Wednesdays 11-1. From 16 January to 6 March.
Typed notes (latex) (updated 8 March), containing problems for credit too.
Tentative List of Main Topics
Baire category theorem and its applications in fractal geometry
- Kakeya (Besicovitch) sets. Proof of existence using the Baire category theorem.
- Typical Nikodym sets.
- Dimension of Kakeya sets. Cordoba's L^2 argument.
Mapping planar sets of positive Lebesgue measure onto balls
- Covering planar sets by Lipschitz strips. The Matousek--Preiss proof using Dilworth's theorem on chains/antichains
- Uy's proof using complex & harmonic analysis
Solid background in measure theory. Previous exposure to Hausdorff dimension and Baire category can be helpful.