Kathryn Hare, Department of Pure Mathematics, University of Waterloo
"Local dimensions of self-similar measures with overlap"
The local dimension of a measure is a way to quantify its local behaviour. For example, the local dimension of Lebesgue measure is one everywhere, reflecting the fact that it is uniform in its concentration. For self-similar measures that satisfy a suitable separation condition, it is well known that the set of attainable local dimensions is a closed interval, but for measures which fail to satisfy this condition the situation is more complicated and unclear. In this talk we will discuss a general theory for a class of measures with overlap, which includes interesting examples such as Bernoulli convolutions and convolutions of Cantor measures, and we will see that different phenomena can arise.
This is joint work with Kevin Hare and various students.
MC 5417