The last day consisted of plenary sessions only. The first plenary, chaired by Anna Hasenfratz, was right after another indoors breakfast. The first speaker was Richard Brower, who gave a non-lattice talk about QCD and string theory, or more specifically the search for a dual description of QCD in the form of string theory on an AdS background. He started out by giving a historical overview of the development of string theory from its beginnings as an attempt to describe the strong interactions based on the observed behaviour of Regge trajectories and s-t duality, recounting the well-known failure of string theory to capture the correct hard scattering behaviour in strong interactions, along with the need to incorporate gravity. The situation changed with the discovery of dualities and the AdS/CFT correspondence: now string theory on an AdS

^{5}x S

^{5}background is dual to N=4 Super-Yang-Mills theory in a 4d spacetime, with the strong coupling limit of SYM corresponding to the weak coupling limit of AdS. Of course we know that QCD is not a superconformal theory, so a description of QCD based on AdS/CFT has to break the conformal symmetry by introducing a boundary along the fifth-dimension of AdS

^{5}; there are a number of models of this kind, and while they manage to reproduce some qualitative features of the QCD glueball spectrum as seen on the lattice, other features are qualitatively different, and the quantitative agreement is usually rather poor. However, there is some hope that an exact string dual of QCD might still be found, returning string theory to its origins as a theory of the strong interactions.

The second talk was by Mark Alford, who spoke about colour superconductivity. Colour superconductivity arises via the BCS mechanism just like ordinary superconductivity, but instead of a weakly attractive phonon-mediated attraction, quarks attract via the much stronger strong interactions, making Cooper-pairing even more efficient. Hence we expect QCD matter to be colour superconducting at large chemical potentials, making this phase probably relevant for the study of the interior of neutron stars. Unfortunately, that region of the QCD phase diagram is not (yet) accessible on the lattice due to the sign problem. In the limit of infinite chemical potential, perturbative descriptions are possible; NJL models provide another qualitative description of this phase. What is found is that in this limit, for N

_{f}=3 massless flavours, a curious phenomenon called colour-flavour locking (CFL) occurs: Light quarks of a given flavour only occur carrying a given colour charge, breaking the symmetry group from SU(3)

_{c}x SU(3)

_{L}x SU(3)

_{R}x U(1)

_{B}to SU(3)

_{CFL}x Z

_{2}. The electromagnetic gauge group U(1)

_{Q}, which was embedded in the SU(3)

_{L}x SU(3)

_{R}chiral group, is now changed into an U(1)

_{Q'}subgroup of SU(3)

_{CFL}due to photon-gluon mixing. This phase is therefore somewhat weird. It becomes complicated due to the fact that the strange mass isn't really zero, and also due to the weak interactions breaking flavour (while this is a weak effect, a compact star exists for a long time, giving the weak interactions time to act and affect the equilibrium); models indicate that this will lead to a complex phase structure in the regime of intermediate chemical potential. However, it is also known that a number of the phase found in the models, the so-called gapless phases, are artifacts and will not exist in full QCD; what will replace them is not known, and may not become known until a way to resolve the sign problem on the lattice is found.

After the coffee break the second plenary session was chaired by Peter Weisz, on behalf of the Local Organising Committee for next year's lattice meeting to be held in Regensburg, Germany. The session started with Tommy Burch extending a warm invitation to Regensburg to everyone and extolling its virtues as a lovely city and excellent conference venue. Lattice 2007 will be at Regensburg from 30th July to 4th August 2007, dates that should be in every lattice theorists diary. Peter Weisz thanked the Local Organizing Committe in Tucson for organizing such a splendid conference, which was met with lots of applause.

The first talk of the last session was Urs Heller speking about Lattice QCD at finite temperature (and zero chemical potential), concentrating especially on the nature of the transition as a function of the light quark masses, and on the QCD equation of state. On the first count, it seems conclusive by now that at the physical values of m

_{u,d}and m

_{s}the phase transition is in fact a crossover rather than a first-order transition. On the second count, the low-temperature description QCD matter by a hadron resonance gas and the high-temperature description by finite-temperature perturbation theory seem to match quite well onto the lattice data in their respective domains of validity. Some studies of non-static finite-temperature physics, such as transport coefficients, also are beginning to be undertaken on the lattice now.

The second speaker was Joel Giedt, who talked about lattice SUSY. Unfortunately this is a sufficiently technical field which is rather remote from my area of expertise, and thus I feel unable to give a reasonable summary of his talk. What I believed to understand was that a number of supersymmetric lattice theories are now known, that there is some problem with the Kähler potential being underconstrained by the symmetries and that actual lattice simulations might be helpful there, as well as in studying the AdS

^{3}/CFT

_{2}correspondence.

The final talk was by Tom DeGrand, who was the only plenary (and probably simply the only) speaker to use foils and an overhead projector instead of a digital presentation to speak about the N

_{f}=1 quark condensate. In the N

_{c}--> &infinity; limit, it is found that N

_{f}=1 QCD with quarks in the antisymmetric representation corresponds to N=1 Super-Yang-Mills theory. N

_{f}=1 QCD is peculiar in that there are no light pions, only a massive η'. When overlap fermions are being used to simulate at a fixed gauge topology, it becomes possible to determine the quark condensate via the spectrum of the overlap Dirac operator; in this way, the 1/N

_{c}corrections to the N

_{c}--> &infinity; limit are found to be small even at N

_{c}=3.

At noon, the symposium was adjourned, and the participants began to scatter.

Since my flight only left in the evening, I managed to go and sneak a look at a very interesting historical monument located near Tucson, the San Xavier de Bac mission church. This mission was founded by the Jesuits in the late 17th century and completed by Franciscans in the mid-18th century. The church itself is built in a colourful version of the baroque style with many elements of "naive" or peasant art in the ornamentation, suggesting that it was planned by the missionaries and executed by the local Natives, the Tohono O'odham, themselves. The white walls of the towers are visible from afar across the desert, giving this remarkable church the nickname "white dove of the desert".

As for the trip to Tucson, I feel little need to bore my readers with the details of our 15-hour zig-zag trip across the North American continent via L.A. and Toronto to Regina, and thus conclude my report on the Lattice 2006 meeting at this point. Thank you for reading; if and when I feel like it, I may follow-up with an overall summary of the conference later.