Local positivity in terms of Newton-Okounkov bodies

In recent years, the study of Newton-Okounkov bodies on normal varieties has become a central subject in the asymptotic theory of linear series, after its introduction by Lazarsfeld-Mustata and Kaveh-Khovanskii. One reason for this is that they encode all numerical equivalence information of divisor classes (by work of Jow). At the same time, they can be seen as local positivity invariants, and K\"uronya-Lozovanu have studied them in depth from this point of view. We determine what information is encoded by the set of all Newton-Okounkov bodies of a big divisor with respect to flags centered at a fixed point of a surface, by showing that it determines and is determined by the numerical equivalence class of the divisor up to negative components in the Zariski decomposition that do not go through the fixed point.Comment: 10 pages. Comments welcom

Small Sample Bias of Alternative Estimation Methods for Moment Condition Models: Monte Carlo Evidence for Covariance Structures and Instrumental Variables

It is now widely recognized that the most commonly used efficient two-step GMM estimator may have large bias in small samples. This problem has motivated the search for alternative estimators with better finite sample properties. Two classes of alternatives are considered in this paper. The first includes estimators which are asymptotically first-order equivalent to the GMM estimator, namely the continuous-updating, exponential tilting, and empirical likelihood estimators. Analytical and bootstrap bias-adjusted GMM estimators form the second class of alternatives. Two extensive Monte Carlo simulation studies are conducted in this paper for covariance structure and instrumental variable models. We conclude that all alternative estimators offer much reduced bias as compared to the GMM estimator, particularly the empirical likelihood and some of the bias-corrected GMM estimators analyzed

ChPT Progress on Non-Leptonic and Radiative Kaon Decays

I discuss recent developments on non-leptonic and radiative kaon decays mainly related to direct CP-violation within the combined ChPT and 1/N_c expansion approaches. In particular, I review the status of K -> pi pi, epsilon_K', direct CP-violating K+ -> 3 pi Dalitz plot slope g and decay rate asymmetries, and the Standard Model prediction for Br(K_L -> pi0 e+ e-).Comment: 14 pages, 1 figure. Invited talk at KAON 07 International Conference, May 21-25 2007, Frascati, Italy. v2: Discussion in Section 3 somewhat enlarged and added references. Matches published verio

CKM angles from non-leptonic B decays using SU(3) flavour symmetry

We discuss the determination of the CKM angles gamma and alpha using recent data from non-leptonic B decays together with flavour symmetries. Penguin effects are controlled by means of the CP-averaged branching ratio B_d \to \pi^\pm K^\mp. The information from A_{CP}(B_d \to J/\Psi K_S) (two solutions for phi_d), Rb and gamma allow us to determine beta, even in presence of New Physics not affecting Delta B=1 amplitudes. In this context we address the question of to what extent there is still space for New Physics.Comment: 3 pages, 2 figures, Invited talk given at International Europhysics Conference on High-Energy Physics (HEP 2003), Aachen, Germany, 17-23 Jul 200