Abstract:
We calculate the kaon semileptonic form factor $f_+(0)$ from lattice QCD, working, for the first time, at the physical light-quark masses. We use gauge configurations generated by the MILC collaboration with $N_f=2+1+1$ flavors of sea quarks, which incorporate the effects of dynamical charm quarks as well as those of up, down, and strange. We employ data at three lattice spacings to extrapolate to the continuum limit. Our result, $f_+(0) = 0.9704(32)$, where the error is the total statistical plus systematic uncertainty added in quadrature, is the most precise determination to date. Combining our result with the latest experimental measurements of $K$ semileptonic decays, one obtains the Cabibbo-Kobayashi-Maskawa matrix element $|V_{us}|=0.22290(74)(52)$, where the first error is from $f_+(0)$ and the second one is from experiment. In the first-row test of Cabibbo-Kobayashi-Maskawa unitarity, the error stemming from $|V_{us}|$ is now comparable to that from $|V_{ud}|$.

Abstract:
The lattice regularization of QCD provides us with the most systematic way of computing non-perturbative properties of hadrons directly from the first principles of QCD. The recent rapid development of parallel computers has enabled us to start realistic and systematic simulations with dynamical quarks. In this paper, I report on the first results from recent systematic studies on the lattice with dynamical quarks.

Abstract:
Enhancement of strangeness production has since long been proposed as a promising signal of quark-gluon plasma production. A convenient indicator for it is the Wroblewski parameter which has been shown to be about a factor two higher in heavy ion collisions. Using a method proposed by us earlier, we obtained lattice QCD results for the Wroblewski parameter from our simulations of QCD with two light quarks both below and above the chiral transition. Our first principles based and parameter free result compare well with the A-A data.

Abstract:
This talk reviews the progress made in the determination of the light quark masses using lattice QCD and QCD sum rules. Based on preliminary calculations with three flavors of dynamical quarks, the lattice estimate is $m_s = 75(15)$ MeV, a tantalizingly low value. On the other hand the leading estimates from scale and pseudo-scalar sum rules are $99(16)$ and $100(12)$ MeV respectively. The $\tau$-decay sum rule estimates depend very sensitively on the value of $|V_{us}|$. The central values from different analyses lie in the range 115-120 MeV if unitarity of CKM matrix is imposed, and in the range 100-105 MeV if the Particle Data Group values for $|V_{us}|$ are used. I also give my reasons for why the lattice result is not yet in conflict with rigorous lower bounds from sum rule analyses.

Abstract:
We present results from a calculation of the QCD equation of state with two light (up, down) and one heavier (strange) quark mass performed on lattices with three different values of the lattice cut-off. We show that also on the finest lattice analyzed by us observables sensitive to deconfinement and chiral symmetry restoration, respectively, vary most rapidly in the same temperature regime.

Abstract:
I review recent progress in the development of Lattice QCD into a calculational tool for nuclear physics. Lattice QCD is currently the only known way of solving QCD in the low-energy regime, and it promises to provide a solid foundation for the structure and interactions of nuclei directly from QCD.

Abstract:
We present the first two-loop calculation of the heavy quark energy shift in lattice nonrelativistic QCD (NRQCD). This calculation allow us to extract a preliminary prediction of $m_b(m_b, n_f = 5) = 4.25(12)$ GeV for the mass of the b quark from lattice NRQCD simulations performed with a lattice of spacing $a=0.12$fm. Our result is an improvement on a previous determination of the b quark mass from unquenched lattice NRQCD simulations, which was limited by the use of one-loop expressions for the energy shift. Our value is in good agreement with recent results of $m_b(m_b) = 4.163(16)$ GeV from QCD sum rules and $m_b(m_b, n_f = 5) = 4.170(25)$ GeV from realistic lattice simulations using highly-improved staggered quarks. We employ a mixed strategy to simplify our calculation. Ghost, gluon and counterterm contributions to the energy shift and mass renormalisation are extracted from quenched high-beta simulations whilst fermionic contributions are calculated using automated lattice perturbation theory. Our results demonstrate the effectiveness of such a strategy.

Abstract:
Recent Lattice QCD results are reviewed with an emphasis on spectroscopic results concerning the charm quark. It is demonstrated that, with accurate computations from lattice QCD in recent years that can be compared with the existing or upcoming experiments, stringent test of the Standard Model can be performed which will greatly sharpen our knowledge on the strong interaction.

Abstract:
In this talk, we review a QCD factorization based approach to extract parton distribution and correlation functions from lattice QCD calculation of single hadron matrix elements of quark-gluon operators. We argue that although the lattice QCD calculations are done in the Euclidean space, the nonperturbative collinear behavior of the matrix elements are the same as that in the Minkowski space, and could be systematically factorized into parton distribution functions with infrared safe matching coefficients. The matching coefficients can be calculated perturbatively by applying the factorization formalism on to asymptotic partonic states.