# All Questions

**-1**

votes

**1**answer

20 views

### Techniques to solve a non linear differential equation related to curvature

Many years ago, I considered the following non linear differential equation:
$y=y''.(1+y'^{2})^{-3/2}$
This equation expresses the equality between the value of a given function $y\in C^{2}(R)$ and ...

**3**

votes

**0**answers

17 views

### Categorification of covering morphisms

Given a category $\mathsf{A}$, let $\mathsf{Fam}(\mathsf{A})$ be its free coproduct cocompletion (which is always extensive). This means every object has a unique up to iso presentation as a coproduct ...

**1**

vote

**0**answers

13 views

### Linear systems of equations with singular coefficient matrix

There are different well-established bounds on solutions to systems of linear equations $Ax=b$ where $A$ is non-singular. In some way or another, they amount to the condition number $\| A^{-1} \| \| A ...

**1**

vote

**0**answers

5 views

### What is the (quasi-) classical limit of categorified quantum groups?

$\newcommand{\g}{\mathfrak g}$
Let $G$ be a reductive group and $U_q(\g)$ the associated quantum group. One can argue that the classical limit of $U_q(\g)$ is $G$ or $\g$, with some Poisson structure, ...

**1**

vote

**0**answers

15 views

### busby invariant of extensions of $C^*$-algebras

I have a question of an explicit example of a busby invariant of a extension, which can be found in Blackadars book "K-theory for Operator Algebras".
Let $0\to B\to E\to A\to 0$ be a short exact ...

**0**

votes

**0**answers

7 views

### Can the extragradient method be computed only based on proximal steps?

As we know, for solving saddle point problems, the forward-backward algorithm is generally not guaranteed to converge. But the extragradient method converges Structured Prediction via the ...

**0**

votes

**1**answer

113 views

### What is the best currently proven bounds on prime gaps?

I did some digging around on the internet but I found tons of different equations on both lower and upper bounds for the largest possible prime gap g(n). I was wondering what are currently the best ...

**3**

votes

**2**answers

147 views

### Does there exist a non-hyperelliptic Riemann surface with automorphism group $C_2\times A_4$?

Does there exist a non-hyperelliptic Riemann surface of genus 5 with automorphism group $C_2\times A_4$?

**-5**

votes

**0**answers

48 views

### Sine, Cosine and Tangent functions [on hold]

Is the input of a Sine, Cosine and Tangent function always an angle?

**2**

votes

**0**answers

51 views

### Nonvanishing of the dual Euler totient on boolean intervals of finite groups

The rank $n$ boolean lattice $B_n$, is the subset lattice of $\{1,2, \dotsm n \}$.
Let $[H,G]$ be a boolean interval of finite groups. Its Euler totient is defined by $$\varphi(H,G):=\sum_{K \in ...

**-5**

votes

**0**answers

20 views

### Newton's second law [on hold]

enter image description here
Which is the speed for x=4m? Given a mass equal to 3kg.

**0**

votes

**0**answers

78 views

### Does an isogeny always define a covering map?

Consider a map $f: G_1 \to G_2$ between two topological groups. If $f$ is an isogeny when viewing $G_1,G_2$ as algebraic groups does $f$ always define a covering map when viewing $G_1,G_2$ as ...

**2**

votes

**0**answers

45 views

### Wave trace on $\mathbb{S}^1$- $\langle w,\varphi\rangle=\int_{\mathbb{S}^ 1} (\sum_{k \geq 1} e^{it \sqrt{\lambda_k}}) \varphi(t) dt$ [on hold]

An exercise asks to find the wave trace $w(t)=\operatorname{tr} \left(e^{it \sqrt\Delta}\right)=\sum_{k \geq 1} e^{it \sqrt{\lambda_k}}$ as a distribution (or generalized function) of the Laplacian ...

**2**

votes

**1**answer

32 views

### Operators on Hilbert $C^*$-module and families of Fredholm operators

If $A$ is a $C^*$-algebra, there is a notion of Hilbert $A$-module (which is something like Hilbert space but the inner product takes values in $A$). The standard example is ...

**2**

votes

**0**answers

79 views

### Semistability of a sheaf on nodal curve

Suppose $X$ is a projective, connected, nodal curve (can be reducible) over an algebraically closed field $k$ of arbitrary characteristic. Let $F$ be a pure sheaf on $X$ and denote by $\pi^{*}(F)$ its ...

**1**

vote

**0**answers

27 views

### Regularization by mean curvature flow

I have a $C^{1,\alpha}$ surface defined as the graph of some function $\varphi : B \to \Bbb{R}_+$ ($B$ is a ball). This surface has positive and bounded mean curvature in the weak sense (since the ...

**-1**

votes

**0**answers

17 views

### Optimal ordering in Jacobi SVD algorithm

In Jacobi SVD algorithm as given here every pair of columns of the matrix is orthogonalized until convergence. I want to know that how does the order of selection of the pair of columns affect the ...

**2**

votes

**1**answer

110 views

### (quasi)metric on Riemannian manifolds via Brownian Motion?

Given points $a$ and $b$ on a Riemannian manifold $M$, I would like a (quasi)metric that corresponds to some property of Brownian Motion from $a$ to $b$ (or rather, to $\epsilon$-ball $B = \{ x : |x - ...

**3**

votes

**0**answers

40 views

### Singular reduction in infinite dimension

In 1991, Sjamaar and Lerman [1] introduced the notion of stratified symplectic spaces. Namely, if $M$ is a symplectic manifold and $G$ a Lie group acting properly (but not necessarily freely) on $M$ ...

**11**

votes

**0**answers

112 views

### What are the indecomposable $U_q\mathfrak{sl}(2)$-modules?

Let $\mathfrak g=\mathfrak{sl}(2)$.
Let $\zeta$ be a primitive root of unity of even order. Say $\zeta=e^{2\pi i/6}$, for concreteness.
Let $U_q\mathfrak g$ be Lusztig's integral form of the ...

**6**

votes

**0**answers

148 views

### Universal Property of Fontaine's Period Ring $B_{dR}^+$

In the introduction to his Asterisque Expose "Le Corps des Periodes p-Adiques",
Fontaine announces a characterization of $B_{dR}^+$ by some universal property. Unfortunatly,
at least for $B_{dR}^+$ ...

**12**

votes

**1**answer

263 views

### List of Applications of the $\partial\overline{\partial}$-lemma

Quoting from Huybrecht's book Complex Geometry on the $\partial\overline{\partial}$-lemma for Kaehler manifolds:
Although it looks like a rather innocent technical statement, it is
crucial for ...

**8**

votes

**0**answers

90 views

### Measuring the failure of pushforward to commute with Steenrod squares

Let $f \colon X \rightarrow Y$ be a map of topological spaces. Let's say that they are (closed) manifolds (not necessarily orientable), though to be honest I'm really interested in the more general ...

**1**

vote

**1**answer

43 views

### IFS maps on circle

A systems $<f_0,f_1>$ is minimal if the set $\{h(x): h=f_{i_n}\circ f_{i_{n-1}}\circ...\circ f_{i_1}, i_k \in \{0,1\},n>0\}$ is dense in $S^1$, for every $x\in S^1$.
Consider $f:S^1 \to S^1, ...

**0**

votes

**0**answers

42 views

### Irreducible root system decomposition

I am looking for the name of and a good reference on the following theorem
Theorem: let $G$ be a connected, compact and semisimple Lie group, and $T \subset G$ a maximal torus of $G$, there exists a ...

**0**

votes

**0**answers

42 views

### Algorithm for checking linear independence of algebraic numbers

Is there any if and only if condition for checking $Q$-linear independence of given a set of numbers say $\alpha_i$ ? More precisely how to check linear independence of given $n$ algebraic numbers ...

**1**

vote

**0**answers

71 views

### Is there a non-integer in the dimension spectrum for the Heisenberg group?

Let $\Gamma = \langle a,b,c \ | \ c=aba^{-1}b^{-1}, \ ac=ca, \ bc = cb \rangle$ be the discrete Heisenberg group.
Let $\ell: \Gamma \to \mathbb{N} $ be the word length on $\Gamma$. This group has a ...

**0**

votes

**0**answers

18 views

### LP or IP necessary? Network Flow Problem with no cycle-condition (unimodularity?) [on hold]

I need your help with a optimization problem.
Recap:
Normal mincost flow networks optimization problems have a constraint matrix which is total unimodular. This is a nice feature since a linear ...

**-3**

votes

**0**answers

37 views

### Find function $h$ so that $h(U,V)$ equals density of $f(a)da$ for $f(a)=\frac{1}{2}e^{-\small|a|} ,a \in \mathbb R$ [on hold]

Let $f(a)=\frac{1}{2}e^{-\small|a|}$, $a \in \mathbb R$
and let $U,V$ be two independently uniformly distributed random variables on $[0,1]$.
Now I want to find a function $h$ so that $h(U,V)$ is ...

**1**

vote

**0**answers

54 views

### Kunneth decomposition of the relative diagonal of a projective bundle

Let $\mathcal{E}$ be a projective bundle of rank $r$ over a smooth complex quasi projective variety $B$, and form its associated projective bundle $\chi :=\mathbb{P}(\mathcal{E})$. Let $\pi : \chi ...

**-5**

votes

**0**answers

34 views

### Difficult derivative of the log of a function [on hold]

Can someone help me figure out how the derivative of log p(x) wrt. theta becomes to solution below ?
$ -\frac{\delta logp(x)}{\delta \theta} = \frac{\delta F(x)}{\delta \theta } - \sum p(x) ...

**0**

votes

**0**answers

48 views

### Reference request: Uniformly totally bounded classes of compact metric spaces are Gromov-Hausdorff precompact

The following Theorem can be found for instance here (Theorem 7.4.15):
Theorem. (author ?) Any uniformly totally bounded class $\mathfrak X$ of compact metric spaces is pre-compact in the ...

**3**

votes

**0**answers

46 views

### How many unimodular lattices does it take to fill a cube with high probability?

Consider $C_a$ in $\Bbb Z^n$ a cube of height $a$ at origin in positive coordinates with one corner at origin.
Consider the set $M_c$ of all unimodular matrices in $\Bbb Z^{n\times n}$ with each ...

**6**

votes

**0**answers

56 views

### Determinants of octonionic hermitian matrices

For quaternionic hermitian matrices (i.e. quaternionic square matrices $(a_{ij})$ satisfying
$a_{ji}=\bar a_{ij}$) there is a nice notion of (Moore) determinant which can be defined as follows.
...

**28**

votes

**2**answers

3k views

### Why is this new result such a big deal?

This popular article reports a recent result in reverse mathematics, showing that a certain theorem in Ramsey theory is provable from RCA$_0$, the base theory in SOSOA. Then there are a bunch of ...

**2**

votes

**0**answers

34 views

### Are Bipartite Matching and General Matching Really Different Problems?

Questions:
Have there been attempts to either prove or disprove, that every general matching problem can be transformed into a bipartite matching problem, from whose solution the solution ...

**8**

votes

**1**answer

91 views

### Does the Turaev-Viro theory for the generalized $E_6$ subfactor for $\mathbb{Z}/7$ distinguish $L(7,1)$ and $L(7,2)$?

In the paper Sato-Wakui "COMPUTATIONS OF TURAEV-VIRO-OCNEANU INVARIANTS OF 3-MANIFOLDS FROM SUBFACTORS" they compute certain Turaev-Viro-Ocneanu invariants of certain lens spaces. One of the results ...

**0**

votes

**0**answers

69 views

### Mathematical consulting or bioinformatics related careers for mathematicians with good statistics and coding experience in West Europe [on hold]

Before I start, apologies if the question is very specific, but these are exactly what I want to be. I should mention that I already studied:
"Industry"/Government jobs for mathematicians
...

**5**

votes

**1**answer

93 views

### Density of non-algebraic leaves in the characteristic foliation

Let $X$ be a compact complex manifold equipped with a holomorphic symplectic form $\omega$. Let $D$ be a smooth divisor on $X$. At each point of $D$, the restriction of $\omega$ to $D$ has ...

**5**

votes

**1**answer

132 views

### Bounding the degree of an algebraic extension containing solutions to polynomials

Also posted on math.stackexchange...
Let $F$ be a field, and let $f_{1},\ldots, f_{s}$ be polynomials in $F[x_{1},\ldots, x_{t}]$. Assume that the degree of the polynomials is bounded by $d$, by ...

**0**

votes

**0**answers

51 views

### Derandomizing AP existence in $A\subseteq \{1,\ldots,N\}$ for $\delta(A) \geq 1/k$

In the answer to the mathoverflow question here, it was established that if we let $p$ be the probability of including point $v$ in $A\subseteq \{1,\ldots,N\}$ and this is done independently for all ...

**0**

votes

**0**answers

47 views

### Splitting of totally geodesic Riemannian foliations

Let $\mathcal F$ be a non-singular Riemannian foliation on $(M,g)$ whose leaves are totally geodesic. Suppose further that the leaves are Riemannian products of irreducible manifolds $L=L_0\times ...

**1**

vote

**3**answers

102 views

### Hadwiger number and minimal degree

Suppose $G$ is a finite simple graph and $\eta(G)$ is the maximal $n\in\mathbb{N}$ such that $K_n$ is a minor of $G$. If $\delta(G)$ is the minimal degree, do we have $\delta(G)\leq\eta(G)$?

**11**

votes

**0**answers

137 views

### Concept associated to the Eudoxus reals

I am aware of three different constructions of the field of real numbers :
The Cauchy sequence construction : in this case, we see the field $\mathbb{Q}$ as a metric space and $\mathbb{R}$ is the ...

**0**

votes

**0**answers

271 views

### Becoming a Mature Mathematician [on hold]

I am currently a sophomore in my undergraduate mathematics program. It has taken me a while to take school seriously; I was one of "those" students who just skated by without studying until Linear ...

**0**

votes

**1**answer

92 views

### Convergence of unitary products on a Hilbert space

First: I'm sorry for the basic question--I can move it to Math SE if necessary...
Let $X$ be a Hilbert space and suppose $\{U_k\}_k$ is a sequence of unitary operators on $X$. Let $\|\cdot\|$ be the ...

**1**

vote

**1**answer

176 views

### Density of Sophie Germain $3\bmod 4$ primes

Is there any reason to expect the density of primes $p$ such that $2p+1$ is also a prime where $p=3\bmod4$ holds would be different from case of $p=1\bmod4$?
What if $2p+1$ is replaced by $2p-1$ and ...

**1**

vote

**0**answers

20 views

### A good version of truncated real radical ideal?

Suppose $\mathbb{R}[X]$ is the normal multivariate polynomial ring where $X = x_1...x_n$. $\mathbb{R}[X]_t$ is the truncated set such that $\mathbb{R}[X]_t =\left\{f: f \in \mathbb{R}[X], deg(f) \leq ...

**1**

vote

**1**answer

152 views

### harmonic analysis on $p$-adic $x^2 + y^2 + z^2 = 1$?

Are there p-adic analogues to spherical harmonics? In the case of $K = \mathbb{R}$, the spherical harmonics form a basis to $L^2 [SO(3)]$ where
What happens in the $p$-adic case? Is there sphere ...

**6**

votes

**1**answer

208 views

### On property of monic polynomial with integer coefficients

For a monic polynomial with integer coefficients $f$ where $\partial f = 2$, we have
$$
\textrm{inf}(f(x)) > 0 \implies
\textrm{inf}(f(x)) \geq \frac{3}{4} .
$$
Could we generalize this (for ...