Ignacio Garcia, Department of Pure Mathematics, University of Waterloo
“Assouad dimensions of complementary sets”
Given a positive, decreasing sequence A whose sum is L, we consider all the closed sub- sets of [0,L] such that the lengths of their complementary open intervals are in one to one correspondence with the sequence A. The sets in this class have zero Lebesgue measure. In this talk I’m going to discuss the possible values that Assouad-type dimensions which can be attained for this class of sets. In many cases, the set of attainable values is a closed interval whose endpoints we determine. This is a joint work with Kathyn Hare and Franklin Mendivil.
MC 5417