Homeomorphism groups of the Airplane and the Basilica Julia sets
By Bruno Duchesne
Numerical quadrature for singular integrals over self-similar measures on fractal sets
By David Hewett
The talk will review recent work on intermediate dimensions which interpolate between Hausdorff and box dimensions. We relate these dimensions to capacities which leading to ‘Marstrand-type’ theorems on the intermediate dimensions of projections of a set in $\mathbb{R}^{n}$ onto almost all m-dimensional subspaces. This is collaborative work with various combinations of Stuart Burrell, Jonathan Fraser, Tom Kempton and Pablo Shmerkin.