many important maps in algebraic combinatorics (the rsk bijection, the schutzenberger involution, etc.) can be described by piecewise-linear formulas. these formulas can then be ``de-tropicalized,'' or ``lifted,'' to subtraction-free rational functions on an algebraic variety, and certain properties of the combinatorial maps become more transparent in the algebro-geometric setting. i will illustrate how this works in the case of the promotion map on semistandard tableaux of rectangular shape. i will also indicate how promotion can be viewed as the combinatorial manifestation of a symmetry coming from representation theory, and how its geometric lift fits into berenstein and kazhdan's theory of geometric crystals.