Morse Boundaries of Proper Geodesic Metric Spaces

We introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with rays that identify the "hyperbolic directions" in that space. This boundary is a quasi-isometry invariant and thus produces a well-defined boundary for any finitely generated group. In the case of a proper $\mathrm{CAT}(0)$ space this boundary is the contracting boundary of Charney and Sultan and in the case of a proper Gromov hyperbolic space this boundary is the Gromov boundary. We prove three results about the Morse boundary of Teichm\"uller space. First, we show that the Morse boundary of the mapping class group of a surface is homeomorphic to the Morse boundary of the Teichm\"uller space of that surface. Second, using a result of Leininger and Schleimer, we show that Morse boundaries of Teichm\"uller space can contain spheres of arbitrarily high dimension. Finally, we show that there is an injective continuous map of the Morse boundary of Teichm\"uller space into the Thurston compactification of Teichm\"uller space by projective measured foliations.Comment: Corrected some proofs and slightly reorganized with comments from referee. To appear in Groups, Geometry, and Dynamic

Searching for Hyperbolicity

This is an expository paper, based on by a talk given at the AWM Research Symposium 2017. It is intended as a gentle introduction to geometric group theory with a focus on the notion of hyperbolicity, a theme that has inspired the field from its inception to current-day research

An embedding of the Morse boundary in the Martin boundary

We construct a one-to-one continuous map from the Morse boundary of a hierarchically hyperbolic group to its Martin boundary. This construction is based on deviation inequalities generalizing Ancona's work on hyperbolic groups. This provides a possibly new metrizable topology on the Morse boundary of such groups. We also prove that the Morse boundary has measure 0 with respect to the harmonic measure unless the group is hyperbolic

Spontaneous dehydrocoupling in peri-substituted phosphine-borane adducts

This work was financially supported by the EPSRC and COST action CM1302 SIPs.Bis(borane) adducts Acenap(PiPr2·BH3)(PRH·BH3) (Acenap = acenaphthene-5,6-diyl; 4a, R = Ph; 4b, R = ferrocenyl, Fc; 4c, R = H) were synthesised by the reaction of excess H3B·SMe2 with either phosphino-phosphonium salts [Acenap(PiPr2)(PR)]+Cl− (1a, R = Ph; 1b, R = Fc), or bis(phosphine) Acenap(PiPr2)(PH2) (3). Bis(borane) adducts 4a–c were found to undergo dihydrogen elimination at room temperature, this spontaneous catalyst-free phosphine-borane dehydrocoupling yields BH2 bridged species Acenap(PiPr2)(µ-BH2)(PR·BH3) (5a, R = Ph; 5b, R = Fc; 5c, R = H). Thermolysis of 5c results in loss of the terminal borane moiety to afford Acenap(PiPr2)(µ-BH2)(PH) (14). Single crystal X-ray structures of 3, 4b and 5a–c are reported.Publisher PDFPeer reviewe

Mechanism of Cu-catalyzed iododeboronation : a description of ligand-enabled transmetalation, disproportionation, and turnover in Cu-mediated oxidative coupling reactions

Funding: Biotechnology and Biological Sciences Research Council - BB/R013780/; Engineering and Physical Sciences Research Council - EP/R025754/1, EP/W007517/1, EP/S027165/1; Leverhulme Trust - RF-2022-014.We report a combined experimental and computational study of the mechanism of the Cu-catalyzed arylboronic acid iododeboronation reaction. A combination of structural and density functional theory (DFT) analyses has allowed determination of the identity of the reaction precatalyst with insight into each step of the catalytic cycle. Key findings include a rationale for ligand (phen) stoichiometry related to key turnover events─the ligand facilitates transmetalation via H-bonding to an organoboron boronate generated in situ and phen loss/gain is integral to the key oxidative events. These data provide a framework for understanding ligand effects on these key mechanistic processes, which underpin several classes of Cu-mediated oxidative coupling reactions.Publisher PDFPeer reviewe

Fast Radio Burst Tomography of the Unseen Universe

The discovery of Fast Radio Bursts (FRBs) at cosmological distances has opened a powerful window on otherwise unseen matter in the Universe. In the 2020s, observations of $>10^{4}$ FRBs will assess the baryon contents and physical conditions in the hot/diffuse circumgalactic, intracluster, and intergalactic medium, and test extant compact-object dark matter models.Comment: Science white paper submitted to the Astro2020 Decadal Survey. 15 pages, 3 color figure

Testing the Dark Matter Annihilation Model for the WMAP Haze

Analyses have found a "haze" of anomalous microwave emission surrounding the Galactic Center in the WMAP sky maps. A recent study using Fermi data detected a similar haze in the gamma-ray. Several studies have modeled these hazes as radiation from the leptonic byproducts of dark matter annihilations, and arguably no convincing astrophysical alternative has been suggested. We discuss the characteristics of astrophysical cosmic ray sources that could potentially explain this microwave and gamma-ray emission. The most promising astrophysical scenarios involve cosmic ray sources that are clustered such that many fall within ~1 kpc of the Galactic Center. For example, we show that several hundred Galactic Center supernovae in the last million years plus a diffusion-hardened electron spectrum may be consistent with present constraints on this emission. Alternatively, it could be due to a burst of activity probably associated with Sagittarius A* occurring ~1 Myr ago and producing >10^51 erg in cosmic ray electrons. Different models predict different trends for the spectral index of the microwave and gamma-ray spectrum as a function of angle from the Galactic Center that should be robust to cosmic ray propagation uncertainties. In particular, if the haze is from dark matter annihilations, it should have a very hard microwave and gamma-ray spectrum for which the spectral shape does not change significantly with angle, which we argue would be difficult to achieve with any astrophysical mechanism. Observations with the Planck and Fermi satellites can distinguish between viable haze models using these signatures.Comment: 15 pages, 7 figures, accepted to MNRA

Extending gravitational wave burst searches with pulsar timing arrays

Pulsar timing arrays (PTAs) are being used to search for very low frequency gravitational waves. A gravitational wave signal appears in pulsar timing residuals through two components: one independent of and one dependent on the pulsar's distance, called the 'Earth term' (ET) and 'pulsar term' (PT), respectively. The signal of a burst (or transient) gravitational wave source in pulsars' residuals will in general have the Earth and pulsar terms separated by times of the order of the time of flight from the pulsar to the Earth. Therefore, both terms are not observable over a realistic observation span, but the ETs observed in many pulsars should be correlated. We show that pairs (or more) of pulsars can be aligned in such a way that the PTs caused by a source at certain sky locations can arrive at Earth within a time window short enough to be captured during a realistic observation span. We find that for the pulsars within the International Pulsar Timing Array (IPTA) ~67 per cent of the sky produces such alignments for pulsars terms separated by less than 10 years. We compare estimates of the source event rate that would be required to observe one signal in the IPTA if searching for the correlated ETs, or in searching via the PTs, and find that event rates would need to be about two orders of magnitude higher to observe an event with the PTs than the ETs. We also find that an array of hundreds of thousands of pulsars would be required to achieve similar numbers of observable events in PT or ET searches. This disfavours PTs being used for all-sky searches, but they could potentially be used target specific sources and be complementary to ET only searches.Comment: version accepted for MNRA

Prospects of observing continuous gravitational waves from known pulsars

Several past searches for gravitational waves from a selection of known pulsars have been performed with data from the science runs of the Laser Inferometer Gravitational-wave Observatory (LIGO) gravitational wave detectors. So far these have lead to no detection, but upper limits on the gravitational wave amplitudes have been set. Here we study our intrinsic ability to detect, and estimate the gravitational wave amplitude for non-accreting pulsars. Using spin-down limits on emission as a guide we examine amplitudes that would be required to observe known pulsars with future detectors (Advanced LIGO, Advanced Virgo and the Einstein Telescope), assuming that they are triaxial stars emitting at precisely twice the known rotation frequency. Maximum allowed amplitudes depend on the stars' equation of state (e.g. a normal neutron star, a quark star, a hybrid star) and the theoretical mass quadrupoles that they can sustain. We study what range of quadrupoles, and therefore equations of state, would be consistent with being able to detect these sources. For globular cluster pulsars, with spin-downs masked by accelerations within the cluster, we examine what spin-down values gravitational wave observations would be able to set. For all pulsars we also alternatively examine what internal magnetic fields they would need to sustain observable ellipticities.Comment: version to be published in Monthly Notices of the Royal Astronomical Societ