## Paul D. Nelson: Catalogue data in Spring Semester 2019 |

Name | Dr. Paul D. Nelson |

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

Department | Mathematics |

Relationship | Assistant Professor |

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

401-3226-01L | Representation Theory of Lie Groups | 8 credits | 4G | P. D. Nelson | |

Abstract | This course will contain two parts: * Introduction to unitary representations of Lie groups * Introduction to the study of discrete subgroups of Lie groups and some applications. | ||||

Objective | The goal is to acquire familiarity with the basic formalism and results concerning unitary representations of Lie groups, and to apply these to the study of discrete subgroups, especially lattices, in Lie groups. | ||||

Content | * Unitary representations of compact Lie groups: Peter-Weyl theory, weights, Weyl character formula * Introduction to unitary representations of non-compact Lie groups: the examples of SL(2,R), SL(2,C) * Example: Property (T) for SL(n,R) * Discrete subgroups of Lie groups: examples and some applications | ||||

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

Prerequisites / Notice | Differential geometry, Functional analysis, Introduction to Lie Groups (or equivalent). | ||||

401-5110-00L | Number Theory Seminar | 0 credits | 1K | Ö. Imamoglu, P. S. Jossen, E. Kowalski, P. D. Nelson, R. Pink, G. Wüstholz | |

Abstract | Research colloquium | ||||

Objective | Talks on various topics of current research. | ||||

Content | Research seminar in algebra, number theory and geometry. This seminar is aimed in particular to members of the research groups in these areas and their graduate students. |