401-3110-68L  Fractal Geometry

SemesterAutumn Semester 2018
LecturersM. Einsiedler, further speakers
Periodicitynon-recurring course
Language of instructionEnglish
CommentNumber of participants limited to 12.
Registration to the seminar will only be effective once confirmed by the organisers. Please contact Link.


AbstractIntroductory seminar about the mathematical foundations of fractal geometry and its applications in various areas of mathematics
Objective
ContentFoundations:
- classical examples
- notions of dimension and their calculation
- local structure
- projections, products, intersections

Possible Applications:
- Dynamical Systems: iterated function systems, self-similar and self-affine sets
- Pure Mathematics: the Kakeya problem, fractal groups and rings, graphs of functions
- Complex Dynamics: Julia sets and the Mandelbrot set, Vitushkin's conjecture
- Number Theory: distribution of digits, continued fractions, Diophantine approximation
- Probability Theory: random fractals, Brownian motion
LiteratureKenneth Falconer: Fractal Geometry, Mathematical Foundations and Applications.
Prerequisites / NoticePrerequisites: Content of the first two years of the ETH Bachelor program in mathematics, especially measure theory and topology. Some applications require complex analysis and probability theory.

In order to obtain the 4 credit points, each student is expected to give two 1h-talks and regularly attend the seminar.