Name | Prof. Dr. Manfred Einsiedler |

Field | Mathematics |

Address | Professur für Mathematik ETH Zürich, HG G 64.2 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 31 84 |

manfred.einsiedler@math.ethz.ch | |

URL | http://www.math.ethz.ch/~einsiedl |

Department | Mathematics |

Relationship | Full Professor |

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

401-3378-19L | Entropy in Dynamics | 8 credits | 4G | M. Einsiedler | |

Abstract | Definition and basic property of measure theoretic dynamical entropy (elementary and conditionally). Ergodic theorem for entropy. Topological entropy and variational principle. Measures of maximal entropy. Equidistribution of periodic points. Measure rigidity for commuting maps on the circle group. | ||||

Learning objective | The course will lead to a firm understanding of measure theoretic dynamical entropy and its applications within dynamics. We will start with the basic properties of (conditional) entropy, relate it to the question of effective coding techniques, discuss and prove the Shannon-McMillan-Breiman theorem that is also known as the ergodic theorem for entropy. Moreover, we will discuss a topological counter part and relate this topological entropy to the measure theoretic entropy by the variational principle. We will use these methods to classify certain natural homogeneous measures, prove equidistribution of periodic points on compact quotients of hyperbolic surfaces, and establish a measure rigidity theorem for commuting maps on the circle group. | ||||

Lecture notes | Entropy book under construction, available online under https://tbward0.wixsite.com/books/entropy | ||||

Prerequisites / Notice | No prior knowledge of dynamical systems will be assumed but measure theory will be assumed and very important. Doctoral students are welcome to attend the course for 2KP. | ||||

401-5370-00L | Ergodic Theory and Dynamical Systems | 0 credits | 1K | M. Akka Ginosar, M. Einsiedler, University lecturers | |

Abstract | Research colloquium | ||||

Learning objective | |||||

401-5530-00L | Geometry Seminar | 0 credits | 1K | M. Burger, M. Einsiedler, P. Feller, A. Iozzi, U. Lang, University lecturers | |

Abstract | Research colloquium | ||||

Learning objective | |||||

406-2005-AAL | Algebra I and IIEnrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 12 credits | 26R | M. Burger, M. Einsiedler | |

Abstract | Introduction and development of some basic algebraic structures - groups, rings, fields including Galois theory, representations of finite groups, algebras. The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. | ||||

Learning objective | |||||

Content | Basic notions and examples of groups; Subgroups, Quotient groups and Homomorphisms, Group actions and applications Basic notions and examples of rings; Ring Homomorphisms, ideals, and quotient rings, rings of fractions Euclidean domains, Principal ideal domains, Unique factorization domains Basic notions and examples of fields; Field extensions, Algebraic extensions, Classical straight edge and compass constructions Fundamentals of Galois theory Representation theory of finite groups and algebras | ||||

Literature | Joseph J. Rotman, "Advanced Modern Algebra" third edition, part 1, Graduate Studies in Mathematics,Volume 165 American Mathematical Society |