A computation of modular forms of weight one and small level

We report on a computation of holomorphic cuspidal modular forms of weight one and small level (currently level at most 1500) and classification of them according to the projective image of their attached Artin representations. The data we have gathered, such as Fourier expansions and projective images of Hecke newforms and dimensions of space of forms, is available in both Magma and Sage readable formats on a webpage created in support of this project

Effect of long-time, elevated-temperature exposures to vacuum and lithium on the properties of a tantalum alloy, T-111

The effect of long-term, elevated-temperature vacuum and lithium exposures on the mechanical properties of T-111 (Ta-8W-2Hf) is determined. Exposure conditions were for 1000 hours at 980 or 1315 C, 5000 hours at 1315 C, and a duplex temperature exposure of 1000 hours at 980 C plus 4000 hours at 1040 C. The exposures resulted in reduced tensile and creep strengths of the T-111 in the 900 to 1100 C temperature range where a dynamic strain-age-strengthening mechanism is operative in this alloy. This strength reduction was attributed to the depletion of oxygen from solid solution in this alloy

On the canonical degrees of curves in varieties of general type

A widely believed conjecture predicts that curves of bounded geometric genus lying on a variety of general type form a bounded family. One may even ask whether the canonical degree of a curve $C$ in a variety of general type is bounded from above by some expression $a\chi(C)+b$, where $a$ and $b$ are positive constants, with the possible exceptions corresponding to curves lying in a strict closed subset (depending on $a$ and $b$). A theorem of Miyaoka proves this for smooth curves in minimal surfaces, with $a>3/2$. A conjecture of Vojta claims in essence that any constant $a>1$ is possible provided one restricts oneself to curves of bounded gonality. We show by explicit examples coming from the theory of Shimura varieties that in general, the constant $a$ has to be at least equal to the dimension of the ambient variety. We also prove the desired inequality in the case of compact Shimura varieties.Comment: 10 pages, to appear in Geometric and Functional Analysi

On certain finiteness questions in the arithmetic of modular forms

We investigate certain finiteness questions that arise naturally when studying approximations modulo prime powers of p-adic Galois representations coming from modular forms. We link these finiteness statements with a question by K. Buzzard concerning p-adic coefficient fields of Hecke eigenforms. Specifically, we conjecture that for fixed N, m, and prime p with p not dividing N, there is only a finite number of reductions modulo p^m of normalized eigenforms on \Gamma_1(N). We consider various variants of our basic finiteness conjecture, prove a weak version of it, and give some numerical evidence.Comment: 25 pages; v2: one of the conjectures from v1 now proved; v3: restructered parts of the article; v4: minor corrections and change

Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence

We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. We also study the (tame) levels of p-adic automorphic forms on these quaternion algebras and give an analogue of Mazur's `level lowering' principle.Comment: Updated version. Contains some minor corrections compared to the published versio

Schemes in Lean

We tell the story of how schemes were formalized in three different ways in the Lean theorem prover

Women's dietary changes before and during pregnancy: A systematic review

Background: dietary intake before and during pregnancy has significant health outcomes for both mother and child, including a healthy gestational weight gain. To ensure effective interventions are successfully developed to improve dietary intake during pregnancy, it is important to understand what dietary changes pregnant women make without intervention. Aims: to systematically identify and review studies examining women's dietary changes before and during pregnancy and to identify characteristics of the women making these changes. Methods: a systematic search strategy was employed using three databases (Web of Science, CINAHL and PubMed) in May 2016. Search terms included those relating to preconception, pregnancy and diet. All papers were quality assessed using the Scottish Intercollegiate Guidelines Network methodology checklist for cohort studies.The search revealed 898 articles narrowed to full-text review of 23 studies. In total, 11 research articles were included in the review, describing nine different studies. The findings were narratively summarised in line with the aims of the review. Findings: the included studies showed marked heterogeneity, which impacts on the findings. However, the majority report an increase in energy intake (kcal or kJ) during pregnancy. Of the studies that reported changes through food group comparisons, a majority reported a significant increase in fruit and vegetable consumption, a decrease in egg consumption, a decrease in fried and fast food consumption and a decrease in coffee and tea consumption from before to during pregnancy. The characteristics of the women participating in these studies, suggest that age, education and pregnancy intention are associated with healthier dietary changes; however these factors were only assessed in a small number of studies. Key conclusions: the 11 included articles show varied results in dietary intake during pregnancy as compared to before. More research is needed regarding who makes these healthy changes, this includes consistency regarding measurement tools, outcomes and time points. Implications for practice: Midwives as well as intervention developers need to be aware of the dietary changes women may spontaneously engage in when becoming pregnant, so that care and interventions can build on these