=1.2, despite the order of magnitude decrease in gas fraction, consistent with results for other galaxies at this epoch. Therefore the physical processes that determine the rate at which gas cools to form stars in distant galaxies appear to be similar to that in local galaxies., Comment: To appear in Nature Astronomy, 9 pages

We present $\sim$100 pc resolution Hubble Space Telescope H$\alpha$ images of 10 galaxies from the DYnamics of Newly-Assembled Massive Objects (DYNAMO) survey of low-$z$ turbulent disk galaxies, and use these to undertake the first detailed systematic study of the effects of resolution and clump clustering on observations of clumps in turbulent disks. In the DYNAMO-{\em HST} sample we measure clump diameters spanning the range $d_{clump} \sim 100-800$~pc, and individual clump star formation rates as high as $\sim5$~M$_{\odot}$~yr$^{-1}$. DYNAMO clumps have very high SFR surface densities, $\Sigma_{SFR}\sim 15$~M$_{\odot}$~yr$^{-1}$~kpc$^{-2}$, $\sim100\times$ higher than in H{\sc ii} regions of nearby spirals. Indeed, SFR surface density provides a simple dividing line between massive star forming clumps and local star forming regions, where massive star forming clumps have $\Sigma_{SFR}> 0.5$~M$_{\odot}$~yr$^{-1}$~kpc$^{-2}$. When degraded to match the observations of galaxies in $z\sim 1-3$ surveys, DYNAMO galaxies are similar in morphology and measured clump properties to clumpy galaxies observed in the high-$z$ Universe. Emission peaks in the simulated high-redshift maps typically correspond to multiple clumps in full resolution images. This clustering of clumps systematically increases the apparent size and SFR of clumps in 1~kpc resolution maps, and decreases the measured SFR surface density of clumps by as much as a factor of 20$\times$. From these results we can infer that clump clustering is likely to strongly effect the measured properties of clumps in high-$z$ galaxies, which commonly have kiloparsec scale resolution., Comment: Accepted to MNRAS

We prove several cases of Zimmer's conjecture for actions of higher-rank cocompact lattices on low dimensional manifolds. For example, if $\Gamma$ is a cocompact lattice in $\mathrm{Sl}(n, \mathbb R)$, $M$ is a compact manifold, and $\omega$ a volume form on $M$ we show that any homomorphism $\rho\colon \Gamma \rightarrow \mathrm{Diff}(M)$ has finite image if the dimension of $M$ is less than $n-1$ and that any homomorphism $\rho\colon \Gamma \rightarrow \mathrm{Diff}(M,\omega)$ has finite image if the dimension of $M$ is less than $n$. The key step in the proof is to show any such action has uniform subexponential growth of derivatives. This is established using ideas from the smooth ergodic theory of higher-rank abelian groups, structure theory of semisimple groups and results from homogeneous dynamics. Having established uniform subexponential growth of derivatives, we apply Lafforgue's strong property (T) to establish the existence of an invariant Riemannian metric., Comment: Revised and improved for referee comments

We present an overview and the first data release of ZFIRE, a spectroscopic redshift survey of star-forming galaxies that utilizes the MOSFIRE instrument on Keck-I to study galaxy properties in rich environments at $1.5

It is well known that surface groups admit free and proper actions on finite products of infinite valence trees. In this note, we address the question of whether there can be a free and proper action on a finite product of bounded valence trees. We provide some obstructions and an arithmetic criterion for existence. The bulk of the paper is devoted to an approach to verifying the arithmetic criterion by studying the character variety of certain surface groups over fields of positive characteristic. The methods may be useful for attempting to determine when groups admit good linear representations in other contexts.

Let $G$ and $G'$ be simple Lie groups of equal real rank and real rank at least $2$. Let $\Gamma

In this review our aim is to summarize the observed properties of pseudobulges and classical bulges. We utilize an empirical approach to studying the properties of bulges in disk galaxies, and restrict our analysis to statistical proper- ties. A clear bimodality is observed in a number of properties including morphology, structural properties, star formation, gas content & stellar population, and kinematics. As well as summarizing known methods to identify pseudobulges and classical bulges we also show new results, including absorption line indices that can be used to identify different bulge types. We conclude by summarizing those properties that isolate pseudobulges from classical bulges. Our intention is to describe a practical, easy to use, list of criteria for identifying bulge types., Comment: Accepted for publication in Springer Review on Bulges

We measure the stellar specific angular momentum jstar=Jstar/Mstar in four nearby (z~0.1) disk galaxies that have stellar masses Mstar near the break M* of the galaxy mass function, but look like typical star-forming disks at z~2 in terms of their low stability (Q~1), clumpiness, high ionized gas dispersion (40-50 km/s), high molecular gas fraction (20-30%) and rapid star formation (~20 Msun/yr). Combining high-resolution (Keck-OSIRIS) and large-radius (Gemini-GMOS) spectroscopic maps, only available at low z, we discover that these targets have about three times less stellar angular momentum than typical local spiral galaxies of equal stellar mass and bulge fraction. Theoretical considerations show that this deficiency in angular momentum is the main cause of their low stability, while the high gas fraction plays a complementary role. Interestingly, the low jstar values of our targets are similar to those expected in the M*-population at higher z from the approximate theoretical scaling jstar~(1+z)^(-1/2) at fixed Mstar. This suggests that a change in angular momentum, driven by cosmic expansion, is the main cause for the remarkable difference between clumpy M*-disks at high z (which likely evolve into early-type galaxies) and mass-matched local spirals., Comment: 4 Figures (including one interactive 3D figure), 1 Table

Nitrogen is the dominant impurity in the majority of natural and synthetic diamonds, and the family of nitrogen vacancy-type ($\mathrm{N_{n}V}$) defects are crucial in our understanding of defect dynamics in these diamonds. A significant gap is the lack of positive identification of $\mathrm{N_{2}V}^{-}$, the dominant charge state of $\mathrm{N_{2}V}$, in diamond that contains a significant concentration of electron donors. In this paper we employ isotopically-enriched diamond to identify the EPR spectrum associated with $^{15}\mathrm{N_{2}V}^{-}$ and use the derived spin Hamiltonian parameters to identify $^{14}\mathrm{N_{2}V}^{-}$ in a natural isotopic abundance sample. The electronic wavefunction of the $\mathrm{N_{2}V^{-}}$ ground state and previous lack of identification is discussed. The $\mathrm{N_{2}V}^{-}$ EPR spectrum intensity is shown to correlate with H2 optical absorption over an order of magnitude in concentration.

The Hobby-Eberly Telescope is used to measure the velocity dispersion profile of the nearest prototypical cD galaxy, NGC 6166 in cluster Abell 2199. We also present surface photometry from many telescopes. We confirm the defining feature of a cD -- a halo of stars that fills the cluster center and that is controlled by cluster gravity, not by the central galaxy. The velocity dispersion of NGC 6166 rises from 300 km/s at the center to 865 +- 58 km/s at 100 arcsec radius in the halo. This shows for the first time that the dispersion rises all the way to the cluster value, 819 +- 32 km/s. We find that the main body of NGC 6166 moves at 206 +- 39 km/s with respect to the cluster velocity, whereas the velocity of the cD halo is 70 km/s closer to the cluster velocity. These results support our picture that cD halos consist of stars that are stripped from cluster galaxies. But we do not confirm the view that cD halos are an extra, low-surface-brightness component that is distinct from the main body of a normal giant elliptical. Instead, all of the brightness profile of NGC 6166 outside its core is described to +- 0.037 mag/arcsec**2 by a single Sersic function with index n ~ 8.3. The cD halo is not recognizable from photometry alone. This blurs the distinction between cDs and similar-n core-boxy-nonrotating ellipticals. Both may have halos made largely via minor mergers and the accumulation of debris. However, the cD halo of NGC 6166 is as enhanced in alpha elements as the main body. Quenching of star formation in <~1 Gyr happened even to the galaxies that contributed the cD halo., Comment: 25 pages, 20 postscript figures, 3 tables, LaTeX, submitted to ApJ

We prove a rigidity theorem that shows that, under many circumstances, quasi-isometric embeddings of equal rank, higher rank symmetric spaces are close to isometric embeddings. We also produce some surprising examples of quasi-isometric embeddings of higher rank symmetric spaces. In particular, we produce embeddings of $SL(n,\mathbb R)$ into $Sp(2(n-1),\mathbb R)$ when no isometric embeddings exist. A key ingredient in our proofs of rigidity results is a direct generalization of the Mostow-Morse Lemma in higher rank. Typically this lemma is replaced by the quasi-flat theorem which says that maximal quasi-flat is within bounded distance of a finite union of flats. We improve this by showing that the quasi-flat is in fact flat off of a subset of codimension $2$., Comment: Exposition improved, outlines of proofs added to introduction. Typos corrected, references added. Also some discussion of the reducible case added

In this letter we report the discovery of CO fluxes, suggesting very high gas fractions in three disk galaxies seen in the nearby Universe (z ~ 0.1). These galaxies were investigated as part of the DYnamics of Newly Assembled Massive Objects (DYNAMO) survey. High-resolution Hubble Space Telescope imaging of these objects reveals the presence of large star forming clumps in the bodies of the galaxies, while spatially resolved spectroscopy of redshifted Halpha reveals the presence of high dispersion rotating disks. The internal dynamical state of these galaxies resembles that of disk systems seen at much higher redshifts (1 < z < 3). Using CO(1-0) observations made with the Plateau de Bure Interferometer, we find gas fractions of 20-30% and depletion times of tdep ~ 0.5 Gyr (assuming a Milky Way-like CO conversion factor). These properties are unlike those expected for low- redshift galaxies of comparable specific star formation rate, but they are normal for their high-z counterparts. DYNAMO galaxies break the degeneracy between gas fraction and redshift, and we show that the depletion time per specific star formation rate for galaxies is closely tied to gas fraction, independent of redshift. We also show that the gas dynamics of two of our local targets corresponds to those expected from unstable disks, again resembling the dynamics of high-z disks. These results provide evidence that DYNAMO galaxies are local analogues to the clumpy, turbulent disks, which are often found at high redshift., Comment: Accepted to ApJ Letters

We study the spatially resolved stellar kinematics of two star-forming galaxies at z = 0.1 from the larger DYnamics of Newly Assembled Massive Objects (DYNAMO) sample. These galaxies, which have been characterized by high levels of star formation and large ionized gas velocity dispersions, are considered possible analogs to high-redshift clumpy disks. They were observed using the GMOS instrument in integral field spectroscopy (IFS) mode at the Gemini Observatory with high spectral resolution (R=5400, equivalent to 24 km/s at the observed wavelengths) and 6 hour exposure times in order to measure the resolved stellar kinematics via absorption lines. We also obtain higher-quality emission line kinematics than previous observations. The spatial resolution (1.2 kpc) is sufficient to show that the ionized gas in these galaxies (as traced by H-beta emission) is morphologically irregular, forming multiple giant clumps while stellar continuum light is smooth and well described by an exponential profile. Clumpy gas morphologies observed in IFS data are confirmed by complementary narrow band H-alpha imaging from the Hubble Space Telescope. Morphological differences between the stars and ionized gas are not reflected dynamically as stellar kinematics are found the be closely coupled to the kinematics of the ionized gas: both components are smoothly rotating with large velocity dispersions (~40 km/s) suggesting that the high gas dispersions are not primarily driven by star-formation feedback. In addition, the stellar population ages of these galaxies are estimated to be quite young (60-500 Myr). The large velocity dispersions measured for these young stars suggest that we are seeing the formation of thick disks and/or stellar bulges in support of recent models which produce these from clumpy galaxies at high redshift., Comment: 18 pages, 11 figures, 4 tables. Accepted for publication, MNRAS

'Normal' galaxies observed at z>6, when the Universe was <1 billion years old, thus far show no evidence of the cold dust that accompanies star formation in the local Universe, where the dust-to-gas mass ratio is 1%. A prototypical example is 'Himiko' (z=6.6), which a mere 840 Myr after the Big Bang is forming stars at a rate of 30-100 Msun/yr, yielding a mass assembly time M^{star}/SFR 150x10^6 yr. Himiko is estimated to have a low fraction (2-3% of the Solar value) of elements heavier than helium (metallicity), and although its gas mass cannot be asserted at this time its dust-to-stellar mass ratio is constrained to be <0.05%. The local galaxy I Zw 18, with a metallicity 4% solar and forming stars less rapidly than Himiko but still vigorously for its mass (M^{star}/SFR 1.6x10^9 yr), is also very dust deficient and perhaps one of the best analogues of primitive galaxies accessible to detailed study. Here we report observations of dust emission from I Zw 18 from which we determine its dust mass to be 450-1800 Msun, yielding a dust-to-stellar mass ratio \approx 10^{-6}-10^{-5} and a dust-to-gas mass ratio 3.2-13x10^{-6}. If I Zw 18 is a reasonable analog of Himiko, then Himiko's dust mass is \approx 50,000 Msun, a factor of 100 below the current upper limit. These numbers are considerably uncertain, but if most high-z galaxies are more like Himiko than like the quasar host SDSS J114816.64+525150.3, then the prospects for detecting the gas and dust in them are much poorer than hitherto anticipated., Comment: 13 pages, 4 figures, accepted for publication in Nature

We investigate the correlation between CO and HI emission in 18 nearby galaxies from the CARMA Survey Toward IR-Bright Nearby Galaxies (STING) at sub-kpc and kpc scales. Our sample, spanning a wide range in stellar mass and metallicity, reveals evidence for a metallicity dependence of the HI column density measured in regions exhibiting CO emission. Such a dependence is predicted by the equilibrium model of McKee & Krumholz, which balances H_2 formation and dissociation. The observed HI column density is often smaller than predicted by the model, an effect we attribute to unresolved clumping, although values close to the model prediction are also seen. We do not observe HI column densities much larger than predicted, as might be expected were there a diffuse HI component that did not contribute to H_2 shielding. We also find that the H_2 column density inferred from CO correlates strongly with the stellar surface density, suggesting that the local supply of molecular gas is tightly regulated by the stellar disk., Comment: 6 pages, to appear in ApJ Letters

The under-abundance of very massive galaxies in the universe is frequently attributed to the effect of galactic winds. Although ionized galactic winds are readily observable most of the expelled mass is likely in cooler atomic and molecular phases. Expanding molecular shells observed in starburst systems such as NGC 253 and M 82 may facilitate the entrainment of molecular gas in the wind. While shell properties are well constrained, determining the amount of outflowing gas emerging from such shells and the connection between this gas and the ionized wind requires spatial resolution <100 pc coupled with sensitivity to a wide range of spatial scales, hitherto not available. Here we report observations of NGC 253, a nearby starburst galaxy (D~3.4 Mpc) known to possess a wind, which trace the cool molecular wind at 50 pc resolution. At this resolution the extraplanar molecular gas closely tracks the H{\alpha} filaments, and it appears connected to molecular expanding shells located in the starburst region. These observations allow us to directly measure the molecular outflow rate to be > 3 Msun/yr and likely ~9 Msun/yr. This implies a ratio of mass-outflow rate to star formation rate of at least {\eta}~1-3, establishing the importance of the starburst-driven wind in limiting the star formation activity and the final stellar content., Comment: Appearing in the July 25 2013 issue of Nature

The Lie algebra version of the Krull-Schmidt Theorem is formulated and proved. This leads to a method for constructing the automorphisms of a direct sum of Lie algebras from the automorphisms of its indecomposable components. For finite-dimensional Lie algebras, there is a well-known algorithm for finding such components, so the theorem considerably simplifies the problem of classifying the automorphism groups. We illustrate this by classifying the automorphisms of all indecomposable real Lie algebras of dimension five or less. Our results are presented very concisely, in tabular form., Comment: (Published version: references corrected)

We present the survey design, data reduction, and spectral fitting pipeline for the VIRUS-P Exploration of Nearby Galaxies (VENGA). VENGA is an integral field spectroscopic survey, which maps the disks of 30 nearby spiral galaxies. Targets span a wide range in Hubble type, star formation activity, morphology, and inclination. The VENGA data-cubes have 5.6'' FWHM spatial resolution, ~5A FWHM spectral resolution, sample the 3600A-6800A range, and cover large areas typically sampling galaxies out to ~0.7 R_25. These data-cubes can be used to produce 2D maps of the star formation rate, dust extinction, electron density, stellar population parameters, the kinematics and chemical abundances of both stars and ionized gas, and other physical quantities derived from the fitting of the stellar spectrum and the measurement of nebular emission lines. To exemplify our methods and the quality of the data, we present the VENGA data-cube on the face-on Sc galaxy NGC 628 (a.k.a. M 74). The VENGA observations of NGC 628 are described, as well as the construction of the data-cube, our spectral fitting method, and the fitting of the stellar and ionized gas velocity fields. We also propose a new method to measure the inclination of nearly face-on systems based on the matching of the stellar and gas rotation curves using asymmetric drift corrections. VENGA will measure relevant physical parameters across different environments within these galaxies, allowing a series of studies on star formation, structure assembly, stellar populations, chemical evolution, galactic feedback, nuclear activity, and the properties of the interstellar medium in massive disk galaxies., Comment: Accepted for publication in AJ, 25 pages, 18 figures, 6 tables

We measure the radial profile of the 12CO(1-0) to H_2 conversion factor (Xco) in NGC 628. The H\alpha emission from the VENGA integral field spectroscopy is used to map the star formation rate surface density (\Sigma_{SFR}). We estimate the molecular gas surface density (\Sigma_{H2}) from \Sigma_{SFR} by inverting the molecular star formation law (SFL), and compare it to the CO intensity to measure Xco. We study the impact of systematic uncertainties by changing the slope of the SFL, using different SFR tracers (H\alpha vs. far-UV plus 24\mu m), and CO maps from different telescopes (single-dish and interferometers). The observed Xco profile is robust against these systematics, drops by a factor of 2 from R~7 kpc to the center of the galaxy, and is well fit by a gradient \Delta log(Xco)=0.06\pm0.02 dex kpc^-1. We study how changes in Xco follow changes in metallicity, gas density, and ionization parameter. Theoretical models show that the gradient in Xco can be explained by a combination of decreasing metallicity, and decreasing \Sigma_{H2} with radius. Photoelectric heating from the local UV radiation field appears to contribute to the decrease of Xco in higher density regions. Our results show that galactic environment plays an important role at setting the physical conditions in star forming regions, in particular the chemistry of carbon in molecular complexes, and the radiative transfer of CO emission. We caution against adopting a single Xco value when large changes in gas surface density or metallicity are present., Comment: 10 pages, 7 figures, accepted for publication in The Astrophysical Journal

In this paper we present gas density, star formation rate, stellar masses, and bulge disk decompositions for a sample of 60 galaxies. Our sample is the combined sample of BIMA SONG, CARMA STING, and PdBI NUGA surveys. We study the effect of using CO-to-H_2 conversion factors that depend on the CO surface brightness, and also that of correcting star formation rates for diffuse emission from old stellar populations. We estimate that star formation rates in bulges are typically lower by 20% when correcting for diffuse emission. We find that over half of the galaxies in our sample have molecular gas surface density >100 M_sun pc^-2. We find a trend between gas density of bulges and bulge Sersic index; bulges with lower Sersic index have higher gas density. Those bulges with low Sersic index (pseudobulges) have gas fractions that are similar to that of disks. We also find that there is a strong correlation between bulges with the highest gas surface density and the galaxy being barred. However, we also find that classical bulges with low gas surface density can be barred as well. Our results suggest that understanding the connection between the central surface density of gas in disk galaxies and the presence of bars should also take into account the total gas content of the galaxy and/or bulge Sersic index. Indeed, we find that high bulge Sersic index is the best predictor of low gas density inside the bulge (not barredness of the disk). Finally, we show that when using the corrected star formation rates and gas densities, the correlation between star formation rate surface density and gas surface density of bulges is similar to that of disks., Comment: Accepted for publication in ApJ

We compare the central mass distribution of galaxies simulated with three different models of the interstellar medium (ISM) with increasing complexity: primordial (H+He) cooling down to 10^4K, additional cooling via metal lines and to lower temperatures, and molecular hydrogen (H_2) with shielding of atomic and molecular hydrogen, in addition to metal line cooling. In order to analyze the effect of these models, we follow the evolution of four field galaxies with V_peak < 120 km/s to a redshift of zero using high-resolution Smoothed Particle Hydrodynamic simulations in a fully cosmological LCDM context. The spiral galaxies produced in simulations with either primordial cooling or H_2 physics have realistic, rising rotation curves. In contrast, the simulations with metal line cooling and otherwise similar feedback and star formation produced galaxies with the peaked rotation curves typical of most previous LCDM simulations of spiral galaxies. The less-massive bulges and non-peaked rotation curves in the galaxies simulated with primordial cooling or H_2 are linked to changes in the angular momentum distribution of the baryons. These galaxies had smaller amounts of low-angular momentum baryons because of increased gas loss from stellar feedback. When there is only primordial cooling, the star forming gas is hotter and the feedback-heated gas cools more slowly than when metal line cooling is included and so requires less energy to be expelled. When H_2 is included, the accompanying shielding produces large amounts of clumpy, cold gas where H_2 forms. Star formation in clumpy gas results in more concentrated supernova feedback and greater efficiency of mass loss. The higher feedback efficiency causes a decrease of low-angular momentum material. (abridged), Comment: 19 pages, 14 figures, submitted to MNRAS

We give a necessary and sufficient condition for a locally compact group to be isomorphic to a closed cocompact subgroup in the isometry group of a Diestel-Leader graph. As a consequence of this condition, we see that every cocompact lattice in the isometry group of a Diestel-Leader graph admits a transitive, proper action on some other Diestel-Leader graph. We also give some examples of lattices that are not virtually lamplighters. This implies the class of discrete groups commensurable to lamplighter groups is not closed under quasi-isometries and, combined with work of Eskin, Fisher and Whyte, gives a characterization of their quasi-isometry class., Comment: 11 pages, no figure