7
votes
1answer
143 views

Consistency strength of being strong cardinal and indestructible under collapses

What is the consistency strength of the following statement: $\kappa$ is a strong cardinals and it is indestructible under $Col(\kappa, <\theta),$ where $\theta> \kappa$ is some fixed ...
5
votes
1answer
150 views

Connes Embedding Conjecture and Fusion Categories

I was recently introduced to Connes' Embedding Conjecture (CEC) which states: Every separable type $II_{1}$ factor is embeddable into $R^{\omega}$. Where $\omega$ is a generic free ultrafilter on ...
-3
votes
0answers
51 views

Can somone explain a global cascade condition in plain english? [on hold]

Details here: https://en.wikipedia.org/wiki/Global_cascades_model#Global_cascades_condition If I have a hierarchical structure, what is the required number of nodes / clusters of nodes required to ...
6
votes
1answer
57 views

Analysis of the Laplacian of a random bipartite graph

My analysis of an engineering problem reduced to analysis of the Laplacian of a (random) bipartite graph. There are a few particular questions I am interested in, but not sure which direction to take ...
2
votes
0answers
27 views

Variance of a functional of transition probabilities using spectral gap of Markov chain

Consider an irreducible, aperiodic, time-reversible, discrete-time Markov chain on a finite state space $S$ whose Markov kernel is $K$ and unique stationary distribution is $\pi.$ Then, reversibility ...
6
votes
1answer
252 views

From polynomial ideal over $\mathbb{Q}$ to polynomial ideal over $\mathbb{Z}$

Is there an algorithm to compute, given a polynomial ideal $I\subset \mathbb{Q}[x_1,\dotsc,x_n]$, the ideal $I\cap \mathbb{Z}[x_1,\dotsc,x_n]$ in $\mathbb{Z}[x_1,\dotsc,x_n]$? The input and ...
5
votes
0answers
187 views

Is the stack of varieties with a big line bundle algebraic

In Starr's paper https://www.math.stonybrook.edu/~jstarr/papers/moduli4.pdf the folk result that the fibred category of pairs $(X\to S, L)$, where $S$ is an affine scheme, $X\to S$ is flat proper ...
3
votes
1answer
116 views

A relative property gamma and $L(\mathbb F_2)$

Given any unital non-commutative subalgebra $\mathcal M$ of $L(\mathbb F_2)$ is it true that $\mathcal M' \bigcap L(\mathbb F_2)^\mathcal U = \mathbb C I$ for any free ultrafilter $\mathcal U$?
1
vote
1answer
106 views

A question on $J(f)$ and $J(f')$

I was confused by the following question for a long time: Does there exists a transcendental entire function $f$ such that $J(f)\cap J(f')=\emptyset$ ? where $J(f)$, ($J(f')$) is the Julia set of ...
-1
votes
0answers
25 views

Total differential of a two dimensional convolution [on hold]

I have two functions h(x,y) and g(x,y). I need to show that the total derivative of their convolution results in $$ d(h ...
2
votes
0answers
41 views

question about the group completion of a simplicial monoid

In Daniel Quillen, On the group completion of a simplicial monoid pdf, MIT preprint 1971, Memoirs of the AMS vol 529, 1994, pp. 89-105, I do not understand the following part with question mark ...
1
vote
1answer
104 views

Are most random variables trivially sub-gaussian? [on hold]

I'm trying to understand sub-gaussian RVs to see if they could be relevant to my work. The common definition of a sub-gaussian RV is the following. X is $\sigma$ sub-gaussian if its laplace transform ...
0
votes
1answer
64 views

A group topology which commutes with closed subgroups

For a topological group $(G,\mathcal T)$ and a subgroup $H\le G$, we say $\mathcal T$ and $H$ are permutable if for every neighborhood $U$ of $1$, there is a neighborhood $V$ of $1$ with $VH\subseteq ...
2
votes
1answer
75 views

How to associate a proper parabolic subgroup of a real s.s Lie group $G$ to a non-trivial unipotent element in a non uniform lattice in $G$?

Let $G$ be a real semi-simple Lie group. Let $\Gamma$ be a non-uniform lattice in $G$. Then it is known that $\Gamma$ contains a non-trivial unipotent element. When $\mathbb{R}$-rank of $G$ is 1, it ...
3
votes
1answer
128 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 ...
3
votes
1answer
49 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 ...
5
votes
1answer
181 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 ...
5
votes
0answers
94 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 ...
-1
votes
0answers
77 views

Neighborhoods of a point in fppf topology [on hold]

Does every point of a scheme (say over a dvr) have an irreducible neighborhood for fppf topology?
-4
votes
0answers
116 views

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

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 ...
0
votes
1answer
92 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 ...
3
votes
4answers
202 views
+50

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 ...
2
votes
1answer
58 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 $g(t)$, ...
8
votes
0answers
170 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 ...
2
votes
0answers
53 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 $f$ $$ ...
0
votes
0answers
19 views

Relaxation of non-convex QCQP with one quadratic and one linear constraint

According to Boyd we know that a non-convex QCQP problem with one quadratic constraint has strong duality with the relaxed SDP or Lagrange counterpart. (check "Convex Optimization" by Boyd, Appendix ...
2
votes
0answers
133 views

Why only Normed Linear Spaces? [closed]

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 ...
1
vote
0answers
42 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 ...
2
votes
0answers
68 views
+50

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 $\nu(y)$ ...
0
votes
0answers
98 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 ...
7
votes
1answer
99 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 ...
8
votes
0answers
234 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, ...
3
votes
1answer
78 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
votes
0answers
33 views

Angle sum of triangle in Schwarzschild solution [on hold]

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 ...
4
votes
3answers
139 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 ...
3
votes
0answers
107 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 ...
2
votes
0answers
76 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, ...
10
votes
1answer
205 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 ...
4
votes
1answer
133 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
1answer
113 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, ...
0
votes
1answer
89 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?
1
vote
0answers
52 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
1answer
95 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 ...
5
votes
0answers
105 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
1answer
94 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 ...
0
votes
0answers
73 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 ...
-2
votes
1answer
87 views

Recursion, Common Term, Combinatorics [closed]

May we find the common term for recursive sequence? if yes that how to find the common term of recursive sequence such: 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 6 ... in a ...
7
votes
1answer
163 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 ...
2
votes
0answers
52 views

A specific class of $(0,1)$-matrices

Let $T_n$ be the class of $(0,1)$-matrices of order n with no row sum equal to a column sum. Is there any name or research about this kind of matrix? For any $A\in T_n$, let $S_A$ be the sum of all ...
3
votes
1answer
89 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 ...

15 30 50 per page