Hi guys,
I'm a mathematician from Miami Florida working in paraquaternionic and symplectic differential geometry, but I come from a very extensive physics background, pretty much well-versed in all modern physics. But my favorite of all is probably the philosophy of mathematics and science as...
Can anyone explain or point me to a good resource to understand these operators? I'm trying to the understand determinants for skew symmetric matrices, more specifically the Moore determinant and it's polarization of mixed determinants. Can hone shed some light? I'm confused as to how the...
For a map between vector bundles (which commute with a certain Lie groups like Sl2R or GL2R), what does it mean exactly for a fiber to be multiplicity free?
Eplanations would be good, but examples would be even better. Thanks in advance, Gauss bless you!
CM
Thanks a lot guys, I especially appreciate the different responses/viewpoints. I'm going to give them all a try and see which fits my mental conception of the manifold best.
Thanks again!
CM
Let n <= m and G:=Gr(n,m) be the (real) Grassmanian manifold. I understand the topology of the simplest case, that of projective space, and am wondering if there is a way to interpret the topology of the G to similar to projective space, with the according generalizations needed.
If V^n is an...
Should \prod_\mathbb{P} \left( \sum_{\mathbb{Z} \ge 0} p^{-s n} \right) ^{-1} have that ^(-1) after it? Or am I missing something..? Are you rewriting 1/(1-p^-s) using geometric series?
Anyways, thanks that was very helpful, I'm looking into the proofs of the product formula via this route.
I need help understanding this equality:
\prod_{p-prime} \frac{1}{1+\frac{1}{p^3}}= \sum_{k=1}^\infty \frac{(-1)^{\sum_p ord_p(k)}}{k^3}
Any help is greatly appreciated!!!
Hi everyone. I'm trying to understand the step where they wrote
1/2 ∏1/(1+p^-3) =1/2 Ʃ(-1)^ord(k)/k^3
How can I see this? I know the Euler product formula, but it has a negative sign before the p^-3, where here we have a + sign.
Thanks for the help.
That it is a linear combination of z and (x-t), g=zg'+(x-t)g" for g',g" in k[x,y,z,t].
The question is what we do from there.
We know that g(0,0,z,t)=0 (because g in I) hence g(0,0,z,t)=zg'(0,0,z,t)-tg"(0,0,z,t)=0.
But from here can we conclude that g',g" are in I? I don't see how to do it..
I have already proved that (and thought of that), but the problem is that these are ideals of a polynomial ring, so that if I+J=k[x] then either I or J IS k[x], otherwise you could not generate the scalars in the field.. (since k-field, it has no nontrivial ideals)
So this approach won't work...
Let k[x,y,z,t] be the polynomial ring in four variables and let I=<x,y>, J=<z, x-t> be ideals of the ring.
I wanna show that IJ=I \cap J and one direction is trivial. But proving I \cap J \subset IJ has stumped me so far. Anyone have any ideas?
Wow Huang is at Rutgers! Omg thanks, I knew posting this was a good idea. I actually have a very good chance of getting into Rutgers, I know people who are there now.
Does anyone know any other big names or good schools for these areas?
In my grad complex analysis class, we reviewed the entire complex variables course in a day and a half. In other words, the variables course is sort of a prereq for the analysis course. Depending on your familiarity with the complex plane, some topology, and calculus, you could probably go into...
I know UC San Diego is good, Rothschild and Ebenfelt are there, but are there any other ones that stand out in these and related fields?
Thanks a bunch
I got into Wisconsin stout, for a project on invariants of complex hypersurfaces. I'm thrilled about the project, but not too excited about leaving Miami for Wisconsin lol. Anyone else got into Stout?
Im applying to an REU in San Diego State where the focus will be Nonunique factorization theory but I'm clueless as to what this actually is. Does anybody know anything about this?
The complex plane is essentially R^2, but it has an extra condition that i^2=-1. This is the unique and unusual part, in nature, we don't encounter or count with numbers which we square and get a negative answer, they seem to be prevalent in the background picture however.
Imaginary numbers are...
also because at the positive even integers, the zeta function is defined the Dirichlet series 1+1/2^s+1/3^s+1/4^s+... which converges for all positive even numbers.