A Proof of the G\"ottsche-Yau-Zaslow Formula

Let S be a complex smooth projective surface and L be a line bundle on S. G\"ottsche conjectured that for every integer r, the number of r-nodal curves in |L| is a universal polynomial of four topological numbers when L is sufficiently ample. We prove G\"ottsche's conjecture using the algebraic cobordism group of line bundles on surfaces and degeneration of Hilbert schemes of points. In addition, we prove the the G\"ottsche-Yau-Zaslow Formula which expresses the generating function of the numbers of nodal curves in terms of quasi-modular forms and two unknown series.Comment: 29 page

SUSY Searches at ATLAS

Recent results of searches for supersymmetry by the ATLAS collaboration in up to 2 fb-1 of sqrt(s) = 7 TeV pp collisions at the LHC are reported.Comment: Presented at the 2011 Hadron Collider Physics symposium (HCP-2011), Paris, France, November 14-18 2011, 6 pages, 12 figure

A Confining Model for Charmonium and New Gauge Invariant Field Equations

We discuss a confining model for charmonium in which the attractive force are derived from a new type of gauge field equation with a generalized $SU_3$ gauge symmetry. The new gauge transformations involve non-integrable phase factors with vector gauge functions \om^a_{\mu}(x). These transformations reduce to the usual $SU_3$ gauge transformations in the special case \om^a_\mu(x) = \p_\mu \xi^a(x). Such a generalized gauge symmetry leads to the fourth-order equations for new gauge fields and to the linear confining potentials. The fourth-order field equation implies that the corresponding massless gauge boson has non-definite energy. However, the new gauge boson is permanently confined in a quark system by the linear potential. We use the empirical potentials of the Cornell group for charmonium to obtain the coupling strength $f^2/(4\pi) \approx 0.19$ for the strong interaction. Such a confining model of quark dynamics could be compatible with perturbation. The model can be applied to other quark-antiquark systems.Comment: 6 page