*V*from

_{us}/V_{ud}*f*and of

_{K}/f_{π}*V*from the K

_{us}_{l3}form factor

*f*, where both the precision and the agreement with the Standard Model are very good, clearly fell into the first category. The determination of

^{+}(0)*B*is less precise and there is a 2σ tension in the resulting value of

_{K}*|ε*. Even more challenging is the decay K --> ππ, for which however progress is being made, whereas the yet greater challenge of nonleptonic B-decays cannot be tackled with presently known methods. Chris closed his talk by reminding the audience that at another lattice conference held in Italy, namely that of 1989 (i.e. when I was just a teenager), Ken Wilson had predicted that it would take 30 years until precise results could be attained from lattice QCD, and that given that we still have nine years we are well on our way.

_{K}|The next plenary talk was given by Jochen Heitger, who spoke about heavy flavours on the lattice. Flavour physics is an important ingredient in the search for new physics, because essentially all extensions to the Standard Model have some kind of flavour structure that could be used to find them from their contributions to flavour processes. On the lattice, "gold-plated" processes with no or one hadron in the final state and a well-controlled chiral behaviour play a crucial role because they can be treated accurately. Still, treating heavy quarks on the lattice is difficult, because on needs to maintain a multiscale hierarchy of

*1/L << m*. A variety of methods are currently in use, and Jochen nicely summarised results from most of them, including, but not limited to, the current-current correlators used by HPQCD, ETMC's interpolation of ratios between the static limit and dynamical masses, and the Fermilab approach, paying special attention to the programme of non-perturbative HQET pursued by the ALPHA collaboration.

_{π}<< m_{Q}<< 1/aThe second plenary session started with a talk by Mike Peardon about improved design of hadron creation operators. The method in question is the "distillation" method that has been talked about a lot for about a year now. The basic insight at its root is that we generally use smeared operators to improve the signal-to-noise ratio, and that smearing tends to wipe out contributions from high-frequency modes of the Laplacian. If one then defines a novel smearing operator by projecting on the lowest few modes of the (spatial) Laplacian, this operator can be used to re-express the large traces appearing in correlation functions with smaller traces over the space spanned by the low-modes. If the smearing or "distillation" operator is

*D(t)=V(t)V(t)*, one defines the "perambulator"

^{+}*τ(t,t')=V(t)*that takes the place of the propagator, and reduced operators

^{+}M^{-1}(t,t')V(t')*Φ(t)=V(t)*, in terms of which to write the small traces. Insertions needed for three-point functions can be treated similarly by defining a generalised perambulator. Unfortunately, this method as it stands has a serious problem in that it scales very badly with the spatial volume -- the number of low-modes needed for a given accuracy scales with the volume, and so the method scales at least like the volume squared. However, this problem can be solved by using a stochastic estimator that is defined in the low-mode space, and the resulting stochastic method appears to perform much better than the usual "dilution" method.

^{+}ΓV(t)The last speaker of the morning was Michele Pepe with a talk on string effects in Yang-Mills theory. The subject of the talk was the measurement of the width of the effective string and the observation of the decay of unstable k-strings in SU(2) gauge theory. By using a multilevel simulation technique proposed by Lüscher and Weisz, Pepe and collaborators have been able to perform these very challenging measurements. The results for the string width agree with theoretical expectations from the Nambu-Goto action, and the expected pattern of k-string decays (1 --> 0, 3/2 --> 1/2, and 2 --> 1 --> 0) could be nicely seen in the plots.

The plenary session was closed by the announcement that LATTICE 2011 will be held from 10-16th July 2011 at the Squaw Valley Resort in Lake Tahoe, California, USA.

In the afternoon there were again parallel sessions.

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