How can one represent a non-smooth space in Euclidean space?

How to approximate Sobolev and Lipschitz functions with functions of small energy? How can one differentiate functions in non-smooth spaces?

These three questions initially seem rather disjoint. I will try to explain a connection between these three via some theorems, tools and ideas from my and others work. We will see at least two of these

connections: how embeddings can be constructed via approximations, and how differentiable structures may pre-empt such approximations from existing. We will also see a theorem of how a differentiable structure together with an embedding will enforce some rigidity on the space. I will try to explain these phenomena through examples and with as few definitions as possible.

When? | 17.10.2023 17:15 |
---|---|

Where? | PER 08 auditoire 2.52 Chemin du Musée 3 1700 Fribourg |

speaker | Prof. Sylvester Eriksson-Bique, University of Jyväskylä |

Contact | Département de mathématiques isabella.schmutz@unifr.ch |