# 401-3110-68L Fractal Geometry

Semester | Autumn Semester 2018 |

Lecturers | M. Einsiedler, further speakers |

Periodicity | non-recurring course |

Language of instruction | English |

Comment | Number of participants limited to 12. Registration to the seminar will only be effective once confirmed by the organisers. Please contact Link. |

### Courses

Number | Title | Hours | Lecturers | |||||||
---|---|---|---|---|---|---|---|---|---|---|

401-3110-68 S | Fractal Geometry Advisors: R. Prohaska and Prof. M. Einsiedler | 2 hrs |
| M. Einsiedler, further speakers |

### Catalogue data

Abstract | Introductory seminar about the mathematical foundations of fractal geometry and its applications in various areas of mathematics |

Objective | |

Content | Foundations: - 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 |

Literature | Kenneth Falconer: Fractal Geometry, Mathematical Foundations and Applications. |

Prerequisites / Notice | Prerequisites: 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. |

### Performance assessment

Performance assessment information (valid until the course unit is held again) | |

Performance assessment as a semester course | |

ECTS credits | 4 credits |

Examiners | M. Einsiedler |

Type | ungraded semester performance |

Language of examination | English |

Repetition | Repetition only possible after re-enrolling for the course unit. |

### Learning materials

Main link | Homepage |

Only public learning materials are listed. |

### Groups

No information on groups available. |

### Restrictions

Places | Limited number of places. Special selection procedure. |

Waiting list | until 20.09.2018 |

End of registration period | Registration only possible until 19.09.2018 |

### Offered in

Programme | Section | Type | |
---|---|---|---|

Mathematics Bachelor | Seminars | W |