All Questions

0
votes
1answer
36 views

William Thurston's quote?

Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding. Is this from Thurston? If yes, where and when it has been said. I've checked "ON PROOF AND ...
2
votes
1answer
22 views

Closures of orbits in the space of representations of a quiver

Let $Q$ be a quiver, and let $d=(d_i)$ be a dimension vector. We can consider Rep($Q,d$), the affine space consisting of representations of $Q$ with dimension vector $d$. The general linear $GL(d)= \...
-6
votes
0answers
28 views

Could someone please explain how these questions can be solved without a calculator

I am currently stuck on these practice questions and was wondering If I could get some advice to help solve them. Questions here
-3
votes
0answers
31 views

It is possible to draw 15 line segment such a way that each line segment intersect exactly 5 others ? Justify your answer [on hold]

i am stuck in above question. 5*5 line i draw then only it is possible to cut 5 points and all 5 need to be parallel horizontally and 5 vertically. how can we prove above.
2
votes
0answers
17 views

Does the cubical nerve preserve weak equivalences of simplicial sets?

The finite cartesian powers of $\Delta[1]$ form a cubical object in simplicial sets, inducing a "cubical nerve" functor $N_\Box: sSet \to Set^{\Box^{op}}$. $N_\Box$ is a right Quillen equivalence, ...
0
votes
0answers
13 views

Fokker-Planck equations where drift and/or diffusion terms are not differentiable at some points

Fokker-Planck equations are given by Is this equation correct if drift ,$\mu(x,t)$, or diffusion term ,$D(x,t)$, are not differentiable with respect to $x$ at some points? If not, then how to drive ...
0
votes
0answers
16 views

A Riccati type integral inequality

Let $x(t),t\in [1,\infty)$ be a nondecreasing positive function satisfying the following inequality: $$ x'(t) \le \int_t^{+\infty} x(s)\frac{k(s)}{s^2}\,ds, $$ for any $t \ge 1$, where $k(t),t\in [1,\...
3
votes
1answer
104 views

Are complete minimal submanifolds closed?

Is it true that any complete minimal submanifold of some Riemannian manifold is closed as a subset? What about the case in which the ambient manifold is an euclidean space?
3
votes
1answer
71 views

Explaining the consistency of PRA and ZF from predicative foundations

Recently I got interested in predicative foundations, mostly because of Laura Crosilla's work and because Agda employs a predicative type theory. From the point of view of a predicative foundation to ...
2
votes
0answers
52 views

Chromatic polynomial and the circle

In https://arxiv.org/pdf/1208.5781.pdf It is proved that there is spectral sequence converging to $H^*(M^G,R)$ with the E1 page given by the graph cohomology complex $C_A(G)$ where $A:=H^*(M,R)$. My ...
0
votes
0answers
17 views

Smallest eigenvalue for Gram matrix of unit norm matrices

Given $n$ symmetric matrices $A_1, \dots, A_n \in \mathbb{R}^{k\times k}$, such that $\|A_i\| \leq 1$ for all $i$, we consider the matrix $M \in \mathbb{R}^{n\times n}$, where $M_{ij} = \langle A_i, ...
0
votes
0answers
129 views

Are there any schools of mathematics that hold that one should know the proof to every theorem that they know? [on hold]

Disclosure: I am not a research mathematician, but an undergraduate in that field. I have noticed that the pedagogical model for my entire math education has depended on memorization of theorems ...
1
vote
0answers
60 views

Flatness of the integral closure

Let $R$ be a $p$-torsion free ring which is integrally closed in $R[1/p]$ and let $S$ be a finite etale extension of $R[1/p]$. Is it true that an integral closure $S^+$of $R$ in $S$ is flat over $...
1
vote
0answers
38 views

Differential equations satisfied by quasi modular forms?

It is known that modular forms are solutions of differential equations. More precisely, let me cite the statement from the following question. Differential Equations Satisfied by Modular Forms ...
0
votes
0answers
19 views

Infinite spectral norm of linear mapping

Suppose we have a linear mapping $A:\mathbb{R}^m\rightarrow \mathbb{R}^n$. We define its $k$-spectral norm as: $\sigma_k(A)=\sup_{x} \frac{||Ax||_k}{||x||_k}$. We know that when $k=2$, $\sigma_2(A)$ ...
2
votes
0answers
55 views

Finding a curve through divisor

Let $k$ be a field. Is it true that for any smooth irreducible projective $k$-variety $X$ and a dense open set $U\subset X$, for any zero-cycle on $X$ one can find an irreducible curve containing its ...
1
vote
0answers
40 views

Hardy-Littlewood in Sobolev Spaces

For an application in kinetic theory I have to apply the Hardy-Littlewood-Sobolev(H-L-S) for $q=\infty$. The dimension is $3$ and H-L-S inequality says that for $1<p<q<\infty$ and $0<\nu&...
1
vote
0answers
41 views

On the exponent of a certain matrix $A$ in characteristic $p > 0$

Let $A$ be a square matrix in characteristic $p > 0$ with both column and row having length $(1 + p + \cdots + p^i)$, where $i > 0$. Suppose that further the $(m,n)$-component $a_{m,n}$ of the ...
-4
votes
0answers
52 views

Euclidean Geometry [on hold]

In Euclidean Geometry we can create a square with side length of $\sqrt2$. as we know, $\sqrt2$ is a number which has no end. so it is physically impossible to have a square with this length in the ...
0
votes
0answers
16 views

Find and prove optimal solution for a linear programming problem

Given $C \in R^+$, $\epsilon \in R^+$, $vec \in R^n$ and $eps = [\epsilon \dots \epsilon]$ vector of n $\epsilon$ I have to $ \textrm{minimize } [vec, eps]^T [x_1, x_2]$ with $x_1, x_2 \in R^n$ ...
1
vote
0answers
39 views

Component Groups of Reductive Groups

Suppose $G$ is a reductive group that is not necessarily connected and $Z \subset G$ is a central subgroup. Suppose $G^0$ is the identity component of $G$. Is it true that $G/G^0Z= \pi_0(G/Z)$? I can ...
0
votes
0answers
20 views

Estimate on Covariant Derivatives of Coordinate Derivatives

I am currently reading Topping's lecture notes on Ricci flow. At one point in the narrative (page 65) he says that using the fact that $\bigg(\frac{\partial}{\partial t}\nabla - \nabla \frac{\...
-3
votes
0answers
22 views

Fundamentals of Networks and Graph theory: listing labelled graphs with given number of edges [on hold]

Under the assumption of simple graph, how it is possible to determine the list of all the labelled graph with order 4, and so vertex set {1,2,3,4} and three edges?
9
votes
1answer
157 views

Quasimorphisms and Bounded Cohomology: Quantitative Version?

Consider maps from a discrete group $\Gamma$ to the additive group $\mathbb{R}$. A function $f:\Gamma \to \mathbb{R}$ is called a quasimorphism if it is locally close to being a group homomorphism. ...
-3
votes
0answers
53 views

Example coordinates for a dodecahedron in x, y, z? [on hold]

Good morning/afternoon/evening all, I'm working on some high-level Python simulations and wanted an example set of coordinates for the vertices of a regular dodecahedron in terms of x, y and z ...
5
votes
2answers
160 views

Compact complex affine Kähler manifold is a torus

Before giving a motivation let me ask the precise question firstly. By a complex affine manifold I mean a complex manifold $M$ with the property that there exists an holomorphic atlas for which ...
0
votes
1answer
36 views

Linear intersection number and chromatic number for infinite graphs

Given a hypergraph $H=(V,E)$ we let its intersection graph $I(H)$ be defined by $V(I(H)) = E$ and $E(I(H)) = \{\{e,e'\}: (e\neq e'\in E) \land (e\cap e'\neq \emptyset)\}$. A linear hypergraph is a ...
5
votes
0answers
53 views

Spectral radius for multiple linear operators

Suppose that $X$ is a finite dimensional Hilbert space. Let $A_{1},\dots,A_{r}:X\rightarrow X$ be linear operators. Then define the multi-spectral radius of $(A_{1},\dots,A_{r})$ to be $$\limsup_{n\...
4
votes
0answers
77 views

Integral geometry for general closed smooth manifolds

Let $M$ be a closed smooth manifold of dimension $2n$ for some positive integer $n$. Let $\mathit{Diff}(M)$ be the group of diffeomorphisms of $M$. Let $L$ be a closed embedded $n$-dimensional ...
-4
votes
0answers
19 views

Taylor series to give estimate for sin(pi/3 + 0.1) to 4d.p [on hold]

Taylor series to give estimate for sin(pi/3 + 0.1) to 4d.p. I know how to do this for sin(x) about x = pi/3 but not sure how to do this specific problem
2
votes
0answers
98 views

Do we believe that the distribution of spacings of successive critical zeros of zeta is log-symmetric?

Let $\gamma^{+}(T)$ be the imaginary part of the critical zero of $\zeta$ closest to $1/2+iT$ with $\gamma^{+}(T)\ge T$ and define similarly $\gamma^{-}(T)$ with a reversed inequality. Let $g(T)$ be ...
1
vote
0answers
41 views

Global solution of second order ODE defined on riemannian manifold

Consider the differential equation $\nabla \dot X + \frac{3}{t} \dot X + gradf(X) =0$, defined on a riemannian manifold $(M,g)$ ($ \nabla$ is the Levi-Civita connection and $gradf(X)$ is the ...
0
votes
0answers
37 views

Are total graph of power of cycles homeomorphic to powers of cycles?

Is the total graph associated to powers of cycles homeomorphic to powers of cycles themselves? I think yes, because the total graph associated to cycles is homeomorphic to cycles(i think?)So, does ...
4
votes
0answers
207 views

Comparing real topological K-theory and algebraic K-theory

Does there exist an integer $0<i<8$ with the following property: for any commutative unital ring $R$, there exists a compact Hausdorff space $X$ such that $KO^i(X)\approx K^i_{alg}(R)$? P.S.: ...
1
vote
1answer
90 views

A totally geodesic triangulation

Let $M$ be a compact orientable $n$ dimensional Riemannian manifold. Is there a triangulation of $M$ such that every $k$ dimensional face of each simplex is a totally geodesic submanifold, $\forall k ...
1
vote
0answers
48 views

Why restrict to $\Sigma_1^0$ formulas in $RCA_0$ induction?

I recently asked this question over on math.se, warmly welcomed by crickets. I hope it's appropriate here. I'm reading Stillwell's Reverse Mathematics, and the induction axiom was just introduced. ...
0
votes
0answers
28 views

Under which conditions the fixed points set is finite?

Let $M$ be a compact smooth manifold with an effective action by a Lie group $G$. Under which condition on the action and on $M$ the set of fixed points by this action is finite?
2
votes
0answers
48 views

Joining metrics of positive Ricci curvature

Let $M$ be a smooth manifold such that there is a closed submanifold $S\subset M$ with a Riemannian metric $g_S$ given by the restriction of a Riemannian metric on $M$ satisfying $\mathrm{Ricci}_{g_S}(...
1
vote
0answers
89 views

Status of locality of perfectoidness for uniform rings

Let $k$ be a perfectoid field of zero characteristic. Recall that a Tate $k$-algebra is called uniform if the set of power-bounded elements is bounded. Let $(A, A^+)$ be a uniform complete affinoid $k$...
2
votes
0answers
59 views

Solutions of a partial differential equations

I'm looking for solutions of a PDE of the form : $ P(t,x):[0,\infty]*[0,b]\rightarrow[0,1]$ $$ \partial_t P(t,x)= \partial_x [(1+2x) P(t,x)]$$ $$ P(0,x)=\delta_x (0)$$ $$P(t,b)=g(t)$$ Where $b$ is a ...
1
vote
0answers
39 views

Regularity minimizer

I am not an expert in calculus of variations and I am getting pretty lost in the vast literature. I've been studying the following functional $$ \int_\Omega (|\nabla f|+|\nabla g|)^2 dxdy $$ where $\...
0
votes
0answers
54 views

Regular intersecting family

Let $n=2k+1$. When $k=3$, the set of lines of Fano plane is a regular intersecting family consisting of some k-subsets of [n]. Do anyone know such examples for general $k$? Thanks.
5
votes
0answers
125 views

Generalizing the formula between Wu class and the Steenrod square

I know that on the tangent bundle of $M^d$, the corresponding Wu class and the Steenrod square satisfy $$ Sq^{d-j}(x_j)=u_{d-j} x_j, \text{ for any } x_j \in H^j(M^d;\mathbb Z_2) . \tag{eq.1}$$ ...
1
vote
0answers
18 views

Density of different types of critical points in an algebra of elementary embeddings

Suppose that $j,k:V_{\lambda}\rightarrow V_{\lambda}$ are elementary embeddings. Let $\mathrm{crit}_{n}(j,k)$ denote the $n$-th element in $\{\mathrm{crit}(\ell)\mid\ell\in\langle j,k\rangle\}$. ...
-7
votes
0answers
55 views

I need help about this math problem it seems i can't find answer [on hold]

Jack chose 25 instead of 24, then he chose 4 instead of 5 and after that he chose 36 instead of 35. If he needs to choose again which of the following numbers will he select ? Given answers: a: 9 ...
1
vote
0answers
69 views

Condition on a Lie groupoid to be represented by manifold/group or an action groupoid

Let $\mathcal{G}$ be a Lie groupoid. I am thinking of following questions. When do we know $\mathcal{G}$ is weakly/Morita equivalent to a Lie groupoid of the form $(G\rightrightarrows *)$ for some ...
0
votes
0answers
37 views

The case of a redundant disjoint sum

I'm trying to calculate $\Sigma (\Gamma_{\sigma})$ as discussed on p.230 of 'Structured meanings and reflexive domains' by Serge Lapierre. Use '$\Sigma(\Gamma)$' to indicate the disjoint sum of all $...
0
votes
0answers
33 views

Ellipticity-type condition

An elliptic operator $L=\mathrm{div}(A(x)\nabla u)$, is called uniformly elliptic if $$C^{-1}\mathrm{Id} \le A(x) \le C \mathrm{Id}$$ If $A$ depends also on $u$, what is the condition $$C^{-1} + C^...
0
votes
0answers
34 views

Need the numerical solution for the following two KdV equations [on hold]

I have been trying to solve the following Korteweg-de Vries (KdV) equation using NDSolve but nothing went right! The first equation is: $6 U_{t} + (9/2) U_{xxx}+ 9 U U_{x} - 6 a U_{x}=0$ and the ...
1
vote
0answers
58 views

Has this result about the number of permutations of a given cycle type (or centralizers) been proved?

I was playing with the cardinality of conjugacy classes of the symmetric groups, which we know is the number of permutations of a given cycle type and there is a natural one-to-one correspondence ...

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