Title:   Counteracting flatness with affine arclength measure
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 Abstract:  There are many operators in harmonic analysis for which the
 curvature of some underlying manifold plays a significant role.  We
 will discuss recent efforts to establish uniform estimates for such
 operators by compensating for degeneracies of curvature with an
 appropriate measure.  We will focus on the case when the underlying
 manifolds are polynomial curves.