Uniformization of Deligne-Mumford curves

We compute the fundamental groups of non-singular analytic Deligne-Mumford curves, classify the simply connected ones, and classify analytic Deligne-Mumford curves by their uniformization type. As a result, we find an explicit presentation of an arbitrary Deligne-Mumford curve as a quotient stack. Along the way, we compute the automorphism 2-groups of weighted projective stacks $\mathcal{P}(n_1,n_2,...,n_r)$. We also discuss connections with the theory of F-groups, 2-groups, and Bass-Serre theory of graphs of groups.Comment: 39 pages, 2 figure

Twisted loop transgression and higher Jandl gerbes over finite groupoids

Given a double cover $\pi: \mathcal{G} \rightarrow \hat{\mathcal{G}}$ offinite groupoids, we explicitly construct twisted loop transgression maps,$\tau_{\pi}$ and $\tau_{\pi}^{ref}$, thereby associating to a Jandl $n$-gerbe$\hat{\lambda}$ on $\hat{\mathcal{G}}$ a Jandl $(n-1)$-gerbe$\tau_{\pi}(\hat{\lambda})$ on the quotient loop groupoid of $\mathcal{G}$ andan ordinary $(n-1)$-gerbe $\tau^{ref}_{\pi}(\hat{\lambda})$ on the unorientedquotient loop groupoid of $\mathcal{G}$. For $n =1,2$, we interpret thecharacter theory (resp. centre) of the category of Real $\hat{\lambda}$-twisted$n$-vector bundles over $\hat{\mathcal{G}}$ in terms of flat sections of the$(n-1)$-vector bundle associated to $\tau_{\pi}^{ref}(\hat{\lambda})$ (resp.the Real $(n-1)$-vector bundle associated to $\tau_{\pi}(\hat{\lambda})$). Werelate our results to Real versions of twisted Drinfeld doubles and pointedfusion categories and to discrete torsion in orientifold string and M-theory.<br

Twisted loop transgression and higher Jandl gerbes over finite groupoids

Given a double cover $\pi: \mathcal{G} \rightarrow \hat{\mathcal{G}}$ of finite groupoids, we explicitly construct twisted loop transgression maps, $\tau_{\pi}$ and $\tau_{\pi}^{ref}$, thereby associating to a Jandl $n$-gerbe $\hat{\lambda}$ on $\hat{\mathcal{G}}$ a Jandl $(n-1)$-gerbe $\tau_{\pi}(\hat{\lambda})$ on the quotient loop groupoid of $\mathcal{G}$ and an ordinary $(n-1)$-gerbe $\tau^{ref}_{\pi}(\hat{\lambda})$ on the unoriented quotient loop groupoid of $\mathcal{G}$. For $n =1,2$, we interpret the character theory (resp. centre) of the category of Real $\hat{\lambda}$-twisted $n$-vector bundles over $\hat{\mathcal{G}}$ in terms of flat sections of the $(n-1)$-vector bundle associated to $\tau_{\pi}^{ref}(\hat{\lambda})$ (resp. the Real $(n-1)$-vector bundle associated to $\tau_{\pi}(\hat{\lambda})$). We relate our results to Real versions of twisted Drinfeld doubles and pointed fusion categories and to discrete torsion in orientifold string and M-theory.Comment: 33 page

Screening for microscopic hematuria in school-age children of the Gorgan city

Screening for hematuria was carried out in 3000 school-age children (6 to14 years old) in Gorgan, Iran, using a fresh morning urine sample. At the initial step, 208 (6.8%) had positive dipstick tests for blood, which decreased to 35 (1.2%) at the second step. Of the 35 children with hematuria, 27 (77.1%) were girls and 8 (22.9%) were boys. Twenty-six children were further evaluated of whom 5 had normal findings, and 7 had hypercalciuria, 13 had nephrolithiasis, and in 1 had a large cystic lesion on ultrasonography, ultimately diagnosed as oncocystoma

Fibrations of topological stacks

In this note we define fibrations of topological stacks and establish their main properties. When restricted to topological spaces, our notion of fibration coincides with the classical one. We prove various standard results about fibrations (long exact sequence for homotopy groups, Leray–Serre and Eilenberg–Moore spec- tral sequences, etc.). We prove various criteria for a morphism of topological stacks to be a fibration, and use these to produce examples of fibrations. We prove that every morphism of topological stacks factors through a fibration and construct the homotopy fiber of a morphism of topological stacks. As an immediate consequence of the machinery we develop, we also prove van Kampen’s theorem for fundamental groups of topological stacks

Non-Hausdorff Symmetries of C*-algebras

Symmetry groups or groupoids of C*-algebras associated to non-Hausdorff spaces are often non-Hausdorff as well. We describe such symmetries using crossed modules of groupoids. We define actions of crossed modules on C*-algebras and crossed products for such actions, and justify these definitions with some basic general results and examples.Comment: very minor changes. To appear in Math. An

From double Lie groupoids to local Lie 2-groupoids

We apply the bar construction to the nerve of a double Lie groupoid to obtain a local Lie 2-groupoid. As an application, we recover Haefliger's fundamental groupoid from the fundamental double groupoid of a Lie groupoid. In the case of a symplectic double groupoid, we study the induced closed 2-form on the associated local Lie 2-groupoid, which leads us to propose a definition of a symplectic 2-groupoid.Comment: 23 pages, a few minor changes, including a correction to Lemma 6.

The integral monodromy of hyperelliptic and trielliptic curves

We compute the \integ/\ell and \integ_\ell monodromy of every irreducible component of the moduli spaces of hyperelliptic and trielliptic curves. In particular, we provide a proof that the \integ/\ell monodromy of the moduli space of hyperelliptic curves of genus $g$ is the symplectic group \sp_{2g}(\integ/\ell). We prove that the \integ/\ell monodromy of the moduli space of trielliptic curves with signature $(r,s)$ is the special unitary group \su_{(r,s)}(\integ/\ell\tensor\integ[\zeta_3])