L^p-Improving Estimates and Restriction in Intermediate Dimensions

Philip Gressman
University of Pennsylvania

I will discuss some recent results dealing with Convolution and Fourier restriction relating to submanifolds of intermediate dimension, i.e., when dimension equals codimension. In some cases it is possible to find submanifolds of nonvanishing rotational curvature and maximal Fourier decay, but it turns out that this can happen in only finitely many cases, and even when such examples may be found they are not generic outside of the case of curves in the plane. The talk will provide some answers to the question of what the appropriate substitutes for curvature are in the intermediate case and show how these substitute notions relate (and sometimes fully supersede) the more common ones.

Presentation (PDF File)

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