### Differential Geometry (Summer Semester 2022)

- Lecturer: Prof. Dr. Wilderich Tuschmann
- Classes: Lecture (0100300), Problem class (0100310)
- Weekly hours: 4+2

The course will take place in a special hybrid format under participation of students from Shanghai Jiao Tong University and, as a second instructor, Prof. Dr. Horst Hohberger from the SJTU - Michigan Joint Institute.

Course material will be made available on the Ilias page.

Schedule | ||
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Lecture: | Wednesday 11:45 - 13:15 (!) (shift due to SJTU schedule requirements) | 20.30 SR 2.59 |

Thursday 9:45-11:15 | 20.30 SR 2.67 | |

Problem class: | Friday 8:00-9:30 | 20.30 1. OG R. 1.66/ 1.67 |

Lecturers | ||
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Lecturer | Prof. Dr. Wilderich Tuschmann | |

Office hours: by appointment | ||

Room 1.002 Kollegiengebäude Mathematik (20.30) | ||

Email: tuschmann@kit.edu | ||

Problem classes | Dr. Philippe Kupper | |

Office hours: | ||

Room 1.016 Kollegiengebäude Mathematik (20.30) | ||

Email: philippe.kupper@kit.edu |

Differential Geometry is one of the most research intensive areas of mathematics in the late twentieth and early twenty-first century. Going back to the seminal studies by Gauss, it has not only a long history, but its modern form given by Riemann can also trace its development back well over a hundred years. Its current prominence stems in part from its position at a crossroads of many active mathematical research fields, such as geometric analysis, topology, discrete and metric geometry, analysis, partial differential equations, Lie and geometric group theory, stochastics on manifolds, etc., and looking beyond the confines of mathematics, the subject continues to influence and be influenced by theoretical physics and has a multitude of further applications as, e.g., in engineering, robotics, computer vision, and machine learning. In particular, being the mathematical backbone of Einstein’s theory of general relativity, Differential Geometry lies at the core of any modern location technologies like the nowadays indispensable global positioning system (GPS), and is a fundamental tool in cutting-edge research in robotics assisted nanoprecision surgery, manifold learning and protein design.

The course itself will cover fundamental concepts, methods and results of differential geometry and analysis on manifolds, together with glimpses into some of their above-mentioned applications. In particular, it will treat smooth manifolds, tensors and Riemannian metrics, linear connections, covariant derivatives and parallel translation, geodesics and curvature.

Prerequisites:

Analysis I-III, Linear Algebra I,II, basic concepts of topology as, e.g., studied in the KIT course 'Elementare Geometrie'.