Recently Active Questions
159,078 questions
1
vote
1
answer
190
views
Is the semigroup M(n, Z) finitely presented? If so, where can I find a presentation of it?
I am new to semigroup research, so I apologize if this is an easy question.
- 25.2k
3
votes
2
answers
1k
views
Constraints on the Fourier transform of a constant modulus function
Considering the function $f:\mathbb{R} \to \mathbb{C}$, with $\left| f(x) \right|=1$ for all $x\in \mathbb{R}$.
Considering $g:\mathbb{R} \to \mathbb{C}$ with $\int_{-\infty}^{\infty}{\left|g(x)\right|...
- 1,981
1
vote
1
answer
700
views
Flux homomorphism for manifolds with boundary
Hi all,
I am wondering whether someone has considered the definition of the flux homomorphism for manifolds with boundary. More specifically, I am looking at the annulus and I want the ...
- 28.9k
3
votes
1
answer
463
views
Decomposition of modules using computer packages
I am interested in computing direct sum decomposition of modules over some quotients of polynomial rings over a field (do not care much about the field at this point). Does any one know a package ...
- 1,626
6
votes
0
answers
264
views
When do equivariant sheaves on a formal neighborhood extend?
Suppose that $X$ is a variety (in char 0) with an action of an affine algebraic group $G$. Let $Y \subset X$ be a subvariety fixed by $G$--the action map agrees with projection upon restriction to $Y$...
- 1,038
3
votes
2
answers
379
views
"Embedding" functions in groups
Hi all, I am looking for some help with the following question. Take a discrete bivariate function $f(x,y)$ (i.e., $x$,$y$ take values in some finite sets). Is there a way to quantify how "embeddable" ...
- 1,036
3
votes
3
answers
728
views
What do you call the product of a circle and an annulus?
What would you call the product of an annulus and $S^1$ (a 'thickened' torus like 3-manifold)?
More generally, is there an archive or list online of names assigned to various (non-standard) manifolds ...
- 345
20
votes
3
answers
2k
views
How does $\pi_1(SO(3))$ relate exactly to the waiters trick?
I hope this is serious enough. It is a well-known fact that $\pi_1(SO(3)) = \mathbb{Z}/(2)$, so $SO(3)$ admits precisely one non trivial covering, which is 2-sheeted.
Another well known fact is that ...
- 15.4k
12
votes
1
answer
2k
views
Can the Quantum Torus be realized as a Hall Algebra?
Background
The Quantum Torus
Let $q$ be an arbitrary complex number, and define (the algebra of) the quantum torus to be
$$T_q:=\mathbb{C}\langle x^{\pm 1},y^{\pm 1}\rangle/xy-qyx$$
For $q=1$, this is ...
CommunityBot
- 1
2
votes
0
answers
396
views
Noether-Lefschetz locus in enumerative geometry.
It is well known that if you have a smooth quartic surface $X\subset \mathbb{P}^3$, it may or may not have lines in it. Indeed, $X$ has the following options, 64 (the maximal number), 32, 16, or none.
...
- 2,132
3
votes
3
answers
2k
views
Generic fiber of morphism between non-singular curves
This is prop 2.6b on p.28 of Silverman's the Arithmetic of Elliptic curves.
It says that let $\phi: C_1 \rightarrow C_2$ be a non-constant map of projective non-singular irreducible curve. (probably ...
- 57.6k
9
votes
0
answers
2k
views
Has the Lie group preserving a probability distribution been used in Bayesian statistics?
For a (possibly signed) nondegenerate probability measure $\pi$ on $\{1,\dots,n\}$ define
$$\langle \pi \rangle := \{R \in \operatorname{STO}(n): \pi R = \pi \}.$$
Here $\operatorname{STO}(n)$ denotes ...
- 15.4k
4
votes
0
answers
158
views
Local structure of the surface of bitangents to a quartic
Let $S \subset \mathbb{P}^3$ be a (possibly singular) quartic. I need some information about the local structure of the surface $Bit(S)$ of bitangents to $S$. I have done the computations, but they ...
- 14.7k
3
votes
2
answers
879
views
44
votes
10
answers
25k
views
Fourier transform for dummies [closed]
So ... what is the Fourier transform? What does it do? Why is it useful (both in math and in engineering, physics, etc)?
(Answers at any level of sophistication are welcome.)
- 1,626
3
votes
1
answer
254
views
How is this action of monoidal derived category induced?
I am reading a paper concerning the action of monoidal category to another category.
Let $k$ be a commutative ring, $R$ is a k-algebra. $A=R-mod$, $B=R^{e}-mod=R\bigotimes _{k}R^{o}-mod$.
Consider ...
- 7,800
3
votes
1
answer
2k
views
Examples of Equivariant Sheaves under Group action
I feel it very unintuitive to understand what an equivariant sheaf is. In the simplest example, L/K is a finite Galois extension, G=Gal(L/K), G acts on Spec L, what are the equivariant sheaves on L?
- 57.6k
3
votes
3
answers
2k
views
"Interesting" properties of sets of natural numbers
On Wikipedia, there is a list of properties of sets of reals, which are in some sense "interesting": just have a look.
I could not find a comparable list of properties of sets of natural numbers (...
CommunityBot
- 1
3
votes
1
answer
320
views
Joint Law with 2 marginals and marginal of the spread
I have a question for you and thank you in advance for your answers and ideas.
Let us suppose that we have the marginal distributions of two r.v X and Y, and also the law of X-Y (or any linear ...
- 498
-1
votes
1
answer
1k
views
cauchy product for general case [closed]
How to multiply this series:
$$(\sum_{t=-\infty}^{\infty}a_{t})(\sum_{k=-\infty}^{\infty}b_{k})$$
- 3
0
votes
2
answers
259
views
Existence of an "anti-additive" (or "never linear") map?
(I've edited this question)
I'm searching for a continuously differentiable function $f:\mathbb R^2\to\mathbb R$ such that $f(x)+f(x+u+v)\neq f(x+u)+f(x+v)$ for all $x$ and all linearly independent $...
- 28.9k
3
votes
1
answer
1k
views
Maximizing Sparsity in l1 Minimization?
Consider the optimization problem
$$\min_x ||Ax||_1 + \lambda||x-b||^2,$$
where $A \in \mathbb{R}^{n \times n}$, $x,b \in \mathbb{R}^n$ and $\lambda$ is strictly greater than 0. (This problem is ...
- 3,059
0
votes
1
answer
1k
views
Kronecker product definition
Some authors (v.g. the creators of Matlab, Campbell, Lo, MacKinlay (1997) in The Econometrics of Financial Markets) define the Kronecker product of two vectors as one single column vector containing ...
- 118k
41
votes
7
answers
5k
views
Simplicial objects
How should one think about simplicial objects in a category versus actual objects in that category? For example, both for intuition and for practical purposes, what's the difference between a [...
- 3,917
2
votes
3
answers
601
views
Given is "model". How many theories may it be a model?
Usually we have axiomatic theory and the we look for model for it - this is book picture. Of course in real math usual one has a "model" that is given structure and looks for proper axiomatizing of ...
- 237k
9
votes
1
answer
1k
views
First-order UFD (factorial ring) condition / pre-Schreier rings
All rings in this post are commutative and with $1$.
Everyone knows the definition of a factorial ring, a. k. a. unique factorization domain (UFD). I have been wondering about some variations ...
- 33.8k
6
votes
1
answer
2k
views
How can an ultrapower of a model of ZFC be "ill-founded" yet still satisfy ZFC?
My understanding (please correct me if I'm wrong) is that if you have some transitive set M which is an $\epsilon$-model of ZFC, and you take an ultrapower of it using an approprate ultrafilter, you ...
- 2,701
2
votes
1
answer
651
views
the proof of "theorem of connectedness"
This theorem is: let f:X--->Y be a proper morphism of noetherian schemes,and the induced morphism of sheaves f^#:O_Y---->f_*O_X is isomorphic.Then for any point y belongs to Y,f^-1(y) is nonempty and ...
- 57.6k
11
votes
3
answers
2k
views
Is any true sentence in the second-order Peano Axioms provable
Forgive the elementary nature of the question. I understand that the second order Peano Axioms are categorical in the sense that all their models are isomorphic. This equivalence class of models is ...
25
votes
4
answers
3k
views
A Peculiar Model Structure on Simplicial Sets?
I'm wondering if there is a Quillen model structure on the category of simplicial sets which generalizes the usual model structure, but where every simplicial set is fibrant? I want to use this to do ...
CommunityBot
- 1
42
votes
2
answers
3k
views
Commutative rings to algebraic spaces in one jump?
Typically, in the functor of points approach, one constructs the category of algebraic spaces by first constructing the category of locally representable sheaves for the global Zariski topology (...
- 9,408
9
votes
4
answers
2k
views
alternative construction of the quotient group
The background for this question is that I know that many students starting to learn algebra focus on the standard construction of the quotient group $G/N$ instead of working with the universal ...
- 57.6k
7
votes
3
answers
1k
views
The continuous as the limit of the discrete
Reading this documment: www.math.ucla.edu/~tao/preprints/compactness.pdf, I got interested in the following thing: "One can also use compactifications to view the continuous as the limit of the ...
- 57.6k
0
votes
1
answer
415
views
If the 4-genus of a link is zero, is it a slice link?
An n-component slice link is a link that bounds n disjoint discs in B^4. And the 4-genus of a link is defined to be the minimal genus of orientable surfaces bounded by it in B^4.
My question is: if ...
- 44.4k
18
votes
2
answers
2k
views
Galois representations attached to newforms
Suppose that $f$ is a weight $k$ newform for $\Gamma_1(N)$ with attached $p$-adic Galois representation $\rho_f$. Denote by $\rho_{f,p}$ the restriction of $\rho_f$ to a decomposition group at $p$. ...
- 4,807
3
votes
1
answer
367
views
Homotopy classes of complex bundle maps and isotropic immersions into contact manifolds
This is a follow-up question to my previous one where I was trying to understand the classes of Legendrian immersions of circles into contact manifolds.
I'm interested in classifying isotropic ...
CommunityBot
- 1
6
votes
1
answer
1k
views
The inverse limit of locally free module
A is an I-adic complete Noetherian ring. M is a finitely generated A module. For any n>0, $M/I^nM$ is a finitely generated locally free A/I^n-module. Is M necessarily a locally free A-module?
CommunityBot
- 1
1
vote
1
answer
1k
views
Extension of a holomorphic vector bundle
Let $E$ be a holomorphic vector bundle over $\mathbb{P}^n\setminus\begin{Bmatrix}[1,0,0,\cdots,0]\end{Bmatrix}$. Let $D$ be a connection on $E$. Let $\widetilde{E}$ be an extension of $E$. Since $\...
- 2,444
6
votes
1
answer
463
views
The (n+1)-st cohomology of K(Z/p,n).
I was looking through my notes for a homotopy theory course and found the following mysterious statement (K is of course the Eilenberg-Maclane space):
$$H^{n+1}(K(\mathbb Z_p,n);\mathbb Z_p) \cong \...
- 4,424
-2
votes
1
answer
6k
views
calculate percentiles from a histogram [closed]
Hi,
Could someone explain to me or point out some documentation on how to compute a given percentile from a histogram ?
0
votes
2
answers
4k
views
Convergence of iterative algorithm.
For quite a long time I'm trying to prove convergence of an iterative algorithm in case of a particular system of nonlinear equations.
Here are some characteristics of this system:
It consists of n ...
CommunityBot
- 1
9
votes
2
answers
1k
views
Borsuk pairs of Banach spaces
Given $X$, $Y$ two real Banach spaces, let's say that $(X,\ Y)$
is a Borsuk pair if for any continuous mapping $T$ : {$x$ $\in$
$X$ ; $||x||\leq1$} $\rightarrow$ $Y$ s.t. $T$ is odd on {$x$
$\in$ $X$ ;...
CommunityBot
- 1
1
vote
2
answers
907
views
Principal Bundles over Complex Projective Varieties
For various reasons, I'm interested in working with complex projective varieties that are also principal bundles. I began by looking at projective spaces themselves $\mathbb{CP}^n = SU(n+1)/U(n)$, ...
- 44.7k
11
votes
2
answers
2k
views
What do the local systems in Lusztig's perverse sheaves on quiver varieties look like?
In "Quivers, perverse sheaves and quantized enveloping algebras," Lusztig defines a category of perverse sheaves on the moduli stack of representations of a quiver. These perverse sheaves are defined ...
- 3,131
6
votes
2
answers
2k
views
groups as categories and their natural transformations
If one views a group as a one object category with the elements of the group as morphisms then a natural transformation between functors of such categories is an inner automorphism, i.e. if we have ...
- 4,519
11
votes
3
answers
1k
views
Does Ribet's level lowering theorem hold for prime powers?
I often use the following theorem (that one can state more generally) in my research.
Let E/Q be an elliptic curve of conductor N corresponding to a modular form f(E), l a prime of good or ...
- 818
4
votes
2
answers
551
views
Normality of an affine semigroup
An affine monoid is a finitely generated commutative submonoid of $\mathbb Z^k$ for some positive integer k. Let S be an affine monoid and let G(S) be the group generated by S. We say the monoid S is ...
- 1
29
votes
10
answers
5k
views
How can I really motivate the Zariski topology on a scheme?
First of all, I am aware of the questions about the Zariski topology asked here and I am also aware of the discussion at the Secret Blogging Seminar. But I could not find an answer to a question that ...
- 12.3k
1
vote
2
answers
175
views
Freeness of the Canonical $SU(n)$ Action
I have another question about $SU(n)$, again I hope it's not too basic. For $n=2$, the action of $SU(2)$ on $C^2$ is free since it's equal to the group of rotations. In general, the group of rotations ...
- 28k
7
votes
1
answer
918
views
Integral expression for zeta(2)
By computing the sum of all Bernoulli numbers via Borel summation (I learned this technique from Varadarajan's excellent book Euler through time. A new look at old themes, 2006) I found that $$\sum ...
- 4,485