## Marc Burger: Katalogdaten im Herbstsemester 2022 |

Name | Herr Prof. Dr. Marc Burger |

Lehrgebiet | Mathematik |

Adresse | Dep. Mathematik ETH Zürich, HG G 37.1 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telefon | +41 44 632 49 73 |

Fax | +41 44 632 10 85 |

marc.burger@math.ethz.ch | |

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

Departement | Mathematik |

Beziehung | Ordentlicher Professor |

Nummer | Titel | ECTS | Umfang | Dozierende | |
---|---|---|---|---|---|

401-3225-DRL | Introduction to Lie Groups Only for ZGSM (ETH D-MATH and UZH I-MATH) doctoral students. The latter need to register at myStudies and then send an email to info@zgsm.ch with their name, course number and student ID. Please see https://zgsm.math.uzh.ch/index.php?id=forum0 | 3 KP | 4G | M. Burger | |

Kurzbeschreibung | Topological groups and Haar measure. Definition of Lie groups, examples of local fields and examples of discrete subgroups; basic properties; Lie subgroups. Lie algebras and relation with Lie groups: exponential map, adjoint representation. Semisimplicity, nilpotency, solvability, compactness: Killing form, Lie's and Engel's theorems. Definition of algebraic groups and relation with Lie groups. | ||||

Lernziel | The goal is to have a broad though foundational knowledge of the theory of Lie groups and their associated Lie algebras with an emphasis on the algebraic and topological aspects of it. | ||||

Literatur | A. Knapp: "Lie groups beyond an Introduction" (Birkhaeuser) A. Sagle & R. Walde: "Introduction to Lie groups and Lie algebras" (Academic Press, '73) F. Warner: "Foundations of differentiable manifolds and Lie groups" (Springer) H. Samelson: "Notes on Lie algebras" (Springer, '90) S. Helgason: "Differential geometry, Lie groups and symmetric spaces" (Academic Press, '78) A. Knapp: "Lie groups, Lie algebras and cohomology" (Princeton University Press) | ||||

Voraussetzungen / Besonderes | Topology and basic notions of measure theory. A basic understanding of the concepts of manifold, tangent space and vector field is useful, but could also be achieved throughout the semester. | ||||

401-3225-00L | Introduction to Lie Groups | 8 KP | 4G | M. Burger | |

Kurzbeschreibung | Topological groups and Haar measure. Definition of Lie groups, examples of local fields and examples of discrete subgroups; basic properties; Lie subgroups. Lie algebras and relation with Lie groups: exponential map, adjoint representation. Semisimplicity, nilpotency, solvability, compactness: Killing form, Lie's and Engel's theorems. Definition of algebraic groups and relation with Lie groups. | ||||

Lernziel | The goal is to have a broad though foundational knowledge of the theory of Lie groups and their associated Lie algebras with an emphasis on the algebraic and topological aspects of it. | ||||

Literatur | A. Knapp: "Lie groups beyond an Introduction" (Birkhaeuser) A. Sagle & R. Walde: "Introduction to Lie groups and Lie algebras" (Academic Press, '73) F. Warner: "Foundations of differentiable manifolds and Lie groups" (Springer) H. Samelson: "Notes on Lie algebras" (Springer, '90) S. Helgason: "Differential geometry, Lie groups and symmetric spaces" (Academic Press, '78) A. Knapp: "Lie groups, Lie algebras and cohomology" (Princeton University Press) | ||||

Voraussetzungen / Besonderes | Topology and basic notions of measure theory. A basic understanding of the concepts of manifold, tangent space and vector field is useful, but could also be achieved throughout the semester. | ||||

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

Kurzbeschreibung | Research colloquium | ||||

Lernziel |