## Joaquim Serra: Catalogue data in Spring Semester 2022 |

Name | Prof. Dr. Joaquim Serra |

Field | Mathematics |

Address | Professur für Mathematik ETH Zürich, HG J 54 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 50 60 |

joaquim.serra@math.ethz.ch | |

Department | Mathematics |

Relationship | Associate Professor |

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

401-3532-DRL | Differential Geometry II Only for ETH D-MATH doctoral students and for doctoral students from the Institute of Mathematics at UZH. The latter need to send an email to Jessica Bolsinger (info@zgsm.ch) with the course number. The email should have the subject „Graduate course registration (ETH)“. | 3 credits | 4V + 1U | J. Serra | |

Abstract | This is a continuation course of Differential Geometry I. Topics covered include: Introduction to Riemannian geometry: Riemannian manifolds, Levi-Civita connection, geodesics, Hopf-Rinow Theorem, curvature, second fundamental form, Riemannian submersions and coverings, Hadamard-Cartan Theorem, triangle and volume comparison, and isoperimetric inequalities. | ||||

Learning objective | Providing an introductory invitation to Riemannian geometry. | ||||

Literature | - M. P. do Carmo, Riemannian Geometry, Birkhäuser 1992 - I. Chavel, "Riemannian Geometry: A Modern Introduction" 2nd ed. (2006), CUP, - S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry, Springer 2004 - S. Kobayashi, K. Nomizu "Foundations of Differential Geometry" Volume I (1963) Wiley, | ||||

Prerequisites / Notice | Differential Geometry I (or basics of differentiable manifolds) | ||||

401-3532-08L | Differential Geometry II | 10 credits | 4V + 1U | J. Serra | |

Abstract | This is a continuation course of Differential Geometry I. Topics covered include: Introduction to Riemannian geometry: Riemannian manifolds, Levi-Civita connection, geodesics, Hopf-Rinow Theorem, curvature, second fundamental form, Riemannian submersions and coverings, Hadamard-Cartan Theorem, triangle and volume comparison, and isoperimetric inequalities. | ||||

Learning objective | Providing an introductory invitation to Riemannian geometry. | ||||

Literature | - M. P. do Carmo, Riemannian Geometry, Birkhäuser 1992 - I. Chavel, "Riemannian Geometry: A Modern Introduction" 2nd ed. (2006), CUP, - S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry, Springer 2004 - S. Kobayashi, K. Nomizu "Foundations of Differential Geometry" Volume I (1963) Wiley, | ||||

Prerequisites / Notice | Differential Geometry I (or basics of differentiable manifolds) | ||||

401-5350-00L | Analysis Seminar | 0 credits | 1K | A. Carlotto, A. Figalli, N. Hungerbühler, M. Iacobelli, L. Kobel-Keller, T. Rivière, J. Serra, University lecturers | |

Abstract | Research colloquium | ||||

Learning objective | |||||

Content | Research seminar in Analysis |