Answer by ERCÜMENT HASAN ORTAÇGİL for Is there an underlying explanation for...
Let G(k,n) be the k'th order jet group in n variables which consists of the set of k-jets of local diffeomorphisms of R(n) fixing the origin under the operation of composition. In coordinates, this...
View ArticleAnswer by user88196 for Is there an underlying explanation for the magical...
One very simple interpretation is possible, if I am not mistaken: Characterizing conformal nets, or more general harmonic nets having in mindthe lift to minimal surfaces, it turns out thatthere exists...
View ArticleAnswer by Tom Copeland for Is there an underlying explanation for the magical...
The velocity for a solution $f(x-c\cdot t)$ of the one dimensional heat equation$$\frac{\partial}{\partial t}f(x-ct)=-c\frac{\partial}{\partial x}f(x-ct)=\alpha\frac{\partial^{2}}{\partial...
View ArticleAnswer by Peter Michor for Is there an underlying explanation for the magical...
The Schwarzian derivative encodes the adjoint action of the Bott-Virasoro group. One version of it is ${Diff}\_{\mathcal S}(\mathbb R)\times \mathbb R$(here $\mathcal S$ stands for "rapidly falling...
View ArticleAnswer by Engineers are better at maths for Is there an underlying...
Let $f:\mathbf{R}\mapsto\mathbf{P}^1$ be a function realised as $y=f(x)$, where $y$ is an affine coordinate on $\mathbf{P}^1$. Since the target space is the projective line it is desirable to lift $f$...
View ArticleAnswer by VA. for Is there an underlying explanation for the magical powers...
Nobody pointed out What is ... Schwarzian Derivative? (Notices of AMS Jan 2009), which succinctly explains quite a lot.
View ArticleAnswer by user8248 for Is there an underlying explanation for the magical...
It's a cocycle in group cohomology.$S[f\circ g]= S[f]^g + S[g]$which is the cocycle condition! The group is Aut(meromorphic functions) and the other group is meromorphic functions.
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Answer by Bill Thurston for Is there an underlying explanation for the...
Like may people (but not all people), I have trouble thinking in terms of formulas such as that for the Schwarzian. For me, a geometric image works much better. I'll describe a geometric picture,...
View ArticleAnswer by Victor Protsak for Is there an underlying explanation for the...
The following book may contain insights of the type you are looking for, at least for the second and third interpretation:V. Ovsienko, S. Tabachnikov, Projective differential geometry old and new. From...
View ArticleIs there an underlying explanation for the magical powers of the Schwarzian...
Given a function $f(z)$ on the complex plane, define the Schwarzian derivative$S(f)$ to be the function$S(f) = \frac{f'''}{f'} - \frac{3}{2} \Big(\frac{f''}{f'}\Big)^2$Here is a somewhat more...
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