What is ... the Nash embedding theorem?

This page hosts information on Ariane Beier's talk "What is ... the Nash embedding theorem?" at the "What is ...?" seminar. The talk will take place on Friday, May 3, 1:00pm at the BMS Loft at Urania. This talk will help you better understand the talk by László Székelyhidi, which will start at 2pm.

Abstract

The notion of a Riemannian manifold evolved from more concrete objects like surfaces in three-dimensional Euclidean space. But how much more general is this concept?

Nash's embedding theorem gives one answer to the question whether or not a Riemannian manifold can be isometrically embedded into Euclidean space. It provides surprising and, at first glance, inconsistent results which we want to illustrate by considering the example of a flat torus.

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