From a Kac-like particle system to the Landau equation for hard potentials and Maxwell molecules

We prove a quantitative result of convergence of a conservative stochastic particle system to the solution of the homogeneous Landau equation for hard potentials. There are two main difficulties: (i) the known stability results for this class of Landau equations concern regular solutions and seem difficult to extend to study the rate of convergence of some empirical measures; (ii) the conservativeness of the particle system is an obstacle for (approximate) independence. To overcome (i), we prove a new stability result for the Landau equation for hard potentials concerning very general measure solutions. Due to (ii), we have to couple, our particle system with some non independent nonlinear processes, of which the law solves, in some sense, the Landau equation. We then prove that these nonlinear processes are not so far from being independent. Using finally some ideas of Rousset [25], we show that in the case of Maxwell molecules, the convergence of the particle system is uniform in time

Classification of polynomials from C^2 to C with one critical value

We give the classification, up to homeomorphisms, of reduced complex polynomials with 2 variables with one critical value.Comment: 17 pages, LaTeX2e, 2 figures, 2 tabulars. To appear in Mathematische Zeitscrift. One remark changed after theorem

Searches for Higgs and BSM at the Tevatron

This paper presents an overview of recent experimental direct searches for Higgs-boson and beyond-the-standard-model (BSM) physics shown in the plenary session at the SUSY07 conference. The results reported correspond to an integrated luminosity of up to 2 fb-1 of Run II data from $p\bar{p}$ collisions collected by the CDF and D0 experiments at the Fermilab Tevatron Collider. Searches covered include: the standard model (SM) Higgs boson (including sensitivity projections), the minimal supersymmetric extension of the standard model (MSSM), charged Higgs bosons and extended Higgs models, supersymmetric decays that conserve R-parity, gauge-mediated supersymmetric breaking models, long-lived particles, leptoquarks, extra gauge bosons, extra dimensions, and finally signature-based searches. Given the excellent performance of the collider and the continued productivity of the experiments, the Tevatron physics potential looks very promising for discovery in the coming larger data sets. In particular, the Higgs boson could be observed if its mass is light or near 160 GeV.Comment: Submitted for the SUSY07 proceedings, 10 pages, LaTeX, 19 eps figure