Analysis Seminar

Kathryn Hare, Department of Pure Mathematics, University of Waterloo

"The size of complementary sets"

Various dimensions have been introduced to quantify the size of subsets of R of Lebesgue measure zero. A classic problem is to ask what dimensions can be achieved by the family that consists of all the closed sets whose complements are the disjoint union of open intervals of the same lengths as a given Cantor set. We will discuss recent work on this problem where we consider a spectrum of dimensions that fall between box and Assouad dimensions. In particular, we will discuss the problem of determining the dimension of a generic set within a given family.

MC 5417