User ethan fetaya - MathOverflow

Answer by Ethan Fetaya for Examples of theorems misapplied to non-mathematical contexts

2011-04-12T17:42:53Z

This isn't exactly what you asked for, but I find it so amusing I could not resist.

The Indiana $\pi$ bill, when they almost passed a bill claiming that $\pi=3.2$, in order to be able to square the circle.

Unbelievable.

Answer by Ethan Fetaya for Elementary+Short+Useful

2011-04-07T15:40:18Z

Something that I found very interesting and very useful is Singular value decomposition. It shows that every operator is "almost diagnosable", and is skipped in a lot of basic linear algebra courses I have seen.

I has many application, for example - solving sum of least squares of example. You can give a 30 minute talk on this in various levels as well.

There are prettier theorems (Stokes, Uniformization, and many more) but I think with the 3 constraints (interesting, useful, little background) this is a good topic.

Generalization of Moise's theorem

2011-04-06T07:53:39Z

I am looking for a generalization of Moise's theorem, which the few professors that I asked treat as a "known geometric fact" but none could find a reference to an article proving it.

The claim is like this: Let $M$ be a compact 3 manifold (Riemannian but I do not think that helps), and let $X,Y$ be compact 2 manifolds (Riemannian aswell) that intersect transversally, then there is a triangulation of $M$ such that $X,Y$ are sub-complexes.

Thank you in advance, Ethan

Reverse engineering a metric from its properties

2011-03-31T16:55:19Z

I have been reading an article, and I am not clear on what he does in this one part.

He starts with a Riemmannian manifold $\Sigma$ that is $\mathbb{H}^2/\Gamma$, a quotient of the hyperbolic space by some group of isometries. He then takes an isometry $\tau:\Sigma\rightarrow\Sigma$ and defines $M=\Sigma\times[0,1]/[(x,0)\sim(\tau(x),1)]$ the mapping torus.

It is claimed in the article that if you take a geodesic $\gamma$ in $M$ then the tube around it has a flat metric on it's boundary. This (unless in am missing something) is not true for the product metric. you can take $(t,\rho,z)$ to be your coordinates when $(t,\rho)$ are the Fermi coordinates in $\mathbb{H}^2$ then $ds^2=d\rho^2+cosh^2(\rho)dt^2+dz^2$ will not be flat at the boundary.

The boundary of a tube around a geodesic is flat, if you you think of a quotient of $\mathbb{H}^3$ (and that is what I originally thought he did) but $(x,r)\rightarrow(\tau(x),r+1)$ is not an isometry of $\mathbb{H}^3$, so you cant get $M=\mathbb{H}^3/G$.

Any thought on how this can be done? I thank you all in advance

Comment by Ethan Fetaya

2011-04-06T08:15:13Z

Thank you very much!

Comment by Ethan Fetaya

2011-04-03T11:55:56Z

To be honest, I am not sure what he meant, but I just took the simple product metric, and show that it has the properties that I want. Thank you all for your help.

Comment by Ethan Fetaya

2011-04-01T05:56:44Z

The map has a finite order, so from Thurston the structure would be H^2xR.

Comment by Ethan Fetaya

2011-04-01T05:38:48Z

The article is "Z2-sytolic freedom and Quantum codes" by M. Friedman.