Original Differentiable Manifolds
Original Differentiable Manifolds
Meetings: Fridays, 8:30 PM
Reference: An Introductory Course on Differentiable Manifolds, Siavash Shahshahani, Dover Publications, 2016.
If you are interested to participate in the meetings, send me an email: masoudma311@gmail.com
Presenter: Masoud Ahmadi
In this session we talked about the following:
-Definition of Topological Manifolds
-Some background and motivation for studying Multilinear Algebra
-An overview of Tensors, especially Alternating Tenors
Presenter: Pegah Mohammadipour
We covered the notions of tangent spaces, tangent bundles and vector fields. We also discussed some of their properties and learned that differentiation is defined on this new frame work.
Presenter: Newsha Karimi
Presenter: Masoud Ahmadi
In this session we talked about the following:
-Review of tangent space, tangent bundle, and tangent map
-Introduction to Derivations
-Taylor's remainder theorem
-Proving the isomorphism between the module of vector fields and the module of derivations
-Definition of Lie bracket and its geometric interpretation
Presenter: Masoud Ahmadi
In this session we talked about the following:
-Definition of topological manifolds
-Smooth structure on manifolds
-Functions on manifolds