Boundary smoothness of analytic functions

We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $\alpha$, with $0<\alpha<1$, in the vicinity of an exceptional boundary point where all such functions exhibit some kind of smoothness. Specifically, we consider the relation between the abstract idea of a bounded point derivation on the algebra of such functions and the classical complex derivative evaluated as a limit of difference quotients. We obtain a result which applies, for example, when the open set admits an interior cone at the special boundary point.Comment: 14 pages. This revision corrects a misprint on p.12: In equation (3), $\alpha$ should have been $1-\alpha$. Also a misprint on page 14 in the formula for $R_a-L_a$. The validity of the argument is not affected and the result stand

Nonperturbative QCD, gauge-fixing, Gribov copies, and the lattice

Perturbative QCD uses the Faddeev-Popov gauge-fixing procedure, which leads to ghosts and the local BRST invariance of the gauge-fixed perturbative QCD action. In the asymptotic regime, where perturbative QCD is relevant, Gribov copies can be neglected. In the nonperturbative regime, one must adopt either a nonlocal Gribov-copy free gauge (e.g., Laplacian gauge) or attempt to maintain local BRST invariance at the expense of admitting Gribov copies. These issues are explored. In addition, we discuss the relationship between recent Dyson-Schwinger based model calculations of the infrared behavior of QCD Green's functions and the lattice calculation of these quantities.Comment: 9 pages, 2 figures, to appear in Prog. Theor. Phys. Suppl. in the proceedings of the Tokyo-Adelaide Joint Workshop on Quarks, Astrophysics and Space Physic

ELSA and the frontiers of astrometry

ELSA stands for the ambitious goal of `European Leadership in Space Astrometry'. In this closing contribution I will examine how the ELSA network has advanced this goal. I also look ahead to the time when the Gaia data will be published and consider what needs to be done to maintain European leadership.Comment: Closing remarks at the ELSA conference "Gaia: at the frontiers of astrometry". Proceedings editors: C. Turon, F. Arenou & F. Meynadie