0
votes
0answers
41 views
Rabin’s Tree Theorem
I've been reading Rabin's article on decidability in Barwise's text, and I came across Rabin's discussion of the decidability proof of his tree theory: the second-order theory with …
0
votes
0answers
10 views
Does equality of Hodge star and symplectic star imply Kähler structure?
Question
The question asked is:
On a manifold $M$ equipped with a Riemann metric $g$ and a symplectic structure $\omega$, with $\ast$ the Hodge star and $\ast_s$ the symplecti …
0
votes
1answer
39 views
about the local ring of $\mathbb{Z}_p[T]/(pT^2+T+1)$ at the prime p
is the localisation of the ring $$A:=\mathbb{Z}_p[T]/(pT^2+T+1)$$ at the prime ideal (p) isomorphic to $\mathbb{Z}_p$?
If not, how to understand this ring very explicitly?
7
votes
1answer
102 views
Integer matrices with a strange divisibility property
Fix an integer $n$. What can you say about a (not necessarily square) matrix $A$ with integer entries that has the property that for any $k$, every $k\times k$ minor of $A$ is divi …
1
vote
0answers
26 views
Tensors with low spectral norm
Consider a tensor $T$ with six indices, $T_{(ii')(jj')(kk')}$, where each index goes from $1$ to $n$. We can think of $T$ as a linear map from $\mathbb{R}^n \otimes \mathbb{R}^n \o …
1
vote
0answers
55 views
An algorithm for checking if a nonlinear function f is always positive
Is there an algorithm to check if a given (possibly nonlinear) function f is always positive?
The idea that I currently have is to find the roots of the function (using newton-rap …
3
votes
3answers
115 views
Functions holomorphic on a region minus a Cantor set
Let $X$ and $Y$ be simply connected open regions of $\mathbb{C}$, and let $Z \subset X$ be a Cantor set. Assume we have a homeomorphism $f$ from $X$ to $Y$, which is holomorphic on …
0
votes
1answer
147 views
What is the difference between “up to conjugacy” and “up to conjugation” ? [closed]
I see many times the words "conjugacy" and "conjugation", and I don't really get the difference between the two. Especially, when we take an element of a group and want to say that …
1
vote
2answers
63 views
Integer square $2 \times 2$ block matrix inverse
Let $\mathbf{M}$ be an integer square $2 \times 2$ block matrix
$$
\mathbf{M} =
\left(
\begin{array}{cc}
\mathbf{A} & \mathbf{B} \
\mathbf{C} & \mathbf{D}
\end{array}
\righ …
3
votes
2answers
164 views
Modular representations with unequal characteristic - reference request
Let $G$ be a finite group, and let $K$ be a finite field whose characteristic does not divide $|G|$. I am interested in the theory of finitely generated modules over $K[G]$. Of c …
0
votes
0answers
53 views
L_2-norm representation
Let
$$
f^{\alpha}_+(x)=\frac{1}{\Gamma(\alpha+1)}\sum_{k\ge 0}(-1)^k{\alpha+1 \choose k}(x-k)^{\alpha}_+,
$$
where $\alpha > -\frac 12$.
I am wondering if one can get nice represen …
3
votes
3answers
88 views
How to find the minimum number of hyperplanes to define a convex hull
Hi everybody,
I have the following problem:
I have a convex hull $\Omega$ defined by a set of n-dimensional hyperplanes $S = [(n_1,d_1), (n_2,d_2),...,(n_k,d_k)]$ such that a poi …
4
votes
3answers
432 views
What is the “Lefschetz Principle” (examples) ?
Hi there,
can anyone explain to me what the "Lefschetz Principle" is by some clear "classical"
examples (not relying explicitly on model theory, say).
Thanks !
4
votes
0answers
85 views
Sum of exponential functions
Suppose that we have $q$ positive integers $a_1, \ldots, a_q$ satisfying $a_1 \leq \cdots \leq a_q$. I'm interested in the possible types of behaviors for the function given by $$ …
3
votes
1answer
44 views
States/functionals on crossed product C*-algebras
Let $A$ be a C*-algebra, $\alpha$ a strongly continuous automorphic action by a locally compact group $G$ on $A$, and consider the crossed product $A\rtimes_\alpha G$. I am looking …
