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

Name | Dr. Paul D. Nelson |

paul.nelson@math.ethz.ch | |

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

Department | Mathematics |

Relationship | Assistant Professor |

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

401-3225-00L | Introduction to Lie Groups | 8 credits | 4G | P. D. Nelson | |

Abstract | 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. | ||||

Objective | 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. | ||||

Literature | 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) | ||||

Prerequisites / Notice | 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. Course webpage: https://metaphor.ethz.ch/x/2018/hs/401-3225-00L/ | ||||

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 |