Motivic Brown-Peterson invariants of the rationals

Fix the base field Q of rational numbers and let BP denote the family of motivic truncated Brown-Peterson spectra over Q. We employ a "local-to-global" philosophy in order to compute the motivic Adams spectral sequence converging to the bi-graded homotopy groups of BP. Along the way, we provide a new computation of the homotopy groups of BP over the 2-adic rationals, prove a motivic Hasse principle for the spectra BP, and deduce several classical and recent theorems about the K-theory of particular fields.Comment: 32 pages, 6 figures; Introduction and exposition improved, typos corrected, now published in Geometry & Topolog

The QCD Phase Diagram, Equation of State, and Heavy Ion Collisions

After some historic remarks and a brief summary of recent theoretical news about the QCD phases, we turn to the issue of $freeze-out$ in heavy ion collisions. We argue that the chemical freeze-out line should actually consists of two crossing lines of different nature. We also consider some inelatic reactions which occure $after$ chemical freeze-out, emphasizing the role of overpopulation of pions. The $hydrodynamics$ (with or without hadronic afterburner) explaines SPS/RHIC data on radial and elliptic flow in unexpected details,for different particles, collision energies, and impact parameters. Apart of Equation of State (EoS), it has basically no free parameters. The EoS which describe these data best agrees quite well with the lattice predictions, with the QGP latent heat $\Delta\epsilon\approx 800 Mev/fm^3$. Other phenomena at RHIC, such as ``jet quenching'' and huge ellipticity at large $p_t$, also point toward very rapid entropy production. Its mechanism remains an outstanding open problem: at the end we discuss recent application of the instanton/sphaleron mechanism. The gg collisions with $\sqrt{s}=2-3 GeV$ may result not in mini-jets but rather in production of sphaleron-like gluomagnetic clusters, which are classically unstable and promptly decay into several gluons and quarks, in sperical mini-Bangs.Comment: Invited talk at "Statistical QCD", Bielefeld, Sept.2001, 13 page

A Maximum Likelihood Analysis of the Low CMB Multipoles from WMAP

The amplitudes of the quadrupole and octopole measured from the Wilkinson Microwave Anisotropy Probe (WMAP) appear to be lower than expected according to the concordance Lambda CDM cosmology. However, the pseudo-Cl estimator used by the WMAP team is non-optimal. In this paper, we discuss the effects of Galactic cuts on pseudo-Cl and quadratic maximum likelihood estimators. An application of a quadratic maximum likelihood estimator to Galaxy subtracted maps produced by the WMAP team and Tegmark, de Oliveira-Costa and Hamilton (2003) shows that the amplitudes of the low multipoles are stable to different Galactic cuts. In particular, the quadrupole and octopole amplitudes are found to lie in the ranges 176 - 250 (micro K)**2 794 - 1183 (micro K)**2 (and more likely to be at the upper ends of these ranges) rather than the values of 123 (micro K)**2 and 611 (micro K)**2 found by the WMAP team. These results indicate that the discrepancy with the concordance Lambda CDM model at low multipoles is not particularly significant and is in the region of a few percent. This conclusion is consistent with an analysis of the low amplitude of the angular correlation function computed from quadratic maximum likelihood power spectrum estimates.Comment: MNRAS (2004) 348 885. Resubmission matches published versio

Solutions of D=2 supersymmetric Yang-Mills quantum mechanics with SU(N) gauge group

We describe the generalization of the recently derived solutions of D=2 supersymmetric Yang-Mills quantum mechanics with SU(3) gauge group to the generic case of SU(N) gauge group. We discuss the spectra and eigensolutions in bosonic as well as fermionic sectors.Comment: 21 pages, no figure

A refinement of Rasmussen's s-invariant

In a previous paper we constructed a spectrum-level refinement of Khovanov homology. This refinement induces stable cohomology operations on Khovanov homology. In this paper we show that these cohomology operations commute with cobordism maps on Khovanov homology. As a consequence we obtain a refinement of Rasmussen's slice genus bound s for each stable cohomology operation. We show that in the case of the Steenrod square Sq^2 our refinement is strictly stronger than s.Comment: 26 pages, 2 figure