Théo Marty

In differential geometry, questions about flexibility or rigidity often arise. For example, can we deform a potato into a whale? Can we embed a flat torus into $\mathbf{R}^3$? Can we flip a lampshade without critical point? So many interesting questions!

The $h$-principle is an important tool in order to study flexibility as it allows to transform an homotopic property into a geometric one. In this talk, we will consider the dark face of this theory, that is, the holonomy theorem of Y. Eliashberg. More precisely we will see an explicit resolution of the problem of the turnaround of the lampshade.