# All Questions

2answers
129 views

### Plane measurable sets and measurable rectangle

Does every measurable set in the plane with positive Lebesgue measure contain a cartesian product of two measurable sets of the real line with positive Lebesgue measures?
1answer
150 views

### Classifying space of a colimit of topological categories

Say I have a diagram $D:I\rightarrow\text{Cat}(\text{Top})$ of categories internal to compactly generated topological spaces. This induces a diagram $BD:I\rightarrow \text{Top}$ of classifying spaces. ...
0answers
108 views

### Reference to forcing with a sigma ideal $\cong$ Cohen forcing

This is a historical question: Who was the first person to notice the following? If $V \models \kappa$ is measurable and $P$ adds $\kappa$ Cohen reals, then in $V^P$, letting $\hat{I}$ to be the ...
0answers
56 views

### Curvature of vector bundles associated to holomorphic fibrations

Let $D=U\times \Omega$ in $\mathbb C^m\times\mathbb C^n$ be a pseudoconvex domain and $\phi$ is a strictly plurisubharmonic function on $D$. We suppose that $\phi$ is smooth up to the boundary. Now, ...
0answers
28 views

### How are residuals calculated in rugarch package [on hold]

I have a question regarding the rugarch package. I try to fit a ARMA(1,1)+GARCH(1,1) to a time series $x$ using the following command: spec <- ugarchspec(variance.model=list(model="sGARCH", ...
0answers
62 views

### Sources on evolution of submanifolds subject to Ricci flow

I am seeking any textbook or paper addressing the evolution of submanifolds of a manifold undergoing Ricci Flow. Please, any pointer towards this topic is more than welcome. This old MO post may be ...
0answers
149 views

### Determine existence of irreducible variety in given homology class

Given a homology class $\alpha \in H_k(X,\mathbb{Z})$ on a variety $X$, is there a way to determine if there exists an irreducible subvariety $Y \subset X$ that has that class, i.e. $[Y] = \alpha$? ...
2answers
317 views

### Group theory in machine learning

I'm a Machine Learning researcher who would like to research applications of group theory in ML. There is a term "Partially Observed Groups" in machine learning theory which has been popularized by ...
1answer
73 views

### Example to show pairwise crossing number is not equal to crossing number

A common point of two edges in a graph drawing that is not an incident vertex is called a crossing. The crossing number $cr(G)$ is defined to be the minimum number of crossings in any drawing of ...
0answers
88 views

### Is the cusp point of the curve $y^2=x^3$ a regular embedding? [on hold]

This question maybe trivial. Let's consider the curve $y^2=x^3$ over a field $k$. It seems to me that the point $(0,0)$ is a regular embedding of codimension $1$ because it is given by the equation ...
1answer
59 views

### Is there a general way to determine the Laplacian of the eigenvalues of a real symmetric matrix? [on hold]

I have a real symmetric $3\times3$ matrix $\mathbf{M}(\mathbf{r}$) which depends on $\mathbf{r} \in \mathbb{R}^3$. Each eigenvalue can be considered a scalar field $e_i(\mathbf{r})$ over ...
2answers
208 views

### Embedding $\mathrm{PGL}(n,q^h)$ in $\mathrm{PGL}(nh,q)$

It is not very hard to see that for each prime power $q$ and natural numbers $n,h$, we have an embedding $$\iota \colon \mathrm{GL}(n,q^h) \hookrightarrow \mathrm{GL}(nh, q),$$ obtained by choosing a ...
1answer
898 views

### Why should have Peter May worked with CGWH instead of CGH in “The Geometry of Iterated Loop Space”?

This is a follow-up to Dan Ramras' answer of this question. The following correction can be found in the errata to The Geometry of Iterated Loop space (Page 484 here). The weak Hausdorff rather ...
0answers
31 views

### When is a cycle in $KK^G(A,A)$ with zero operator the identity cycle?

Given a cycle of the form $(\pi,H,0)$ in $KK^G(A,A)$, when is it equivalent to the identity cycle $1_A=(i_A,A,0)$? The operator $T=0$, and $\pi:A \rightarrow L(H)$ may be injective. Any criterions ...
0answers
61 views

### What is the importance of the number $k+h^{∨}$ (level+dual Coxeter number)?

The number $k+h^{∨}$ appears at many places in the representation theory of affine Lie algebras (and probably elsewhere). Here $h^{∨}$ is the dual Coxeter number of the root system, and $k$ is the ...
0answers
52 views

### indecomposable finite groups [on hold]

A finite group $G$ is called indecomposable if it is non trivial and it cannot be decomposed as direct products of two non trivial subgroups, if not it's called decomposable. $\textbf{Examples:}$ ...
0answers
53 views

### Is this set compact? [on hold]

Let A denote the set of $m\times n$ matrices whose entries bounded by $1$ in absolute one. Is the set $A$ a compact set in the smooth function space $C^1(R^n,R^m)$ with $C^1$ topology?
0answers
24 views

### Find coordinate infinity points from unity point using synthetic geometric constructions [migrated]

A common way to put coordinates on $\mathbb P^k\mathbb R$ is to choose $k+2$ points (such that no one of them lies on the hyperplane generated by any $k$ of the others) and interpret them as the ...
0answers
51 views

### valuations on residue field of an algebraically closed nonarchimedean field [on hold]

Let $C$ be an algebraically closed nonarchimedean field, and $k$ be its residue field (like $\mathbb{C}_p$ and $\bar{F_p}$). We know that continous valuations on $C$ are 1-1 corresponds to valuations ...
0answers
65 views

### Is there any explicit result on the triangulated category of singularities of a curve?

This question is related to this MO question. Let $X$ be a projective curve over a field $\mathbb{C}$. We have the bounded derived category of coherent sheaves $D^b_{coh}(X)$ and the derived category ...
0answers
24 views

### Derive a closed formula for the generating function of this recurrence relation [on hold]

This is a given recurrence relation $a_n=19(F_0a_{n-1}+F_1a_{n-2}+...+F_{n-1}a_0)$ where $F_n$ is Fibonacci number and $a_0=9$. Find the generating function $A(x)$ of the sequence $a_n$ I get the ...
0answers
28 views

### Packing, Optimization [on hold]

I have a large box of 82cm * 82cm * 120 cm(this is always constant). How many smaller boxes of size 59cm* 34cm *43 cm can I fix in the large box? The size of the smaller boxes are the same and ...
0answers
36 views

### Hess-Schrader-Uhlenbrock inequality for non-symmetric operators

Let $M$ be a (compact, let's say) Riemannian manifold, $\mathcal{V}$ a vector bundle over $M$ with covariant derivative $\nabla$ and a fiber metric. Let $L = - \mathrm{tr}(\nabla^2) + V$ with some ...
0answers
64 views

### Pull-back of reflexive sheaves

Let $X$ be a noetherian, projective scheme, $\mathcal{F}$ be a reflexive sheaf on $X$ pure of dimension $\dim(X)$ and $Y \subset X$ be a closed subscheme of $X$. Is it possible that the pull-back of ...
2answers
462 views

### Obstructions for a group to be the multiplicative group of a field [duplicate]

It is well known that every finite multiplicative subgroup of a field is cyclic. I somehow got interested in a possible reverse implication: Assume we have an abelian group $G$ whose every finite ...
0answers
47 views

### lower bound on A(k,4,floor(k/2))

A(k,4,r) is the independence number of the Johnson graph J(k,r). What is the best known asymptotic lower bound on A(k,4,floor(k/2)) ? I only obtained ...
0answers
27 views

### Lattice-isotopic essentialization of arrangements

I'm working on a problem related to $\textbf{Randell's isotopy theorem}$ for complex hyperplane arrangements. I have a question which seems quite obvious. However, I haven't found a rigorous proof ...
1answer
143 views

3answers
256 views

### Has this formula for $G_{k}:=\lim\inf_{n\to\infty}p_{n+k}-p_{n}$ been conjectured?

I give here a heuristics that suggests that the quantity $\displaystyle{G_{k}:=\liminf_{n\to\infty}p_{n+k}-p_{n}}$ should be approximately equal to $k(1+H_{k})$, where $H_{k}$ is the $k$-th harmonic ...
0answers
96 views

0answers
72 views

### Generalization of Schur polynomials

I am making a list of generalizations of Schur polynomials and other closely related polynomials that appear in representation theory. My motivation is to eventually make a nice poster of ...
1answer
65 views

### Algebraic Groups of Type H_3 and H_4 [closed]

By coincidence i stumbled over this page http://www.fields.utoronto.ca/programs/scientific/11-12/exceptional/abstracts.html , which was installed for a workshop on algebraic groups in 2012. In the ...

15 30 50 per page