## Alessandra Iozzi: Catalogue data in Autumn Semester 2020 |

Name | Prof. em. Dr. Alessandra Iozzi |

Address | Dep. Mathematik ETH Zürich, HG G 37.4 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 35 88 |

alessandra.iozzi@math.ethz.ch | |

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

Department | Mathematics |

Relationship | Retired Adjunct Professor |

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

401-3225-00L | Introduction to Lie Groups Self-service registration for this course unit in myStudies has been closed. | 8 credits | 4G | A. Iozzi | |

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/2020/hs/401-3225-00L/ | ||||

401-5000-00L | Zurich Colloquium in Mathematics | 0 credits | R. Abgrall, A. Bandeira, M. Iacobelli, A. Iozzi, S. Mishra, R. Pandharipande, University lecturers | ||

Abstract | The lectures try to give an overview of "what is going on" in important areas of contemporary mathematics, to a wider non-specialised audience of mathematicians. | ||||

Objective | |||||

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

Abstract | Research colloquium | ||||

Objective | |||||

401-5990-00L | Zurich Graduate Colloquium | 0 credits | 1K | A. Iozzi, University lecturers | |

Abstract | The Graduate Colloquium is an informal seminar aimed at graduate students and postdocs whose purpose is to provide a forum for communicating one's interests and thoughts in mathematics. | ||||

Objective |