On the automorphisms of moduli spaces of curves

In the last years the biregular automorphisms of the Deligne-Mumford's and Hassett's compactifications of the moduli space of n-pointed genus g smooth curves have been extensively studied by A. Bruno and the authors. In this paper we give a survey of these recent results and extend our techniques to some moduli spaces appearing as intermediate steps of the Kapranov's and Keel's realizations of $\bar{M}_{0,n}$, and to the degenerations of Hassett's spaces obtained by allowing zero weights.Comment: 15 pages. The material of version 1 has been reorganized and expanded in this paper and in arXiv:1307.6828 on automorphisms of Hassett's moduli space

Properties of the unusual galaxy PSC 09104+4109

The IRAS source PSC 09104+4109 is tentatively identified with a faint emission line galaxy having z = 0.442. Assuming this identification is correct, the total infrared luminosity of this galaxy is estimated to be 5 x 10 to the 12th power L sub 0, among the highest for galaxies detected by IRAS. This energy is concentrated at wavelengths less than 30 micrometers, and is approx. 50 times greater than the estimated optical luminosity. The serendipitous way in which this source was found in the PSC catalog suggests that many more similar objects may be found at the lowest levels of the IRAS survey

A simulation survey of galaxy interactions

Many carefully selected samples of interacting galaxies have been observed extensively in attempts to clarify whether interaction produces activity in galaxies. Because the sample members represent a wide range of encounter parameters and times, one can then study whether there are correlations between observable encounter features and, for example, Seyfert activity. On the other hand, in theoretical studies, simulations typically deal with either time-consuming detailed modelling of single galaxy pairs or tracing a few model encounters over time. The authors extend the observational survey approach by combining it with a simulation survey. The authors are conducting a survey of model encounters, covering the most important encounter parameters over a wide range. Some parameters, such as companion structure and initial velocity, are demonstratably less important and can be ignored in a first pass. The parameter range must be richly enough sampled so that the authors can evaluate the uniqueness of the observable morphology and velocity structure of the resulting simulated pairs to diagnose unobservable companion orbit parameters. They are using a self-gravitating polar n-body code run on the Cray X-MP at the Alabama Supercomputer Network. For each simulation, the authors have stellar and gas distributions predicted over, typically, a billion years, along with information on gas motions within the disk and any material captured by the companion or lost to the system. Features of disturbed spiral galaxies are sensitive enough to time and encounter parameters so that a match of the simulation survey results to observations can be applied as starting points to infer unobservable orbital or system parameters in actual sample members. This should enable them to examine whether interesting observed properties (Seyfert activity, nuclear star-formation rate) are functions of unobservable dynamical properties which characterize each encounter. Any correlations (or lack of some expected ones) will provide strong clues as to how or whether these phenomena are related to interactions. Aside from its use with such observed samples, this survey should greatly speed determination of initial orbital parameters for more detailed subsequent simulations of individual systems

Global well-posedness for KdV in Sobolev Spaces of negative index

The initial value problem for the Korteweg-deVries equation on the line is shown to be globally well-posed for rough data. In particular, we show global well-posedness for initial data in H^s({\mathbb{R}), -3/10<s.Comment: 5 pages. Electronic Journal of Differential equations (submitted