Mathematics

If a set has a relatively nice geometry, one can show that singular integrals such as the Hilbert transform are bounded. However, it turns out that the converse is true as well; if certain singular integrals are bounded, then the set must have a relatively nice geometry. This talk will discuss the co-dimension 1 case, where it has been shown that there is an equivalence between the continuity of the Riesz transforms and the underlying set it is defined on being uniformly rectifiable.