to incremental development of known techniques, and

-   fantasies – grand problems that we can articulate, but presently lack usable tools to address.

I’ve had fun using this framework to think strategically about the future, in general. I’ll use it here to touch on three major branches of lattice gauge theory – few-body, many-body, and conceptual/algorithmic aspects – by providing a couple of examples in each category.

Fundamental Particle Physics
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Opportunities
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### The Best Determination of $\alpha_s$

A major triumph of lattice QCD is already enshrined in the Particle Data Book, as shown in Figure 1. Nonperturbative calculations of heavy quark spectroscopy provide a precision determination of $\alpha_s$ competitive with the most accurate determinations from perturbative QCD. There is probably more room for improvement on the nonperturbative side, because on that side the relation of the calculations to observables are in principle more tightly controlled (no structure functions, jet parameterizations, ... ), the experimental measurements are very precise, and one is accessing $\alpha_s$ (or $\alpha_s^p, p>0$) effects directly, rather than digging them out as corrections. It is important to pursue this direction further, for several reasons.

Most obviously, a better determination of $\alpha_s$, by sharpening input to the 