**1**

vote

**1**answer

16 views

### The term $H^1(N,A)^{G/N}$ in the inflation-restriction exact sequence

[a repost from SE due to the lack of response]
Given a group $G$, let $A$ be a $G$-module and let $N\trianglelefteq G$.
If I understand it correctly, the superscript "G/N" in the third term of the ...

**-1**

votes

**0**answers

20 views

### Neighborhoods of a point in fppf topology

Does every point of a scheme (say over a dvr) have an irreducible neighborhood for fppf topology?

**2**

votes

**0**answers

20 views

### Isotrivial families with non-zero Kodaira spencer map

Let $S$ be a smooth quasi-projective curve over the complex numbers. Let $P$ be a closed point in $S$. Let $f:\mathcal X \to S$ be a polarized family of smooth projective connected varieties. To this ...

**-1**

votes

**0**answers

60 views

### If wolfram rule 110 is universal , does it mean it can solve mathematical equations? [on hold]

Stephan wolfram states that Rule 110 in Elementary Cellular Automata is computational universal .
Does it mean that it can solve mathematical equations , like the quadritic equations ???
And if it ...

**1**

vote

**1**answer

9 views

### Matroids similar to the cycle matroid

Let $G=(V,E)$ be a graph (loops and multiple edges are permitted). Three following systems of dependent sets in $E$ define matroids:
1) Set $A\subset E$ is dependent if $A$ contains cycle. This is a ...

**0**

votes

**1**answer

36 views

### quasi-projective and separated as topological properties

Let $X$ be a non-reduced noetherian scheme over $\mathbb{Z}$ or $\mathbb{C}$. Assume that $X^{red}$ is quasi-projective and separated, does the same hold for $X$ ?
(By the way, projective implies a ...

**1**

vote

**0**answers

21 views

### Terminology for polygons

As you may know term "polygon" might mean few different things
and its meaning has to guessed from context.
By some reason I have to use few of these meaning in one place.
So I converge to the ...

**1**

vote

**1**answer

18 views

### Coupled differential equations

I'm looking at the following coupled set of differential equations. Because of the symmetry, I'm hoping to be able to write down the solution for $x_n(t)$ and $y_n(t)$ in terms of $f(t)$ and $g(t)$, ...

**2**

votes

**0**answers

43 views

### Is this (funny) combinatorial optimization problem NP-hard ? (cutting numbers and placing them in urns)

The parameters of the problem are $m$ numbers which are integers (these numbers are denoted $b_i$), $n$ urns and in each urn, we can place $C$ numbers. We assume $nC \geq m$ so that the problem is ...

**1**

vote

**0**answers

18 views

### presentations of subalgebras

Assume that I have a finitely presented algebra $A$ over the complex numbers (by which I mean that $A$ is generated over $\mathbb{C}$ by finitely many elements $x_1,...,x_n$ subject to finitely many ...

**2**

votes

**0**answers

16 views

### Decomposition of the space according to the Ergodic Theorem

Given a space $(X, T)$, it is well known that for every $T$-invariant ergodic measure $\mu$, there exists a set $E_\mu$ of $\mu$-measure $1$ s.t. for every "nice" function $f$
$$ ...

**1**

vote

**0**answers

16 views

### A Feynman-Kac style derivation of a survival probability of a Compound Poisson process

Let $$R_t = u + \beta t - \sum^{N_t}_{i=1}U_i$$where $u\geq 0$, $\beta > 0$, $N_t$ is a Poisson counting process with intensity $\lambda$ and $U_i$ are jumps having a probability density $\nu(y)$ ...

**15**

votes

**2**answers

897 views

### Distributing points evenly on a sphere

I am looking for an algorithm to put $n$-points on a sphere, so that the minimum distance between any two points is as large as possible.
I have found some related questions on stackoverflow but ...

**1**

vote

**0**answers

86 views

### Why only Normed Linear Spaces? [on hold]

It is well known that "Norm on a vector space can be used to obtain a metric on that space."
I think easily we can generalize the notion of norms to groups and rings.
My questions are,
Why ...

**3**

votes

**1**answer

31 views

### Surgery along an arc connecting the components of a $2$-component link gives the unknot

Math Overflow seems to have a dearth of low dimensional topology, but this seems like an interesting question. Let $L$ be a $2$-component link in $S^3$. Suppose that there is a framed arc joining the ...

**1**

vote

**0**answers

29 views

### Root number of an anticyclotomic twist

Let $\lambda$ be a self-dual Hecke character over a CM field $K$ with root number $-1$. How to show the existence of a finite order anticyclotomic Hecke character $\chi$ over $K$ such that the twist ...

**5**

votes

**0**answers

78 views

### Coherent cohomology of the moduli space of curves

Is $H^i\left(\overline{\mathcal M}_g, \mathcal O_{\overline{\mathcal M}_g}\right)$ nontrivial for any $i>0$ and any $g$?
I was not able to find literature on this after searching for a bit, ...

**6**

votes

**0**answers

33 views

### Detecting positive endomaps of the formal reals

A locale is a sort of "formal topological space", which "may not have enough points to separate its open sets". For instance, there is a "locale of all real numbers that are both rational and ...

**7**

votes

**1**answer

110 views

### Does stationary reflection imply Mahloness?

Suppose $\kappa$ is strongly inaccessible and every stationary subset of $\kappa$ reflects. Must $\kappa$ be Mahlo?
Remarks:
It is possible for every stationary subset of $\kappa$ to reflect, but ...

**2**

votes

**0**answers

69 views

### What's the relationship between the different versions of the BBD decomposition theorem?

I have a few questions relating to the BBD decomposition theorem.
I have come across the following two versions of the decomposition theorem.
Version 1. Let $f : X \to Y$ be a proper map of ...

**1**

vote

**1**answer

85 views

### Purely inseparable field extensions of degree p

Take a field $k$. If $k'/k$ is a field extension of degree $p$, it is known that there are many possibilities for the isomorphism class of $k'$. See
...

**3**

votes

**3**answers

268 views

### Genus of a plane curve of the form $\prod_{i=1}^n (a_iX+b_iY+Z) = Z^n$

Does anybody know the genus of the following (projective) plane curve?:
$$\prod_{i=1}^n (a_iX+b_iY+Z) = Z^n$$
where the $a_i$'s and the $b_i$'s are complex numbers with $a_j \ne a_i\ne b_i \ne b_j$ ...

**8**

votes

**2**answers

291 views

### Witten's proof of Morse inequalities, question on eigenvalues?

See here. I present Theorem 6 and Corollary 7 as follows.
Theorem 6. For large $s$, $\Delta_s$ and $H$ have the same number of eigenvalues in the interval $[0, s^{-2/5}]$.
Corollary 7. $\dim ...

**2**

votes

**1**answer

336 views

### Weierstrass form of genus one $y^{10} z^{30} - 8000 y^{4} z^{20} + 12800000 z^{20} + 1600 y^{2} z^{10} - 64=0$

Related to the n-conjecture.
We are looking for Weierstrass form and map from it of the genus one curve:
$$ y^{10} z^{30} - 8000 y^{4} z^{20} + 12800000 z^{20} + 1600 y^{2} z^{10} - 64=0 $$
It is ...

**2**

votes

**1**answer

56 views

### Any formula for the partial sum of a remainder series?

Let $N \ge 1$ be an integer, and there is a series $ \{ N \mod 1, N \mod 2, ... , N \mod i, ... \}$. Obviously when $i \gt N+1$, the series will become $\{N, N, N, ..., \}$. So only take $i \le N$ ...

**1**

vote

**0**answers

56 views

### Questions about “On the homology of configuration spaces”

In the paper On the homology of configuration spaces, Bodigheimer-Cohen-Taylor, Topology 1989, Section 2.5, line 6 - line 8:
Question: How to prove this claim?
My attempt: I tried to prove that when ...

**-1**

votes

**0**answers

21 views

### Angle sum of triangle in Schwarzschild solution

Curvature of space is often intuitively explained as angles of a triangle not adding up to 180 degrees. I was wondering how well that applies in the context of General Relativity.
Suppose you have a ...

**0**

votes

**1**answer

64 views

### Adjointable Abelian Monoidal Functor

Given two abelian monoidal categories ${\cal C,D}$ (where the monoidal operation is bilinear) and an additive monoidal functor $F:{\cal C} \to {\cal D}$. Will $F$ always admit an adjoint?

**3**

votes

**1**answer

91 views

### Can we always add sets without collapsing cardinals or adding [very] bounded sets?

Given a model of $\sf ZFC$, and an infinite ordinal $\alpha$. Can we prove that there is always a cardinal $\kappa$, and a forcing $\Bbb P$, such that:
$\Bbb P$ does not add sets of rank ...

**2**

votes

**1**answer

81 views

### Counting elements with certain word length in abelian groups

Given a (finite) abelian group $G = \langle S \mid R \rangle$, has the problem of counting the number of elements which can be expressed as a word (in $S$) of length $\leq k$ been studied? If so, ...

**2**

votes

**1**answer

73 views

### Does the following characterize local presentability?

Let $\mathcal C$ be a cocomplete category. Consider the following two conditions:
$\mathcal C$ is locally presentable.
The Yoneda embedding $$\mathcal C \hookrightarrow \{\text{continuous functors ...

**2**

votes

**0**answers

57 views

### cross-sections of a sphere bundle

Let $M$ be a $m$-manifold and $M_0$ a submanifold of $M$. Let $X$ be a pointed topological space. In the paper On the homology of configuration spaces, Bodigheimer-Cohen-Taylor, Topology 1989, ...

**0**

votes

**1**answer

176 views

### Are there infinitely many $k$ for which $\frac{\sigma(k)}{k}=n^p$ and $p$ is an odd prime? [on hold]

I would like to know if there are infinitely many $k$ for which $$\sigma(k)/k=n^p$$ such that $m=k{n}^{p-1}$ with $m,n>0$ and $p$ is an odd prime?
Note: $\sigma(\frac{m}{{n}^{p-1}})$ is the sum of ...

**3**

votes

**0**answers

68 views

### Are smooth solutions to a PDE dense in the space of $L^2$ solutions to the PDE?

Let's say I have a linear differential operator $P$ with smooth coefficients between bundles $E$ and $F$ over a smooth compact manifold $X$ with smooth boundary. Let's consider $P$ as an operator ...

**2**

votes

**2**answers

130 views

### Divisibility among discriminants

Let $f(x)$ be an algebraic function over the field $\mathcal F$ of algebraic numbers over $\mathbb{Q}$. Suppose that $r \in \mathcal F$. Does the discriminant of $f(r)$ divide the discriminant of ...

**6**

votes

**1**answer

141 views

### Frobenius $A_{\infty}$-bialgebras?

Recall that a finite dimensional associative algebra $A$ over a field $k$ is called a symmetric Frobenius algebra (sometimes called "closed" Frobenius algebra) if its equipped with a symmetric non ...

**0**

votes

**0**answers

36 views

### How to find PDF of ordered random variables? [on hold]

Assumpion: Let $X_1, X_2, \ldots, X_L$ be $L$ independent and identical random variables (RVs). Let $F_{X_i}(x_i)$ and $f_{X_i}(x_i)$ be CDF and PDF of $X_i$. Suppose that $F_{X_i}(x_i) = F_X(x_i)$ ...

**0**

votes

**0**answers

62 views

### Hilbert scheme of relative subschemes of lenght 2

Let $\mathfrak X \rightarrow S$ a smooth projective family over the spectrum of a dvr. We know that $(\mathfrak X _{\eta_R})^{[2]}$ and $(\mathfrak X _{p})^{[2]}$ are smooth, where $p$ is the closed ...

**1**

vote

**0**answers

25 views

### concentration inequalities for quadratic forms of correlated random vectors

Let $\mathbf{n}$ is a Gaussian random vector with mean $\mathbf{0}$ and co-variance matrix $\mathbf{H}$. Let $\mathbf{r} = Sign(\mathbf{n})$, where $Sign(n_i) = 1$ if $n_i>0$ and $Sign(n_i) = -1$ ...

**1**

vote

**0**answers

96 views

### A true statement about sets; expressible? [on hold]

For any pair $(x,y)$ of sets, we obtain a unique set
$z=F(x,y)$ by letting $F(\emptyset,y)=y$ and
$F(\{x_i\}_{i\in I},y)=\{F(x_i,y)\}_{i\in I}$
if $I\ne\emptyset$ (the recursion eventually reaches the ...

**0**

votes

**0**answers

66 views

### Graphs from which two vertices can be exchanged

A graph is vertex transitive if $x \mapsto y$ by an automorphism. Let $P$ denote the stronger property that $x \mapsto y \mapsto x$ by an automorphism.
Simple facts:
$P \rightarrow$ unimodular. ...

**2**

votes

**0**answers

29 views

### Non-degenerate periodic orbits in the boundary of Lefschetz fibration over a disk

Suppose that $\pi:E \to D$ is a 4-dimensional Lefschetz fibration over a disk, and let $\Omega$ be a closed 2-form on $E$ such that it is non-degenerate fiberwise.
For any $x \in E$, there is a ...

**6**

votes

**0**answers

72 views

### A tensor product for triangulated categories?

Many triangulated categories which show up in mathematics, such as derived categories of various sorts, arise as the homotopy category of a stable $\infty$-category.
Stable $\infty$-categories give ...

**1**

vote

**0**answers

82 views

### Set of smooth curves on the Hilbert scheme is open. H

Let $H = Hilb_{d,g,r}$ be the Hilbert scheme of genus $g$ curves of degree $d$ in proyective space $\mathbb{P}^r$, over an algebraically closed field $k$.
Is it true that the set of points of $H$ ...

**6**

votes

**0**answers

124 views

### Bundles over Grassmanian with given top Chern class

So, I have been working on Chern classes for my master thesis and apparently (My proofs could be wrong and a few things are still vague) I was able to give a construction method and exhibit, via ...

**7**

votes

**1**answer

300 views

### Do modular forms show up in the cohomology of moduli spaces of unmarked curves?

Let $\overline{\mathcal M}_{g,n}$ be the compactified Deligne-Mumford moduli stack (although I don't think taking the coarse moduli space will make much of a difference here). If we decompose $g = 1 + ...

**10**

votes

**1**answer

197 views

### On the global structure of the Gromov-Hausdorff metric space

This is a purely idle question, which emerged during a conversation with a friend about what is (not) known about the space of compact metric spaces. I originally asked this question at ...

**2**

votes

**0**answers

72 views

### binomial coefficients and irrationals

The following, probably either currently impossible to deal with, or
having a negative solution, arose from an ergodic theory question,
presumably itself currently intractible. I am not a number ...

**1**

vote

**0**answers

107 views

### Probability of correlated residues

Given $N,c\in\Bbb N$, where $c\ll(\log N)^{1/b}$ for any $b>1$ is fixed, what is the probability that given $A_1,A_2,A_3\in\Bbb N$ with ...

**17**

votes

**1**answer

449 views

### Is there a generalization of homotopy groups to fractional dimensions

Does there exist a reasonable candidate for such an object as $\pi_{\frac12}(X)$?