Title: Resonance between Cantor sets and applications.

Abstract: if C_1 and C_2 are two subsets of the real line, we say that
they are geometrically resonant if the Hausdorff dimension of the sumset
C_1+C_2 is strictly less than the sum of the Hausdorff dimensions of C_1
and C_2 (assuming the latter is at most 1). I will review a joint result
with Y. Peres which gives the sharp condition for geometric resonance in
the case where C_1 and C_2 are self-similar sets, and discuss related
recent work (much of it in progress) and, if time allows, some
applications.