All Questions
152,871
questions
4
votes
0
answers
161
views
composition of t-structures "par recollement"
It is a classical result in Beilinson-Bernstein-Deligne's "Faisceaux Pervers" (thm. 1.4.9) that given three triangulated categories $\mathbf{D}_0, \mathbf{D}_1, \mathbf{D}_{01}$ and a recollement ...
4
votes
1
answer
131
views
Differential topology, maximal isotropy of a manifold
I am interested in the degree of isotropy of a connected (by arc) manifold in general.
Is it true that every connected manifold M (of dimension n) is maximally isotropic in the sense that you can ...
3
votes
1
answer
648
views
Is each rationally chain connected surface rational?
Consider a 2-dimensional smooth projective algebraic surface S over complex numbers. Could you recommend any exact references to the proofs of the following assertions (of course, if they are true):
...
5
votes
1
answer
313
views
Compactness of adelic quotients for unipotent groups over global fields
Let $K$ be a global field, $\mathbb{A}_K$ the ring of adeles, and $U$ a unipotent algebraic group over $K$. Why is $U(\mathbb{A}_K)/U(K)$, when endowed with the quotient topology, compact?
8
votes
2
answers
441
views
Is this problem on weighted bipartite graph solvable in polynomial time or it is NP-Complete
I encounter this problem recently and I want to know whether it is NP-Complete or solvable in polynomial time:
Given a undirected weighted bipartite graph $G = (V, E)$ where $V$ can be partitioned ...
1
vote
1
answer
411
views
Laplacian with singular potential
Let $S$ be a $2$-dimensional sphere. Let $p$ be a point in $S$. Let $L$ be a second order elliptic partial differential operator with smooth coefficients defined over the complement of $p$. Near $p$, $...
3
votes
1
answer
187
views
Lipschitz function with somewhere dense image
Let $Q=[-1,1]^2$ denote the unit square and let $f:Q\to Q$ be a Lipschitz function such that for any ball $B(a,r)\subset Q$ with radius $r$, the width of the image $f(B(a,r))$ is at least $cr$ for ...
9
votes
1
answer
720
views
Is there a straightedge and compass construction of incommensurables in the hyperbolic plane?
In other words, given a segment in the hyperbolic plane is there a straightedge and compass construction of a segment incommensurable with it? In the Euclidean plane one can take the diagonal of the ...
14
votes
1
answer
543
views
Which finite simple groups can be characterized by their action on a small set?
It is well known that a finite 4-times transitive permutation group is Matthieu, symmetric, or alternating. Another way of stating this is that the set
$$
\Omega = \{(x_1, x_2, x_3, x_4), 1\leq x_i\...
5
votes
0
answers
137
views
Stationary point processes with arbitrarily slow decorrelation
A point process $P$ (a probability measure on simple, locally finite point configurations $\mathcal{C}$ on $\mathbb{R}$ - I'm restricting to the one-dimensional setting) is stationary when law-...
3
votes
1
answer
304
views
Two matrix Fisher distributions on SO(3)?
After the uniform distribution (normalized Haar measure), the matrix Fisher distribution seems to be the most popular probability distribution on the Lie group SO(3). The density is proportional to ...
1
vote
0
answers
100
views
This weaker version of CR-structure: is it studied somewhere
When I study 5-dimensional $\mathcal{N} = 1$ supersymmetry, I came across such structure as follows.
$(R, \kappa, \Phi, M)$ is an almost contact 5-manifold, such that
\begin{equation}
\kappa \...
4
votes
0
answers
160
views
Large co-H-spaces
I'm searching for examples of co-H-spaces that are not suspensions and that do not admit a finite cone decomposition with respect to the collection of finite type wedges of spheres.
We have many ...
1
vote
1
answer
96
views
Extending connections [closed]
Usually, one views the connection $\nabla$ on a vector bundle $E \to M$ as a map $\Gamma(M, E) \to \Gamma(M,T^*M) \otimes \Gamma(M,E)) \simeq \Gamma(M,T^*M\otimes E)$. One can extend this to the ...
1
vote
1
answer
577
views
Hamiltonian Isotopy class of Lagrangian Submanifold
Let $(X,\omega)$ be a symplectic manifold, $L\subset X$ be a Lagrangian submanifold, $[L]$ denotes the Hamiltonian isotopy class. How to represent $L'\in[L]$ via $L$ (for example, a graph over $L$)? ...
19
votes
1
answer
944
views
Recognize this strange expression from linear algebra?
I've come across an odd-looking expression and oh how I wish I had a more elegant description of it. Maybe someone who enjoys symmetric bilinear forms in characteristic two will recognize it? Or ...
15
votes
2
answers
1k
views
Error in Maurins proof for the nuclear spectral theorem?
I am currently studying the nuclear spectral theorem as presented in K. Maurins Monograph [2], second chapter or alternatively his paper [1] which contains basically the same proof.
Let $\Phi\subset H\...
3
votes
1
answer
164
views
Pivotal functors of that are substantially different from finite group homomorphisms
Fusion categories can be seen as generalisations of the representation category of finite groups. I'm interested in spherical fusion categories. I'm trying to find "interesting" functors from a ...
3
votes
1
answer
288
views
Approximation of the form $\frac{1}{u}\pm\frac{1}{v}$
Given positive integers $m<n\in\mathbb{N}$ is there an algorithm to find integers $z_1, z_2\in \mathbb{Z}\setminus\{0\}$ such that $\frac{m}{n}$ is best approximated by $\frac{1}{z_1}+\frac{1}{z_2}$...
1
vote
0
answers
306
views
Is a finite depth-index irreducible subfactor, intermediate of a depth ≤ 3 one?
Let $(N \subset M)$ be a finite depth-index irreducible subfactor.
Main question: Is $(N \subset M)$ the intermediate of a finite index depth $\le 3$ irreducible subfactor?
(In others words, is ...
8
votes
3
answers
498
views
Binary relations as the topological closure of the diagonal
If $(X,\tau)$ is a topological space, we can consider the product topology on $X\times X$ and take the closure of the diagonal $\Delta_X = \{(x,x): x\in X\}$, which we denote by $\mathrm{cl}(\Delta_X)$...
5
votes
1
answer
959
views
Are Besov spaces $B^{s}_{p,q}$ invariant under Fourier transform?
(This may be very easy question for MO; as I am just trying to understand Besov spaces)
Let $\phi \in C^{\infty}(\mathbb R^{n})$ with
$ \operatorname{supp} \phi \subset \{\xi \in \mathbb R^{n}: |\xi|...
6
votes
1
answer
443
views
(Smooth) Borel Conjecture for 4-dimensional torus
Given an aspherical 4-dimensional closed manifold $M$ with fundamental group $\mathbb{Z}^4$, it is homotopy-equivalent to $T^4 = S^1 \times \ldots S^1$, the 4-dimensional torus.
Question 1: Since I ...
2
votes
0
answers
110
views
Characterization of externally definable sets
Let $\cal U$ be a saturated model of inaccessible cardinality $\kappa$. For arbitrary $\cal D\subseteq U$ denote by $\langle\cal U,D\rangle$ the expansion of $\cal U$ with a new predicate for $\cal D$....
2
votes
0
answers
261
views
Is every irreducible unitary class one representation induced?
Let $G$ be a connected semi simple Lie group with finite center.
Fix a maximal compact subgroup $K$.
An irreducible representation $(\pi,V)$ of $G$ is called a "class-one representation", if it ...
8
votes
0
answers
376
views
Silver's unpublished work on reverse Easton iteration
Silver was the first person who used the method of reverse Easton iterations in connection with large cardinals, and used it to force the failure of $GCH$ at some measurable cardinal.
At most papers ...
5
votes
2
answers
5k
views
Proof for a Rank-One Decomposition Theorem of Positive (semi) Definite Matrices
Consider the following result which I recently came across in a research paper in my area (Signal Processing)
Let $X$ be a $N\times N$ positive semidefinite (psd) matrix whose rank
is $r$. Let $A$...
5
votes
1
answer
265
views
$L^2$ discrepancy bound for sequences in $[0,1)$
Given a sequence $x_1,x_2,\dots$, let $D_n$ be the $L^2$-norm of the function $f_n$ whose value at $t \in [0,1)$ is $nt$ minus the number of $1 \leq i \leq n$ with $x_i \leq t$. What can be said ...
7
votes
1
answer
391
views
A conjecture about the measure estimates of a trigonometric polynomial
Formulation of the Conjecture
Let $\Omega =(0,\pi)\times (0,2\pi)\subset\mathbb R^2$ and let $\psi:\Omega\to \mathbb{R}$ defined by $$\psi(x,t)=\sum_{k\in S \,j\in S'} \sin(kx)\left( a_{kj}\sin(jt)+...
1
vote
1
answer
300
views
A question on degree 4 binary forms
Suppose that we have a binary form $f(x,y) \in \mathbb{Z}[x,y]$ of degree 4, and that we explicitly have
$$\displaystyle f(x,y) = a_0 x^4 + a_1 x^3 y + a_2 x^2 y^2 + a_3 xy^3 + y^4,$$
so that $(0,1)$ ...
16
votes
0
answers
440
views
Does $S^4$ have a "symplecto-homeomorphic" structure?
The 4-sphere cannot be a symplectic manifold. In particular, it does not admit an atlas whose transition maps are symplectomorphisms $(\mathbb{R}^4,\omega_\text{std})\to(\mathbb{R}^4,\omega_\text{std})...
1
vote
0
answers
284
views
L2 norm of a M-Whittaker function
Let $M_{\kappa,\mu}(z)$ be the Whittaker function, as defined here http://en.wikipedia.org/wiki/Whittaker_function.
Does any one know the evaluation of the following integral?
$$\int_{-\infty}^\...
1
vote
0
answers
139
views
on reductive monoids which are gorenstein
Let $M$ a reductive monoid, i.e. a integral normal affine scheme, which is a monoid whose group of units is a connected reductive group.
By Rittatore http://www.cmat.edu.uy/cmat/docentes/alvaro/...
6
votes
3
answers
371
views
Does this property of a first-order structure imply categoricity?
Let $\mathfrak{A}$ be a first-order structure over a relational language and let $\kappa$ be an infinite cardinal. Lets say that $\mathfrak{A}$ has the $\kappa$-property if for every structure $\...
1
vote
0
answers
3k
views
Possible ways to create a graph representation from a distance matrix (through approximation)
Forgive me, Im not math professional, but a computer scientist at the beginning of my base research from my thesis, so bare with me if I miss something blatantly obvious.
I have a Euclidean distance ...
7
votes
1
answer
455
views
Group structure on an arbitrary completely regular topological space that makes $(x,y)\mapsto xy^{-1}$ continuous at $(1,1)$
Let $(G,\mathcal T)$ be a completely regular topological space. Is there a group structure on $G$ such that the function
$$f:G\times G\to G$$
$$f(x,y)=xy^{-1}$$
is continuous at $(1,1)$?
2
votes
0
answers
91
views
Why does $\pi_t$ preserve pullbacks in this special case?
Let $X$ be a fibrant pointed cosimplicial space.
Following Bousfield-Kan, let $\text{lim}^{\partial \Delta_{n+1}} X = M^{n}X$ be the nth matching object of $X$. Onecan then show that there is a ...
6
votes
1
answer
512
views
A "good scale" that is not really a scale
I don't know much about singular cardinal combinatorics, so I apologize in advance if I write something that is wrong or looks funny. First let me recall some basic definitions.
Let $\lambda$ be a ...
6
votes
2
answers
164
views
Which criteria guarantee an orthogonal circuit in $\mathbb R^3$ to be rigid?
For $n\ge4$, define an orthogonal circuit or O-circuit as a closed circuit of $n$ unit segments in $\mathbb R^3$ such that any two neighboring segments form a right angle. (Physically this could be ...
3
votes
1
answer
2k
views
Use a graphic tablet to write in Latex or MathML [closed]
I have a Graphic Tablet and I am looking for a software which have the following features:
Math equation recognition I want to write and solve math equations in Graphic Tablet and auto recognized to ...
3
votes
1
answer
214
views
Uniformly permutation and the length of a size biased cycle
The cycle containing $1$ of a uniform permutation has length which is uniformly distributed. I was wondering if the converse is true:
Suppose $\sigma$ is a permutation on $\{1,\dots,n\}$ and let $u ...
4
votes
1
answer
411
views
q-th powers and roots of polynomials
Let $p,q,r$ be integers with $r\ge2$; let $f$ be a polynomial of the form $f(X) = g((X+1)^r)$, which is not a $q$-th power. Let $\omega$ be a $p$-th root of unity.
Prove or disprove that the ...
1
vote
1
answer
5k
views
Largest eigenvalue of the sum of Hermitian matrices [closed]
Is there an expression for the largest eigenvalue of the sum of two Hermitian matrices in terms of the spectrum of the same matrices?
13
votes
2
answers
943
views
Vanishing eigenvalues of Jacobian
Let $f: \mathbb{R^2}\to \mathbb{R^2}$ be a Schwartz function. If the eigenvalues of $Df$ vanish everywhere, must $f$ be constant? Does an analogous result hold when we replace $2$ by $n$?
Any ...
6
votes
1
answer
405
views
Are there superexponential Pfaffian functions?
This question is motivated by model theory, but it's really an analysis question (which means it may have an easy analysis answer that I just don't have the background for). Here's the main question, ...
0
votes
0
answers
182
views
Repeatedly changing queue behavior
I'm not sure if this question is suited to MO. I will happily delete if not.
Situation
Consider a general queueing system $\mathscr{S}$, whose customer arrival times are independent, and whose ...
2
votes
0
answers
57
views
Semi-simple controlling operator
I've just come across this paper by Coleman and Edixhoven called "On the semi-simplicity of the $U_p$ operator on modular forms", where (as the title says) they show that the $U_p$ operator is semi-...
1
vote
0
answers
157
views
breadth of a finite p-group
The breadth of an element $x$ in a finite $p$-group G is defined to be that integer $b = br(x)$ such that $p ^b = |G : C_ G (x)|$, while the breadth $br(G)$ of $G$ is the
supremum of $\{br_ G (x) | x \...
5
votes
0
answers
161
views
Are the integer index finite depth irreducible subfactors Kac-coideal?
Is every integer index finite depth irreducible subfactors planar algebra, the intermediate of an irreducible finite index depth $2$ subfactors planar algebra?
In other words, of the following form (...
18
votes
1
answer
2k
views
What is the geometric fixed points of an (equivariant) Eilenberg Maclane Spectrum?
The following was posted to math.stackexchange to no avail: https://math.stackexchange.com/questions/908756/an-exercise-in-homology-computation-what-is-the-geometric-fixed-points-of-an-e
The question ...