Schottky uniformization and vector bundles over Riemann surfaces

We study a natural map from representations of a free group of rank g in GL(n,C), to holomorphic vector bundles of degree 0 over a compact Riemann surface X of genus g, associated with a Schottky uniformization of X. Maximally unstable flat bundles are shown to arise in this way. We give a necessary and sufficient condition for this map to be a submersion, when restricted to representations producing stable bundles. Using a generalized version of Riemann's bilinear relations, this condition is shown to be true on the subspace of unitary Schottky representations.Comment: 16 pages; AMSLate

Higgs bundles and representation spaces associated to morphisms

Let $G$ be a connected reductive affine algebraic group defined over the complex numbers, and $K\subset G$ be a maximal compact subgroup. Let $X , Y$ be irreducible smooth complex projective varieties and $f: X \rightarrow Y$ an algebraic morphism, such that $\pi_1(Y)$ is virtually nilpotent and the homomorphism $f_* : \pi_1(X) \rightarrow\pi_1(Y)$ is surjective. Define $${\mathcal R }^f(\pi_1(X),\, G)\,=\, \{\rho\, \in\, \text{Hom}(\pi_1(X),\, G)\, \mid\, A\circ\rho \ \text{ factors through }~ f_*\}\, ,$$ $${\mathcal R }^f(\pi_1(X),\, K)\,=\, \{\rho\, \in\, \text{Hom}(\pi_1(X),\, K)\, \mid\, A\circ\rho \ \text{ factors through }~ f_*\}\, ,$$ where $A: G \rightarrow \text{GL}(\text{Lie}(G))$ is the adjoint action. We prove that the geometric invariant theoretic quotient ${\mathcal R }^f(\pi_1(X, x_0), G)/\!\!/G$ admits a deformation retraction to ${\mathcal R }^f(\pi_1(X, x_0),\, K)/K$. We also show that the space of conjugacy classes of $n$ almost commuting elements in $G$ admits a deformation retraction to the space of conjugacy classes of $n$ almost commuting elements in $K$

Occupational mismatch and moonlighting of Spanish physicians: Do couples matter?

There are important gender differences in the labour-market status of health sciences graduates in Spain: (i) female physicians have lower participation rates than male physicians and, when they work, they are subject to higher occupational mismatch, and (ii) moonlighting is more frequent among male physicians. In this paper we investigate whether such differences are related to the monopsonistic features of the labour market of health-care professionals. Spanish physicians also exhibit another characteristic reducing their geographical mobility in search of a better occupational adjustment: among all university graduates, they are the ones most often coupled to partners with the same educational level and/or same type of studies. Consequently, optimal occupational adjustment of both partners can be a complex process. This stylised fact allows us to provide empirical evidence on a new type of gender discrimination labelled as ?within-couple discrimination?, which arises when geographical mobility of couples is favourable to men, so that they achieve better occupational adjustment than women despite having the same human capital. Finally, we analyse if moonlighting can be interpreted as a way of avoiding monopsonistic effects by increasing the labour supply elasticity.Fundación BBVA / Banco de Santander / La Caix

Comparison of NASTRAN analysis with ground vibration results of UH-60A NASA/AEFA test configuration

Preceding program flight tests, a ground vibration test and modal test analysis of a UH-60A Black Hawk helicopter was conducted by Sikorsky Aircraft to complement the UH-60A test plan and NASA/ARMY Modern Technology Rotor Airloads Program. The 'NASA/AEFA' shake test configuration was tested for modal frequencies and shapes and compared with its NASTRAN finite element model counterpart to give correlative results. Based upon previous findings, significant differences in modal data existed and were attributed to assumptions regarding the influence of secondary structure contributions in the preliminary NASTRAN modeling. An analysis of an updated finite element model including several secondary structural additions has confirmed that the inclusion of specific secondary components produces a significant effect on modal frequency and free-response shapes and improves correlations at lower frequencies with shake test data

Simultaneous similarity and triangularization of sets of 2 by 2 matrices

Let $\mathcal{A}=(A_{1},...,A_{n},...)$ be a finite or infinite sequence of $2\times2$ matrices with entries in an integral domain. We show that, except for a very special case, $\mathcal{A}$ is (simultaneously) triangularizable if and only if all pairs $(A_{j},A_{k})$ are triangularizable, for $1\leq j,k\leq\infty$. We also provide a simple numerical criterion for triangularization. Using constructive methods in invariant theory, we define a map (with the minimal number of invariants) that distinguishes simultaneous similarity classes for non-commutative sequences over a field of characteristic $\neq2$. We also describe canonical forms for sequences of $2\times2$ matrices over algebraically closed fields, and give a method for finding sequences with a given set of invariants.Comment: 22 page