The theory of convex integration has proven itself to be a very powerful tool to construct surprising, unexpected examples in various context. For instance
- irregular stationary points to generalized convex functionals
- surprising "quasiconformal" maps lacking seemingly natural integrability
- flexible isometric embeddings, e.g. for spheres
- unphysical solutions to the Euler equation
to mention just a view.
In this seminar we invite you to join us while entering the subject.
We will start from the very basics. In particular we begin with the so called laminate convex hull, the construction of piecewise affine maps and Tartar's framework.
These geometric and analytic tools create the underlying framework for the mentioned applications.
Afterwards we will look at some of the above mentioned examples.
As prerequisite a basic knowledge of functional analysis and PDE will be benefical but not crucial.
- Trainer/in: Jonas Hirsch
Semester: WiSe 2021/22