Totally geodesic surfaces in twist knot complements

In this article, we give explicit examples of infinitely many non-commensurable (non-arithmetic) hyperbolic $3$-manifolds admitting exactly $k$ totally geodesic surfaces for any positive integer $k$, answering a question of Bader, Fisher, Miller and Stover. The construction comes from a family of twist knot complements and their dihedral covers. The case $k=1$ arises from the uniqueness of an immersed totally geodesic thrice-punctured sphere, answering a question of Reid. Applying the proof techniques of the main result, we explicitly construct non-elementary maximal Fuchsian subgroups of infinite covolume within twist knot groups, and we also show that no twist knot complement with odd prime half twists is right-angled in the sense of Champanerkar, Kofman, and Purcell

Impermissibility of Impersonal Harm: Impersonal Harm, Social Values, and Genetic Enhancement

https://openworks.mdanderson.org/sumexp22/1110/thumbnail.jp

Families of four-dimensional integrable systems with S1S^1-symmetries

The aim of this paper is to give new insights about families of integrable systems lifting a Hamiltonian $S^1$-space. Specifically, we study one-parameter families $(M^4,\omega,F_t=(J,H_t))_{0 \leq t \leq 1}$ of systems with a fixed Hamiltonian $S^1$-space $(M,\omega,J)$ and which are semitoric for certain values of the parameter $t$, with a focus on such families in which one singular point undergoes a Hamiltonian-Hopf bifurcation (also called nodal trade in the context of semitoric systems, and more generally almost toric fibrations). Beyond semitoric systems, we also study families containing hypersemitoric systems, and we investigate the local theory of a nodal trade. Building on and generalizing the ideas of a previous paper, we show how such families can be used to find explicit semitoric systems with certain desired invariants (bundled in the marked semitoric polygon). This allows us to make progress on the semitoric minimal model program by understanding and coming up with explicit systems for each strictly minimal type (i.e. those not admitting any toric or semitoric type blowdown). In order to obtain these systems, we develop strategies for constructing and understanding explicit examples of semitoric (and hypersemitoric) systems in general. One strategy we make use of is to start from a well-understood system (such as a toric system) and to explicitly induce Hamiltonian-Hopf bifurcations to produce focus-focus singular points. This is an expanded version of the technique used in the aforementioned previous paper, in order to apply it to semitoric systems which include non-trivial isotropy spheres in the underlying $S^1$-space (i.e. $\mathbb{Z}_k$-spheres), which occurs in several of the strictly minimal systems. In particular, we give an explicit one-parameter family of systems on $\mathbb{CP}^2$ which transitions between being of toric type, semitoric type, and hypersemitoric type depending on the value of the parameter. We study this system at each stage, computing the marked semitoric polygon of the semitoric system and determining several properties of the hypersemitoric system, including the existence of a unique flap and two parabolic orbits. Furthermore, we study the transitions between these stages. We also come up with new explicit semitoric systems on all Hirzebruch surfaces which, together with the previous systems and the systems already contained in the literature, gives an explicit model for every type of strictly minimal system. Moreover, we show how to obtain every strictly minimal system by applying sequences of alternating toric type blowups and blowdowns to simple explicit systems. In particular, we obtain that every strictly minimal semitoric system is part of a family $(M,\omega,F_t=(J,H_t))$ which is semitoric for all but a finite number of values of $t$, called a semitoric family.Comment: 145 pages, 53 figures. Comments welcome

First year student expectations: Results from a university-wide student survey

Although much has been written on the first-year experience of students at higher education institutions, less attention has been directed to the expectations of students when they enter an institution for the first time. This paper provides additional insights into the expectations of students at an Australian university and highlights areas in which students’ expectations may not necessarily align with the realities of common university practices. By providing opportunities for students to articulate their expectations, staff are able to use the responses for a constructive dialogue and work towards a more positive alignment between perceived expectations and levels of student satisfaction with their experience.Geoffrey Crisp, Edward Palmer, Deborah Turnbull, Ted Nettelbeck, Lynn Ward, Amanda LeCouteur, Aspa Sarris, Peter Strelan, and Luke Schneide

Beyond aspect: will be -ing and shall be -ing

This article discusses the synchronic status and diachronic development of will be -ing and shall be -ing (as in I’ll be leaving at noon).2 Although available since at least Middle English, the constructions did not establish a significant foothold in standard English until the twentieth century. Both types are also more prevalent in British English (BrE) than American English (AmE). We argue that in present-day usage will/shall be -ing are aspectually underspecified: instances that clearly construe a situation as future-in-progress are in the minority. Similarly, although volition-neutrality has been identified as a key feature of will/shall be -ing, it is important to take account of other, generally richer meanings and associations, notably ‘future-as-matter-of-course’ (Leech 2004), ‘already-decided future’ (Huddleston & Pullum et al. 2002) and non-agentivity. Like volition-neutrality, these characteristics appear to be relevant not only in contemporary use, but also in their historical expansion. We show that the construction has evolved from progressive aspect towards more subjectivised evidential meaning

Effects of fire on the hydrology, biogeochemistry, and ecology of peatland river systems

Peatlands are found around the world and cover ~3.4% of the Earth’s surface. In the UK, peatlands cover 17.2% or ~1.58 Mha of the land surface and occur mainly in upland areas covering the headwaters of most major British rivers. However, large areas are now subject to prescribed vegetation burning despite policy guidance that recommends a strong presumption against burning deep blanket peat. Wildfires occur sporadically but are forecast to increase in frequency in the future. This paper provides a synthesis of current knowledge about how UK peatland-dominated river catchments respond to fires caused by prescribed vegetation burning and uncontrolled wildfire. We provide insight into the effects of fire on the hydrology, biogeochemistry, and biota of peatland river ecosystems, and the peatland-soil-driven controls on these effects at the catchment-scale. Burning increases the depth to water table and water-table variability, although some small-scale studies indicate shallower water table in some places. More work is needed on fire effects on peatland river flow, but recent results suggest a complex response with smaller flow peaks for burned systems associated with most rainfall events, but enhanced peaks compared to unburned systems for the top quintile of rainfall events with the largest total rain. Evidence from biogeochemical studies suggests that fire leads to increased dissolved organic C concentrations in rivers. River biota responses primarily include significant reductions in the density of grazing mayflies but increases among detritivores including Chironomidae and Baetis mayflies. We provide a conceptual synthesis that links the main responses of terrestrial and aquatic systems to fire, and we summarize some major research gaps that should be prioritized to inform future policy around peatland management

The influence of slope and peatland vegetation type on riverine dissolved organic carbon and water colour at different scales

Peatlands are important sources of fluvial carbon. Previous research has shown that riverine dissolved organic carbon (DOC) concentrations are largely controlled by soil type. However, there has been little work to establish the controls of riverine DOC within blanket peatlands that have not undergone major disturbance from drainage or burning. A total of 119 peatland catchments were sampled for riverine DOC and water colour across three drainage basins during six repeated sampling campaigns. The topographic characteristics of each catchment were determined from digital elevation models. The dominant vegetation cover was mapped using 0.5 m resolution colour infrared aerial images, with ground-truthed validation revealing 82 % accuracy. Forward and backward stepwise regression modelling showed that mean slope was a strong (and negative) determinant of DOC and water colour in blanket peatland river waters. There was a weak role for plant functional type in determining DOC and water colour. At the basin scale, there were major differences between the models depending on the basin. The dominance of topographic predictors of DOC found in our study, combined with a weaker role of vegetation type, paves the way for developing improved planning tools for water companies operating in peatland catchments. Using topographic data and aerial imagery it will be possible to predict which tributaries will typically yield lower DOC concentrations and which are therefore more suitable and cost-effective as raw water intakes