Seminar ''Differential Forms on Smooth Manifolds''
Dozent: Prof. Dr. Alexander Lytchak
The seminar is take place on Wednesdays 11:30 - 13:00 at SR 2.059 (UG) Geb. 20.30
Content:
The smooth manifolds are everywhere in Mathematics. They appear as Riemannian manifolds in differential geometry, spacetimes in general relativity, phase spaces in mechanics, and so on. On this seminar we will investigate extending the main ideas of calculus – differentiation and integration - to multidimensional smooth manifolds.
This seminar will cover the following key concepts: tangent and cotangent bundle, tensor algebra, differential forms, derivative and integration of forms on manifolds.
The highlights of the seminar are
- the Generalized Stoke's Theorem
- the Introduction to De Rham cohomology.
References:
- C. Gorodski, Smooth Manifolds, Springer, 2020
- V. Guillemin, and P. Haine, Differential Forms, New Jersey : World Scientific, 2019.
- R. Bishop, S. Goldberg, Tensor Analysis on Manifolds, NY, 1968
- Tu L. Tu, Differential Geometry, Springer, 2017
Literature references are provided to offer an initial overview of presentation topics. Upon topic assignment, participants will receive more detailed information on the specific results, proofs, definitions, etc. to be presented.
Prerequisites: Linear algebra I-II, Analysis I-III, understanding the basic notion of a smooth manifold
For more information please visit the corresponding ILIAS page.
Registration: closed
Kontakt: If you have any questions, please contact: Dr. Darya Sukhorebska, darya.sukhorebska@kit.edu