1
vote
2answers
62 views
Symmetric sums and Representations of SO(3)
I had tried to help someone on math.StackExchange to prove the identity:
$$ (1-Tr(A))^2+\sum_{1\le i\le j\le 3}(a_{ij}-a_{ji})^2=4$$
I guess you could argue the left hand side is …
6
votes
1answer
191 views
Anything special (historical?) about surface $x\cdot y\cdot z\ +\ x+y+z=0$?
QUESTION
I wanted to introduce and develop the complex logarithm from scratch. As the result I've arrived a couple of months ago at the following identity after which the road to …
0
votes
0answers
7 views
When is an ample line bundle on an abelian variety base point free?
So, any line bundle $L$ on an abelian variety $X$ determines a type $(d_1,\ldots,d_g)$ where $d_i|d_{i+1}$. It's well known that if $d_1\geq 3$ then $L$ defines an embedding, that …
0
votes
0answers
18 views
blow-ups and singularities
Let $X$ be a smooth and projective variety over a field of characteristic zero. Let $Y$ be a normal variety, with finite quotient singularities (an orbifold!) and let $\pi: Y \to X …
0
votes
0answers
16 views
Updated: finding an integer $k$ that minimizes $1/(N-k) (1+1/k)$
For any positive integer $N$ and real number $a > 0$. Define $f(k) = \frac{1}{N-k} (1+\frac{a}{k})$. The problem is to find a positive integer $k$ that minimizes $f(k)$.
It is qu …
0
votes
0answers
2 views
Spectrum gap of large random weighted semiregular bipartite graph
Hi
I need the bound for the spectrum gap of random semiregular ($\ell$, $r$)-bipartite graph. This paper (http://arxiv.org/abs/1212.5216) gives the bound for $\ell$-regular bipar …
0
votes
0answers
20 views
Full $n$-torsion of elliptic curves and the cyclotomic field of order $n$
Hi, overflowers.
I have a question concerning the torsion of elliptic curves over number fields.
Let us consider an elliptic curve $E$ defined over ${\mathbb Q}$. From the Weil …
0
votes
0answers
47 views
finding an integer that minimizes a function
For any positive integer $N$ and real number $a > 0$. Define $f(k) = \frac{1}{N-k} (1+\frac{a}{k})$. The problem is to find a positive integer $k$ that minimizes $f(k)$.
It is qu …
3
votes
2answers
227 views
strong nilpotent elements
An element x in a noncommutative ring R is strongly nilpotent if any chain
$x_1=x, x_2, ... $, with $x_{n+1}\in x_n R x_n$ terminates at zero. It becomes clear
why this is a good d …
3
votes
0answers
115 views
mixed Hodge polynomial
Let $X$ be a smooth projective algebraic variety over a field of characteristic zero. Let $U$ be the complement in $X$ of a simple normal crossings divisor $D$. For each degree $k$ …
0
votes
0answers
15 views
Topology of Asymmetric Symmetric Products
Let $X_1,...,X_m$ be connected, simply-connected CW sub-complexes of a CW complex $X$. Let the symmetric group on $m$ letters, $S_m$, act on $P:=X_1\times\cdots\times X_m$ in $X^m$ …
1
vote
1answer
43 views
Asymptotic bounds on $\pi^{-1}(x)$ (inverse prime counting function)
What are the current best asymptotic bounds on $\pi^{-1}(x)$, where $\pi(x)$ denotes the prime counting function (number of primes at most $x$)?
In other words, I am curious about …
2
votes
0answers
49 views
Composition of spans as a morphism of profunctors
Let $\bf C$ be a category with pullbacks. Define $Span\colon (A,B)\mapsto \{ (X,f,g)\mid A\xleftarrow{f}X\xrightarrow{g}B\}$ and notice that it is a profunctor $s\colon \bf C^\text …
0
votes
0answers
13 views
What are the upperbounds of the Nil radical?
The main radicals of a non-commutative ring (with 1) are the Sum of all nilpotent ideals $\subseteq$ Prime radical $\subseteq$ Nil radical $\subseteq$ Jacobson radical $\subseteq$ …
0
votes
0answers
21 views
Existence and uniqueness of a matrix differential equation with L^1 coefficients
I came across the following differential equation when considering some direct scattering problems:
$$
N'_x(x,z)=G(x,z)N(x,z)
$$
where $N(x,z)$ is a $2\times2$ complex matrix wit …
