Congruences between Hilbert modular forms: constructing ordinary lifts

Under mild hypotheses, we prove that if F is a totally real field, k is the algebraic closure of the finite field with l elements and r : G_F --> GL_2(k) is irreducible and modular, then there is a finite solvable totally real extension F'/F such that r|_{G_F'} has a modular lift which is ordinary at each place dividing l. We deduce a similar result for r itself, under the assumption that at places v|l the representation r|_{G_F_v} is reducible. This allows us to deduce improvements to results in the literature on modularity lifting theorems for potentially Barsotti-Tate representations and the Buzzard-Diamond-Jarvis conjecture. The proof makes use of a novel lifting technique, going via rank 4 unitary groups.Comment: 48 page

What happens when interviewers ask repeated questions in forensic interviews with children alleging abuse?

This study was designed to explore 1) the ways in which interviewers refocus alleged victims of abuse on their previous responses and 2) how children responded when they were refocused on their previous responses. Transcripts of 37 forensic interviews conducted by British police officers trained using the best practices spelled out in the Memorandum of Good Practice were examined. The instances in which interviewers asked repeated questions were isolated and coded into categories with respect to the reasons why interviewers needed to ask the repeated question (i.e., there was no apparent reason, to challenge a child’s response, clarification, no answer the first time the question was asked, digression, or compound question). The children’s responses to the repeated questions were further categorised into mutually exclusive categories (i.e., elaboration, repetition, contradiction, or no answer). On average interviewers asked children 8 repeated questions per interview. Most of the time interviewers asked repeated questions to challenge a previous response (62%), but they were also sometimes asked for no apparent reason (20%). Children repeated previous responses or elaborated on a previous response 81% of the time and contradicted themselves 7% of the time when re-asked the same question. We conclude that children did not appear unduly pressured to change their answers, and, more importantly, did not contradict themselves when interviewers attempted to refocus them on particular responses

The Sato-Tate conjecture for Hilbert modular forms

We prove the Sato-Tate conjecture for Hilbert modular forms. More precisely, we prove the natural generalisation of the Sato-Tate conjecture for regular algebraic cuspidal automorphic representations of \GL_2(\A_F), $F$ a totally real field, which are not of CM type. The argument is based on the potential automorphy techniques developed by Taylor et. al., but makes use of automorphy lifting theorems over ramified fields, together with a 'topological' argument with local deformation rings. In particular, we give a new proof of the conjecture for modular forms, which does not make use of potential automorphy theorems for non-ordinary $n$-dimensional Galois representations.Comment: 59 pages. Essentially final version, to appear in Journal of the AMS. This version does not incorporate any minor changes (e.g. typographical changes) made in proo

Cultivating Lifelong Donors: Stewardship and the Fundraising Pyramid

This handbook helps nonprofits build long-term giving programs that span the entire supporter lifecycle, from engagement through the end of life. It highlights strategies for engaging new supporters online, investigates the characteristics of loyal donors, examines the importance of developing personal relationships with transitional giving prospects, and discusses donor cultivation

Local-global compatibility for l=p, II

We prove the compatibility at places dividing l of the local and global Langlands correspondences for the l-adic Galois representations associated to regular algebraic essentially (conjugate) self-dual cuspidal automorphic representations of GL_n over an imaginary CM or totally real field. We prove this compatibility up to semisimplification in all cases, and up to Frobenius semisimplification in the case of Shin-regular weight.Comment: 13 page

The Rate of Short-Duration Gamma-Ray Bursts in the Local Universe

Following the faint gamma-ray burst, GRB 170817A, coincident with a gravitational wave-detected binary neutron star merger at $d\sim40$ Mpc, we consider the constraints on a local population of faint short duration GRBs (defined here broadly as $T_{90}<4$ s). We review proposed low-redshift short-GRBs and consider statistical limits on a $d\lessapprox200$ Mpc population using Swift/Burst Alert Telescope (BAT), Fermi/Gamma-ray Burst Monitor (GBM), and Compton Gamma-Ray Observatory (CGRO) Burst and Transient Source Experiment (BATSE) GRBs. Swift/BAT short-GRBs give an upper limit for the all-sky rate of $<4$ y$^{-1}$ at $d<200$ Mpc, corresponding to $<5$% of SGRBs. Cross-correlation of selected CGRO/BATSE and Fermi/GBM GRBs with $d<100$ Mpc galaxy positions returns a weaker constraint of $\lessapprox12\ {\rm y^{-1}}$. A separate search for correlations due to SGR giant flares in nearby ($d<11$ Mpc) galaxies finds an upper limit of $<3\ {\rm y^{-1}}$. Our analysis suggests that GRB 170817A-like events are likely to be rare in existing SGRB catalogues. The best candidate for an analogue remains GRB 050906, where the Swift/BAT location was consistent with the galaxy IC0327 at $d\approx132$ Mpc. If binary neutron star merger rates are at the high end of current estimates, then our results imply that at most a few percent will be accompanied by detectable gamma-ray flashes in the forthcoming LIGO/Virgo science runs.Comment: 16 pages, 4 figures, 1 table. Published in Galaxies as part of the Special Issue, "Observations and Theory of Short GRBs at the Dawn of the Gravitational Wave Era

Repetition of contaminating question types when children and youths with intellectual disabilities are interviewed

Background The present study examined the effects of repeating questions in interviews investigating the possible sexual abuse of children and youths who had a variety of intellectual disabilities. We predicted that the repetition of option-posing and suggestive questions would lead the suspected victims to change their responses, making it difficult to understand what actually happened. Inconsistency can be a key factor when assessing the reliability of witnesses. Materials Case files and transcripts of investigative interviews with 33 children and youths who had a variety of intellectual disabilities were obtained from prosecutors in Sweden. The interviews involved 25 females and 9 males whose chronological ages were between 5.4 and 23.7 years when interviewed (M = 13.2 years). Results Six per cent of the questions were repeated at least once. The repetition of focused questions raised doubts about the reports because the interviewees changed their answers 40% of the time. Conclusions Regardless of the witnesses' abilities, it is important to obtain reports that are as accurate and complete as possible in investigative interviews. Because this was a field study, we did not know which responses were accurate, but repetitions of potentially contaminating questions frequently led the interviewees to contradict their earlier answers. This means that the interviewers' behaviour diminished the usefulness of the witnesses' testimony