Organizer

Roland Prohaska

Time

Thursday 15-17

Room

CLA E 4

The first meeting will be on September 20th.

Week	Topics	References	Speakers
1	Introduction Box-counting dimension	[Fa] Introduction [Fa] §2.1-2.2	Roland Prohaska Massimo Jörin
2	Review of some Measure Theory Hausdorff measure and dimension	[Fa] §1.3, [Fo] §1, §11.2 [Fa] §3.1-3.4	Roland Prohaska Jacopo Nannini
3	Mass distribution principle Diophantine approximation	[Fa] §4.1 [Fa] §10.3, [BGP] §1.1-1.3	Amanda Jenny Erik Jahn
4	Iterated function systems (IFS) IFS: dimension of self-similar sets	[Fa] §9.1, §9.5 [Fa] §9.2	Ryan Mukherjee Xiao Yang
5	IFS: self-affine sets IFS: variations	[Fa] §9.4, [Fa3] §2, §4 [Fa] §9.3, §10.2	Joel Schmitz Laura Chalabi
6	Graphs of functions Potential theoretic method	[Fa] §11.1 [Fa] §4.2-4.3	Marc Dollmann Antoine Tinguely
7	Local structure	[Fa] §5.1 [Fa] §5.2-5.3	Alessandro Imparato Charlotte Dombrowsky
8	Projections	[Fa] §6.1-6.2, [Fa2] §6.4 [Fa] §6.3, [Fa4] §2-5	Amanda Jenny Marc Dollmann
9	Products Kakeya problem	[Fa] §7.1 [Fa] §12.1, [Fa2] §7.1-7.2	Charlotte Dombrowsky Massimo Jörin
10	Julia sets and the Mandelbrot set	[Fa] §14.1 [Fa] §14.2	Antoine Tinguely Jacopo Nannini
11	Julia sets and the Mandelbrot set (contd.)	[Fa] §14.3	Alessandro Imparato
12	Julia sets and the Mandelbrot set (contd.) Fractal groups and rings	[Fa] §14.4-14.5, [FaM] [Fa] §12.4, [EM] §1	Laura Chalabi Ryan Mukherjee
13	Random fractals Brownian motion	[Fa] §15.1 [Fa] §16.1 [Fa] §16.2	Erik Jahn Xiao Yang Joel Schmitz
14	Early Christmas break

• [Fa] Kenneth Falconer. Fractal Geometry: Mathematical Foundations and Applications. Wiley, Chichester, third edition, 2014.
• [Fa2] K. J. Falconer. The geometry of fractal sets. Cambridge University Press, Cambridge, 1985.
• [Fa3] K. J. Falconer. The Hausdorff dimension of self-affine fractals. Math. Proc. Cambridge Philos. Soc. 103 (1988), no. 2, 339-350.
• [Fa4] K. J. Falconer. Sets with prescribed projections and Nikodym sets. Proc. London Math. Soc. (3) 53 (1986), no. 1, 48-64.
• [FaM] K. J. Falconer, D. T. Marsh. Classification of quasi-circles by Hausdorff dimension. Nonlinearity 2 (1989), no. 3, 489-493.
• [Fo] Gerald B. Folland. Real Analysis: Modern Techniques and Their Applications. Wiley, New York, second edition, 1999.
• [BGP] Badziahin, Gorodnik, Peyerimhoff (editors). Dynamics and Analytic Number Theory. Cambridge University Press, Cambridge, 2016.
• [EM] G. A. Edgar, Chris Miller. Borel subrings of the reals. Proc. Amer. Math. Soc. 131 (2003), no. 4, 1121-1129.