Freitag, 10.07.2026: The Nash embedding theorems
Dr. Rodrigo Avalos (Universität Tübingen)
The objective of this talk is to provide a review of J. Nash’s embedding theorems in the context
of Riemannian geometry. The conclusion of Nash’s work is that any Riemannian manifold can
be isometrically embedded in a Euclidean space of sufficiently large dimension. This result
constitutes a cornerstone in Riemannian geometry, closing the long-standing problem of
showing that the class of intrinsically defined Riemannian manifolds is the same as that given
by the Riemannian submanifolds of Euclidean space. Moreover, historically, these results
provided deep connections with the theory of partial differential equations and led to analytic
developments with a broad scope of applications. In this setting, the goal for this talk is to
contextualise the problem and its historical relevance; review prior results before Nash’s work;
stress the difficulties faced by the general problem for smooth metrics; showcase the key
ideas from Nash to overcome these difficulties; and comment on recent developments and
open problems related to Nash’s theorems. These last developments include the search for
the optimal codimensions for the isometric embedding and extensions to semi-Riemannian
geometry
| Uhrzeit: |
11:30 |
| Ort: |
7E02 / Hörsaalzentrum Morgenstelle |
| Gruppe: |
Habilitationsvortrag im Fachbereich Mathemat |
| Einladender: |
MNF Der Dekan |
