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 | |
---|---|---|---|---|---|

401-3226-01L | Unitary Representations of Lie Groups | 8 credits | 4G | M. Einsiedler | |

Abstract | This course will introduce unitary representations of Lie groups, discuss spectral gap in general, and discuss concrete unitary representations of SL(2,R). | ||||

Learning objective | The goal is to acquire familiarity with the basic formalism and results concerning Lie groups and their unitary representations. In the second part we will consider concrete representations of SL(2,R) and decompose these into irreducible representations or at least understand whether spectral gap is present. | ||||

Content | The course will start with the general framework of unitary representations of locally compact groups, which is in some sense a general theory of Fourier analysis related to groups. For this some functional analysis (in particular spectral theory of bounded selfadjoint operators, Krein-Milman and Choquet) will be important. In the interest of time we will only summarise the case abelian groups and use the abelian theory to understand some metabelian groups. After this we will discuss some more general theory. Some of the general phenomena will be discussed for the concrete group of SL(2,R). Moreover, we will understand the unitary dual of SL(2,R), discuss the notion of spectral gap for SL(2,R), and decompose the unitary representation of SL(2,R) arising from the hyperbolic plane into irreducible representation. | ||||

Lecture notes | Unitary Representations and Unitary Duals, book project joint with Tom Ward, see https://tbward0.wixsite.com/books/unitary | ||||

Literature | Bekka, de la Harpe and Valette: "Kazhdan's Property (T)", Cambridge University Press. | ||||

Prerequisites / Notice | Prerequisites: Functional Analysis I and a bit of Lie Groups I. The simultaneous course Functional Analysis II in SS 22 by M. Burger will treat some of the prerequisites of this course and also some related but different aspects of unitary representations. This course will be cancelled if it should it be impossible to teach in presence, but according to info by Bundesrat and ETH it seems that we will be able to hold the course. | ||||

401-3227-DRL | Unitary Representations of Lie Groups Only for ETH D-MATH doctoral students and for doctoral students from the Institute of Mathematics at UZH. The latter need to send an email to Jessica Bolsinger (info@zgsm.ch) with the course number. The email should have the subject „Graduate course registration (ETH)“. | 2 credits | 4G | M. Einsiedler | |

Abstract | This course will introduce unitary representations of Lie groups, discuss spectral gap in general, and discuss concrete unitary representations of SL(2,R). | ||||

Learning objective | The goal is to acquire familiarity with the basic formalism and results concerning Lie groups and their unitary representations. In the second part we will consider concrete representations of SL(2,R) and decompose these into irreducible representations or at least understand whether spectral gap is present. | ||||

Content | The course will start with the general framework of unitary representations of locally compact groups, which is in some sense a general theory of Fourier analysis related to groups. For this some functional analysis (in particular spectral theory of bounded selfadjoint operators, Krein-Milman and Choquet) will be important. In the interest of time we will only summarise the case abelian groups and use the abelian theory to understand some metabelian groups. After this we will discuss some more general theory. Some of the general phenomena will be discussed for the concrete group of SL(2,R). Moreover, we will understand the unitary dual of SL(2,R), discuss the notion of spectral gap for SL(2,R), and decompose the unitary representation of SL(2,R) arising from the hyperbolic plane into irreducible representation. | ||||

Lecture notes | Unitary Representations and Unitary Duals, book project joint with Tom Ward, see https://tbward0.wixsite.com/books/unitary | ||||

Literature | Bekka, de la Harpe and Valette: "Kazhdan's Property (T)", Cambridge University Press. | ||||

Prerequisites / Notice | Prerequisites: Functional Analysis I and a bit of Lie Groups I. The simultaneous course Functional Analysis II in SS 22 by M. Burger will treat some of the prerequisites of this course and also some related but different aspects of unitary representations. This course will be cancelled if it should it be impossible to teach in presence, but according to info by Bundesrat and ETH it seems that we will be able to hold the course. | ||||

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 |