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

The intrinsic normal cone

We suggest a construction of virtual fundamental classes of certain types of moduli spaces.Comment: LaTeX, Postscript file available at http://www.math.ubc.ca/people/faculty/behrend/inc.p

Donaldson-Thomas invariants and wall-crossing formulas

Notes from the report at the Fields institute in Toronto. We introduce the Donaldson-Thomas invariants and describe the wall-crossing formulas for numerical Donaldson-Thomas invariants.Comment: 18 pages. To appear in the Fields Institute Monograph Serie

π0→γ∗γ\pi^0\to\gamma^*\gamma transition form factor within Light Front Quark Model

We study the transition form factor of $\pi^0\to\gamma^* \gamma$ as a function of the momentum transfer $Q^2$ within the light-front quark model (LFQM). We compare our result with the experimental data by BaBar as well as other calculations based on the LFQM in the literature. We show that our predicted form factor fits well with the experimental data, particularly those at the large $Q^2$ region.Comment: 11 pages, 4 figures, accepted for publication in PR

On the Classification of Bulk and Boundary Conformal Field Theories

The classification of rational conformal field theories is reconsidered from the standpoint of boundary conditions. Solving Cardy's equation expressing the consistency condition on a cylinder is equivalent to finding integer valued representations of the fusion algebra. A complete solution not only yields the admissible boundary conditions but also gives valuable information on the bulk properties.Comment: 7 pages, LaTeX; minor correction

Photon-meson transition form factors of light pseudoscalar mesons

The photon-meson transition form factors of light pseudoscalar mesons $\pi ^{0}$, $\eta$, and $\eta ^{\prime}$ are systematically calculated in a light-cone framework, which is applicable as a light-cone quark model at low $Q^{2}$ and is also physically in accordance with the light-cone pQCD approach at large $Q^{2}$. The calculated results agree with the available experimental data at high energy scale. We also predict the low $Q^{2}$ behaviors of the photon-meson transition form factors of $\pi ^{0}$, $\eta$ and $\eta ^{\prime }$, which are measurable in $e+A({Nucleus})\to e+A+M$ process via Primakoff effect at JLab and DESY.Comment: 22 Latex pages, 7 figures, Version to appear in PR

The Boundary Conformal Field Theories of the 2D Ising critical points

We present a new method to identify the Boundary Conformal Field Theories (BCFTs) describing the critical points of the Ising model on the strip. It consists in measuring the low-lying excitation energies spectra of its quantum spin chain for different boundary conditions and then to compare them with those of the different boundary conformal field theories of the $(A_2,A_3)$ minimal model.Comment: 7 pages, no figures. Talk given at the XXth International Conference on Integrable Systems and Quantum Symmetries (ISQS-20). Prague, June 201

Next to leading order eta production at hadron colliders

Inclusive eta production at hadron colliders is considered,based on evaluation of eta fragmentation functions at next to leading order. Absolute predictions at LHC and SSC are presented, including the ratio $\eta/\pi^0$, together with the estimate of the theoretical uncertainty, as a possible neutral background to the $H\to \gamma\gamma$ detection.Comment: 8 pages, latex, FNT/T-93/13,14 figures avilable upon reques

The symplectic Deligne-Mumford stack associated to a stacky polytope

We discuss a symplectic counterpart of the theory of stacky fans. First, we define a stacky polytope and construct the symplectic Deligne-Mumford stack associated to the stacky polytope. Then we establish a relation between stacky polytopes and stacky fans: the stack associated to a stacky polytope is equivalent to the stack associated to a stacky fan if the stacky fan corresponds to the stacky polytope.Comment: 20 pages; v2: To appear in Results in Mathematic

The Resolved Asteroid Program - Size, shape, and pole of (52) Europa

With the adaptive optics (AO) system on the 10 m Keck-II telescope, we acquired a high quality set of 84 images at 14 epochs of asteroid (52) Europa on 2005 January 20. The epochs covered its rotation period and, by following its changing shape and orientation on the plane of sky, we obtained its triaxial ellipsoid dimensions and spin pole location. An independent determination from images at three epochs obtained in 2007 is in good agreement with these results. By combining these two data sets, along with a single epoch data set obtained in 2003, we have derived a global fit for (52) Europa of diameters (379x330x249) +/- (16x8x10) km, yielding a volume-equivalent spherical-diameter of 315 +/- 7 km, and a rotational pole within 7 deg of [RA; Dec] = [257,+12] in an Equatorial J2000 reference frame (ECJ2000: 255,+35). Using the average of all mass determinations available forEuropa, we derive a density of 1.5 +/- 0.4, typical of C-type asteroids. Comparing our images with the shape model of Michalowski et al. (A&A 416, 2004), derived from optical lightcurves, illustrates excellent agreement, although several edge features visible in the images are not rendered by the model. We therefore derived a complete 3-D description of Europa's shape using the KOALA algorithm by combining our imaging epochs with 4 stellar occultations and 49 lightcurves. We use this 3-D shape model to assess these departures from ellipsoidal shape. Flat facets (possible giant craters) appear to be less distinct on (52) Europa than on other C-types that have been imaged in detail. We show that fewer giant craters, or smaller craters, is consistent with its expected impact history. Overall, asteroid (52) Europa is still well modeled as a smooth triaxial ellipsoid with dimensions constrained by observations obtained over several apparitions.Comment: Accepted for publication in Icaru