## Geometry Seminar - Abstracts

### Talk

Wednesday 1 June 2016, 16:00 - 17:00, in HG00.310

**Joost Hulshof** (VU Amsterdam)

*The hard implicit function theorem revisited*

### Abstract

Last summer Jason Frank was looking for someone to give a talk
at the Stieltjes-Wonder afternoon in Tilburg on the work of Nash. Since
the theorem in the title was on the one hand essentially due to Nash and
on the other hand on my list of theorems to be understood at some point in
my time of being, I opted for a talk on just this theorem, also as I had
recently bought the Krantz and Parks book on implicit function theorems. I
will explain what I learned since then with a possible small improvement
that of course may very well have been noted before. The original
application by Nash to the embedding problem of abstract Riemannian
manifolds in Euclidean space I had not not studied at the time, but the
idea is explained in old lecture notes of Jacob T. Schwartz, who is also
mentioned by Nash in his original article, which I have begun reading only
recently.

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