Higgs bundles and surface group representations in the real symplectic group

In this paper we study the moduli space of representations of a surface group (i.e., the fundamental group of a closed oriented surface) in the real symplectic group Sp(2n,R). The moduli space is partitioned by an integer invariant, called the Toledo invariant. This invariant is bounded by a Milnor-Wood type inequality. Our main result is a count of the number of connected components of the moduli space of maximal representations, i.e. representations with maximal Toledo invariant. Our approach uses the non-abelian Hodge theory correspondence proved in a companion paper arXiv:0909.4487 [math.DG] to identify the space of representations with the moduli space of polystable Sp(2n,R)-Higgs bundles. A key step is provided by the discovery of new discrete invariants of maximal representations. These new invariants arise from an identification, in the maximal case, of the moduli space of Sp(2n,R)-Higgs bundles with a moduli space of twisted Higgs bundles for the group GL(n,R).Comment: 55 pages; v2: main results are unchanged but paper has been completely reorganized and presentation significantly improved; v3, v4: various corrections and improvements; Part 1 of v2 has been split off as the independent paper arXiv:0909.4487v1 [math.DG

Intersecting Solitons, Amoeba and Tropical Geometry

We study generic intersection (or web) of vortices with instantons inside, which is a 1/4 BPS state in the Higgs phase of five-dimensional N=1 supersymmetric U(Nc) gauge theory on R_t \times (C^\ast)^2 \simeq R^{2,1} \times T^2 with Nf=Nc Higgs scalars in the fundamental representation. In the case of the Abelian-Higgs model (Nf=Nc=1), the intersecting vortex sheets can be beautifully understood in a mathematical framework of amoeba and tropical geometry, and we propose a dictionary relating solitons and gauge theory to amoeba and tropical geometry. A projective shape of vortex sheets is described by the amoeba. Vortex charge density is uniformly distributed among vortex sheets, and negative contribution to instanton charge density is understood as the complex Monge-Ampere measure with respect to a plurisubharmonic function on (C^\ast)^2. The Wilson loops in T^2 are related with derivatives of the Ronkin function. The general form of the Kahler potential and the asymptotic metric of the moduli space of a vortex loop are obtained as a by-product. Our discussion works generally in non-Abelian gauge theories, which suggests a non-Abelian generalization of the amoeba and tropical geometry.Comment: 39 pages, 11 figure

Solitons in the Higgs phase -- the moduli matrix approach --

We review our recent work on solitons in the Higgs phase. We use U(N_C) gauge theory with N_F Higgs scalar fields in the fundamental representation, which can be extended to possess eight supercharges. We propose the moduli matrix as a fundamental tool to exhaust all BPS solutions, and to characterize all possible moduli parameters. Moduli spaces of domain walls (kinks) and vortices, which are the only elementary solitons in the Higgs phase, are found in terms of the moduli matrix. Stable monopoles and instantons can exist in the Higgs phase if they are attached by vortices to form composite solitons. The moduli spaces of these composite solitons are also worked out in terms of the moduli matrix. Webs of walls can also be formed with characteristic difference between Abelian and non-Abelian gauge theories. We characterize the total moduli space of these elementary as well as composite solitons. Effective Lagrangians are constructed on walls and vortices in a compact form. We also present several new results on interactions of various solitons, such as monopoles, vortices, and walls. Review parts contain our works on domain walls (hep-th/0404198, hep-th/0405194, hep-th/0412024, hep-th/0503033, hep-th/0505136), vortices (hep-th/0511088, hep-th/0601181), domain wall webs (hep-th/0506135, hep-th/0508241, hep-th/0509127), monopole-vortex-wall systems (hep-th/0405129, hep-th/0501207), instanton-vortex systems (hep-th/0412048), effective Lagrangian on walls and vortices (hep-th/0602289), classification of BPS equations (hep-th/0506257), and Skyrmions (hep-th/0508130).Comment: 89 pages, 33 figures, invited review article to Journal of Physics A: Mathematical and General, v3: typos corrected, references added, the published versio

Modifiable risk factors associated with prediabetes in men and women: A cross-sectional analysis of the cohort study in primary health care on the evolution of patients with prediabetes

Background: Prediabetes is a high-risk state for diabetes development, but little is known about the factors associated with this state. The aim of the study was to identify modifiable risk factors associated with the presence of prediabetes in men and women. Methods: Cohort Study in Primary Health Care on the Evolution of Patients with Prediabetes (PREDAPS-Study) is a prospective study on a cohort of 1184 subjects with prediabetes and another cohort of 838 subjects without glucose metabolism disorders. It is being conducted by 125 general practitioners in Spain. Data for this analysis were collected during the baseline stage in 2012. The modifiable risk factors included were: smoking habit, alcohol consumption, low physical activity, inadequate diet, hypertension, dyslipidemia, and obesity. To assess independent association between each factor and prediabetes, odds ratios (ORs) were estimated using logistic regression models. Results: Abdominal obesity, low plasma levels of high-density lipoprotein cholesterol (HDL-cholesterol), and hypertension were independently associated with the presence of prediabetes in both men and women. After adjusting for all factors, the respective ORs (95% Confidence Intervals) were 1.98 (1.41-2.79), 1.88 (1.23-2.88) and 1.86 (1.39-2.51) for men, and 1.89 (1.36-2.62), 1.58 (1.12-2.23) and 1.44 (1.07-1.92) for women. Also, general obesity was a risk factor in both sexes but did not reach statistical significance among men, after adjusting for all factors. Risky alcohol consumption was a risk factor for prediabetes in men, OR 1.49 (1.00-2.24). Conclusions: Obesity, low HDL-cholesterol levels, and hypertension were modifiable risk factors independently related to the presence of prediabetes in both sexes. The magnitudes of the associations were stronger for men than women. Abdominal obesity in both men and women displayed the strongest association with prediabetes. The findings suggest that there are some differences between men and women, which should be taken into account when implementing specific recommendations to prevent or delay the onset of diabetes in adult population

Growth and Demography of the Solitary Scleractinian Coral Leptopsammia pruvoti along a Sea Surface Temperature Gradient in the Mediterranean Sea

The demographic traits of the solitary azooxanthellate scleractinian Leptopsammia pruvoti were determined in six populations on a sea surface temperature (SST) gradient along the western Italian coasts. This is the first investigation of the growth and demography characteristics of an azooxanthellate scleractinian along a natural SST gradient. Growth rate was homogeneous across all populations, which spanned 7 degrees of latitude. Population age structures differed between populations, but none of the considered demographic parameters correlated with SST, indicating possible effects of local environmental conditions. Compared to another Mediterranean solitary scleractinian, Balanophyllia europaea, zooxanthellate and whose growth, demography and calcification have been studied in the same sites, L. pruvoti seems more tolerant to temperature increase. The higher tolerance of L. pruvoti, relative to B. europaea, may rely on the absence of symbionts, and thus the lack of an inhibition of host physiological processes by the heat-stressed zooxanthellae. However, the comparison between the two species must be taken cautiously, due to the likely temperature differences between the two sampling depths. Increasing research effort on determining the effects of temperature on the poorly studied azooxanthellate scleractinians may shed light on the possible species assemblage shifts that are likely to occur during the current century as a consequence of global climatic change

Validation of the Scientific Program for the Dark Energy Spectroscopic Instrument

The Dark Energy Spectroscopic Instrument (DESI) was designed to conduct a survey covering 14,000 deg$^2$ over five years to constrain the cosmic expansion history through precise measurements of Baryon Acoustic Oscillations (BAO). The scientific program for DESI was evaluated during a five month Survey Validation (SV) campaign before beginning full operations. This program produced deep spectra of tens of thousands of objects from each of the stellar (MWS), bright galaxy (BGS), luminous red galaxy (LRG), emission line galaxy (ELG), and quasar target classes. These SV spectra were used to optimize redshift distributions, characterize exposure times, determine calibration procedures, and assess observational overheads for the five-year program. In this paper, we present the final target selection algorithms, redshift distributions, and projected cosmology constraints resulting from those studies. We also present a `One-Percent survey' conducted at the conclusion of Survey Validation covering 140 deg$^2$ using the final target selection algorithms with exposures of a depth typical of the main survey. The Survey Validation indicates that DESI will be able to complete the full 14,000 deg$^2$ program with spectroscopically-confirmed targets from the MWS, BGS, LRG, ELG, and quasar programs with total sample sizes of 7.2, 13.8, 7.46, 15.7, and 2.87 million, respectively. These samples will allow exploration of the Milky Way halo, clustering on all scales, and BAO measurements with a statistical precision of 0.28% over the redshift interval $z<1.1$, 0.39% over the redshift interval $1.1<z<1.9$, and 0.46% over the redshift interval $1.9<z<3.5$.Comment: 42 pages, 18 figures, accepted by A

The Early Data Release of the Dark Energy Spectroscopic Instrument

\ua9 2024. The Author(s). Published by the American Astronomical Society. The Dark Energy Spectroscopic Instrument (DESI) completed its 5 month Survey Validation in 2021 May. Spectra of stellar and extragalactic targets from Survey Validation constitute the first major data sample from the DESI survey. This paper describes the public release of those spectra, the catalogs of derived properties, and the intermediate data products. In total, the public release includes good-quality spectral information from 466,447 objects targeted as part of the Milky Way Survey, 428,758 as part of the Bright Galaxy Survey, 227,318 as part of the Luminous Red Galaxy sample, 437,664 as part of the Emission Line Galaxy sample, and 76,079 as part of the Quasar sample. In addition, the release includes spectral information from 137,148 objects that expand the scope beyond the primary samples as part of a series of secondary programs. Here, we describe the spectral data, data quality, data products, Large-Scale Structure science catalogs, access to the data, and references that provide relevant background to using these spectra