## Tagged Questions

0answers
1 views

### von Staudt-Clausen for other special values

The von Staudt-Clausen theorem expresses that the Bernoulli numbers' denominators have a very special form (see the wikipedia page on the theorem for more details). What interests …
1answer
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### Doubt in the proof of Stickelberger’s Theorem

I was going through the proof of Stickelberger's Theorem, as given in the book 'Algebraic Number Theory' by Richard A Mollin, and I am having some problem in understanding the proo …
0answers
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### complex Morse function on a four-manifold

If we have a complex Morse function on a complex four-manifold, $f: X\to \mathbb{C}$, can we tell from the function how the genus of inverse images $f^{-1}(z)$ (for regular values …
1answer
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### Algorithm to find exponential map of differential operators acting on function

I am trying to write a computer program which computes the action of the exponential of a differential operator on a function, for any given differential operator. Examples: \$\ex …
1answer
33 views

### Importance of separability vs. second-countability

For me second-countability always felt like to be the more important and fundamental concept from general topology than separability. I wonder whether there are any points which ca …
0answers
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### Possible diagonal values of a product of matrices with some specific characteristics

Hello all, This is a question that might or might not be related to my previous one. Imagine you have two matrices: Matrix \$\mathbf{\Phi}=[\Phi_1,\ldots,\Phi_M]\in\mathbb{R}^{L …
44answers
9k views

### An example of a beautiful proof that would be accessible at the high school level?

The background of my question comes from an observation that what we teach in schools does not always reflect what we practice. Beauty is part of what drives mathematicians, but w …
1answer
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### On finite groups with same complex-valued character table

What are the necessary and sufficient conditions for two finite groups $G$ and $H$ to have same complex-valued character table? Is there any criterion for which one could know abou …
0answers
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### Who first computed the integral cohomology ring of a weighted projective space (WPS) ?

After Jun-Ichi Igusa' talk at ICM 1962, H.J. Tramer computed the ring structure of the integral cohomology of such a space ( not yet called WPS ). In 1971 M.F. Atiyah called it W …
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### Who first computed the integral cohomology ring of a weighted projective space (WPS) ?

After Jun-Ichi Igusa' talk at ICM 1962, H.J. Tramer computed the ring structure of the integral cohomology of such a space ( not yet called WPS ). In 1971 M.F. Atiyah called it W …
0answers
14 views

### In cell-decomposed manifolds, how easy is it to arrange for the tubular neighborhood of a diagonal to contract onto the diagonal?

Suppose that you have decomposed a manifold $M$ into cells (I care most, if it matters, about compact oriented smooth manifolds; but if my question can be solved in the PL category …
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### Connectedness of hyperplane sections (reference request)

Dear colleagues, Could you give me a reference (not a proof:) to the following folklore result. If $X\subset\mathbb P^n$ is a smooth irreducible projective variety of dimension \$ …
1answer
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### How to determine the number of a cube within a bigger cube?

Hi all, I have a cube, sized 39 x 13 x 8. I need to find out how many of them can fit in a cube of 100 x 100 x 100. I need to find the highest number possible. Do you know of a w …
0answers
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### What is the ring structure of the complex topological K-theory of a non-singular complex quadric?

I would like to know the ring structure of $K(Q_n)$ explicitly where $Q_n \subset \mathbb{P}^{n+1}$ is the non-singular $n$-dimensional complex quadric and $K(Q_n) = K^0(Q_n)$ is …
13answers
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### Is there any proof that you feel you do not “understand”?

Perhaps the "proofs" of ABC conjecture or newly released weak version of twin prime conjecture or alike readily come to your mind. These are not the proofs I am looking for. Indeed …

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