## Ergänzungsvorlesung Einführung in das Atiyah-Singer-Index-Theorem

Instructors: apl. Prof. Dr. Stephan KlausCourse No.: 08.105.0228

Course Type: Vorlesung

### Contents

Evolution equations on manifolds are connecting geometry, topology and analysis. The most simple case consists of tangent vector fields and their associated flows, generalizing the connection between Lie algebras and Lie groups. More interesting evolution equations are coming from geometry, in particular from Riemannian manifolds and their embeddings in other spaces. Examples are given by the mean curvature flow and the Ricci flow. In the past years, there were spectacular new results in these topics, in particular by the work of Perelman. In our lectures we give a survey on methods, results and application, concerning for example positive curvature, Thurston's geometrization conjecture, the Poincaré conjecture and space forms.#### Dates

Date (Day of the week) | Time | Location |
---|---|---|

11/03/2022 (Thursday) | 14:15 - 16:00 | 04 422 2413 - Neubau Physik/Mathematik |

11/17/2022 (Thursday) | 14:15 - 16:00 | 04 422 2413 - Neubau Physik/Mathematik |

12/01/2022 (Thursday) | 14:15 - 16:00 | 04 422 2413 - Neubau Physik/Mathematik |

12/15/2022 (Thursday) | 14:15 - 16:00 | 04 422 2413 - Neubau Physik/Mathematik |

01/12/2023 (Thursday) | 14:15 - 16:00 | 04 422 2413 - Neubau Physik/Mathematik |

01/26/2023 (Thursday) | 14:15 - 16:00 | 04 422 2413 - Neubau Physik/Mathematik |

02/02/2023 (Thursday) | 14:15 - 16:00 | 04 422 2413 - Neubau Physik/Mathematik |