Moduli in N=1 heterotic/F-theory duality

The moduli in a 4D N=1 heterotic compactification on an elliptic CY, as well as in the dual F-theoretic compactification, break into "base" parameters which are even (under the natural involution of the elliptic curves), and "fiber" or twisting parameters; the latter include a continuous part which is odd, as well as a discrete part. We interpret all the heterotic moduli in terms of cohomology groups of the spectral covers, and identify them with the corresponding F-theoretic moduli in a certain stable degeneration. The argument is based on the comparison of three geometric objects: the spectral and cameral covers and the ADE del Pezzo fibrations. For the continuous part of the twisting moduli, this amounts to an isomorphism between certain abelian varieties: the connected component of the heterotic Prym variety (a modified Jacobian) and the F-theoretic intermediate Jacobian. The comparison of the discrete part generalizes the matching of heterotic 5brane / F-theoretic 3brane impurities.Comment: Latex, 26 pages. Acknowledgements adde

Structural and Functional Analysis of a β2-Adrenergic Receptor Complex with GRK5.

The phosphorylation of agonist-occupied G-protein-coupled receptors (GPCRs) by GPCR kinases (GRKs) functions to turn off G-protein signaling and turn on arrestin-mediated signaling. While a structural understanding of GPCR/G-protein and GPCR/arrestin complexes has emerged in recent years, the molecular architecture of a GPCR/GRK complex remains poorly defined. We used a comprehensive integrated approach of cross-linking, hydrogen-deuterium exchange mass spectrometry (MS), electron microscopy, mutagenesis, molecular dynamics simulations, and computational docking to analyze GRK5 interaction with the β2-adrenergic receptor (β2AR). These studies revealed a dynamic mechanism of complex formation that involves large conformational changes in the GRK5 RH/catalytic domain interface upon receptor binding. These changes facilitate contacts between intracellular loops 2 and 3 and the C terminus of the β2AR with the GRK5 RH bundle subdomain, membrane-binding surface, and kinase catalytic cleft, respectively. These studies significantly contribute to our understanding of the mechanism by which GRKs regulate the function of activated GPCRs. PAPERCLIP

Remarks on Contact and Jacobi Geometry

We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts are Kirillov manifolds and linear Kirillov structures, i.e., homogeneous Poisson manifolds and, respectively, homogeneous linear Poisson manifolds. The difference with the existing literature is that the homogeneity of the Poisson structure is related to a principal ${\rm GL}(1,{\mathbb R})$-bundle structure on the manifold and not just to a vector field. This allows for working with Jacobi bundle structures on nontrivial line bundles and drastically simplifies the picture of Jacobi and contact geometry. Our results easily reduce to various basic theorems of Jacobi and contact geometry when the principal bundle structure is trivial, while giving new insights into the theory