0
votes
0answers
7 views

What are the invariants of $U\otimes V\otimes W$ under action of $GL(U)\times GL(V) \times GL(W)$

The tensor product of some (finite dimensional real) vector spaces is acted on by the direct product of their general linear groups. I would like to know if there are explicit invariants in the case ...
1
vote
0answers
15 views

What year was Hechler forcing created?

Hechler forcing is described on page 278, Jech. Does anyone know when Hechler forcing was first used in a publication?
4
votes
0answers
43 views

Comparison of K-groups of (affine) singular schemes with K'=G-groups

It is well known that Quillen K-theory coincides with $K'=G$-theory for regular schemes, and can be distinct from it for singular ones. Are there any methods for studying this distinctions? In ...
2
votes
2answers
65 views

Tomography problem involving a set of point masses

Consider a set of $N$ points in $n$-dimensional space, i.e. \begin{align*} \{x_1, \dots, x_N\} \subset \mathbb R^n. \end{align*} Let us be given a finite family of non-injective matrices ...
9
votes
1answer
247 views

Is the space of *-homomorphisms between two $C^*$-algebras locally path connected

Given the set of *-homomorphisms between two $C^*$-algebras $A$ and $B$, we may define a metric on it by setting $d(f,g):= \sup_{0<\|a\|\le 1}\|f(a)-g(a)\|$. Could it be true that, for each ...
2
votes
0answers
27 views

Extremal graph theory for directed graphs

In extremal graph theory, there are results such as $$t(C_4,G)\geq t(K_2,G)^4,$$ where $G$ is an undirected graph, $C_4$ is a cycle graph on 4 nodes, $K_2$ is a complete graph of $2$ nodes, and ...
1
vote
0answers
117 views
+50

Pullback of a sheaf associated to a divisor

I am reading a paper Desingularisation des varietes de Schubert generalisees by Demazure. I am interested in Lemma 3 on page 58. In particular, I would like to know whether the lemma is true and how ...
0
votes
0answers
29 views

Are the only discrete groups with nontrivial p-adic Haar measure finite?

Let K be a complete non-archimedean field (say $\mathbb{C_p}$) and let G be a discrete group. Since {e} is an open p-compatible compact subgroup of G, G admits a (left) K-valued Haar measure $\mu$. ...
3
votes
1answer
27 views

Zero currents localized along a submanifold

Let $\mathcal{D}(\mathbb{R})$ be the continuous dual of $C^\infty_c(\mathbb{R})$, the space of compactly-supported smooth functions. There is a nice characterization of distributions ...
0
votes
1answer
94 views

An extension of the real semiring with multiple degrees of infinity

Is it possible to define an extension of the probability semiring $(\mathbb{R}^+, +, \times, 0, 1)$ such that Closure $a^* = 1 + a + a^2 + \ldots$ is defined for every element of the semiring, not ...
-2
votes
0answers
22 views

Simplifying Trig Equation with Identifities [on hold]

I have an equation I have been given to solve, I know how to start but I do not know what to do after I use the Trig Identities. Any help? Here is what I was given (cos(A + B) + cos(A - B)) / ...
0
votes
0answers
18 views

Can finitely generated subgroups of limit groups be detected in free group quotients?

In Henry Wilton's excellent paper "Hall's Theorem for limit groups" (Geom. Funct. Anal. 18, pp. 271–303, 2008 ) he proves the following result (see his paper or here and here for the relevant ...
1
vote
2answers
180 views

Lifting a birational map of $X/G$ to a birational map of $X$?

Let $X$ be a projective complex manifold and $G$ a finite group. Assume that $G$ acts on $X$ holomorphically and freely. Is it true that any birational map $\phi \in Bir(X/G)$ lifts to some birational ...
2
votes
0answers
22 views

Universal property of module categories over monads

Let $T$ be a monad on a cocomplete category $\mathcal{C}$. Let's assume that $T$ preserves reflexive coequalizers (or something weaker?). Then $\mathsf{Mod}(T)$ is cocomplete, and I think that we have ...
1
vote
0answers
29 views

What is the early history of the concepts of probabilistic independence and conditional probability/expectation?

In the 1738 second edition of The Doctrine of Chances, de Moivre writes, Two Events are independent, when they have no connexion one with the other, and that the happening of one neither forwards ...
1
vote
0answers
87 views

Effective bound on $\sum_{N\mathfrak p \leq x}\chi(\mathfrak p)\ln(N\mathfrak p)$

I'm looking for an effective bound for $f(x) = \sum_{N\mathfrak p \leq x}\chi(\mathfrak p)\ln(N\mathfrak p)$, where $\chi$ is a Hecke character for a number field $K$ of degree $n$, on the ideals ...
5
votes
2answers
117 views

Is any quadric birational to a product of Brauer-Severi varieties?

Let $k$ be a field with algebraic closure $\bar k$. Assume that $k$ is perfect and not of characteristic $2$ for simplicity. Let $$X: \quad Q(x)=0, \quad \subset \mathbb{P}^n_k,$$ be a non-singular ...
2
votes
1answer
215 views

Does the property (P) holds true for the derivatives of $L$?

Let $$L(C,s)=\sum_{n=1}^\infty \frac{a_n}{n^s}$$ be the Dirichlet series of the Hasse--Weil L-function of an elliptic curve $C$ over $ℚ$. As $s$ takes on real negative values, there are trivial zeros ...
0
votes
0answers
14 views

Grassmann algebra morphism with universal property

I'm pretty sure that the following doesn't work, but nevertheless i wanted to ask, maybe this is a kind of well-known construction i've never heard of: Let $\Lambda(\mathbb{R}^n)$ be a finite ...
3
votes
0answers
53 views

Normal Subgroup Growth

Let $F$ be a free group on $d$ generators. Denote by $F_{k}$ the $k$-th term in $F$'s derived series. Put $G = F/F_k$. What is the normal subgroup growth of $G$? Explicitly, for each natural number ...
0
votes
0answers
25 views

Is there inverse FFT algorithm for Fourier transform of a integer-valued random variable?

In many applications, it is possible to derive an explicit expression for the fourier transform of a random variable $X$ $$\varphi (\theta ) = \sum\limits_{n = 0}^\infty {{p_n}} {e^{in\theta }}$$ ...
2
votes
1answer
27 views

Simple example of isolated critical point with non-semisimple monodromy

Consider a polynomial map $f :\mathbb{C}^{n+1} \rightarrow \mathbb{C}$ with $f(0)=0$ (no constant term) and with isolated critical point at $0 \in \mathbb{C}^{n+1}$. We can choose a disc $D$ of some ...
4
votes
1answer
191 views

Equivariant derived category and invariant divisor

I'm looking for a reference of the following (folklore?) result. Let $X$ be a smooth projective variety equipped with a $G=\mathbb{Z}/2\mathbb{Z}$ action (we consider the simplest case, everything ...
1
vote
0answers
19 views

A comparison principle for degenerate parabolic equation

Let $\Omega$ be a bounded smooth domain and let $p < 0$ be real. Suppose that $u, v \in L^2(0,T;H^1(\Omega) \cap L^2(0,T;L^2(\partial\Omega))$ with $|u|^{p+1} \in L^2(0,T;L^2(\partial\Omega))$ and ...
7
votes
1answer
112 views

Semiring of vector bundles on $\mathbb{C}\mathbb{P}^1$

Consider the semiring $$\mathbb{N}[H,H^{-1}]/(H^p+H^q = H^{p+q}+1)_{p,q \in \mathbb{Z}}.$$ Is it finitely presentable? Is there any simplification of the relations (except for $p \geq q \geq 0$)? ...
13
votes
0answers
209 views

The topologies for which a presheaf is a sheaf?

Given a set $S$, let $Top(S)$ denote the partially ordered set (poset) of topologies on $S$, ordered by fineness, so the discrete topology, $Disc(S)$, is maximal. Suppose that $Q$ is a presheaf on ...
-1
votes
0answers
11 views

regu tools l_curve regularization stanford ee 263 [migrated]

I am trying to solve one of the famous stanford EE263 problems, which gives me matrix A representing blurring of an image and y, representing the blurred image. For that I have been trying to use ...
6
votes
1answer
90 views

Immersions of $n$-manifolds in $\mathbb{R}^n$ versus embeddings in $\mathbb{R}^{n+1}$

Let $M$ be a connected noncompact parallelisable smooth $n$-manifold. (By Hirsch-Smale theory, $M$ can be immersed into $\mathbb{R}^n$.) I am interested in the following two properties: P1: $M$ can ...
2
votes
0answers
139 views

Advice for number theory library

Hi I just got a faculty position and it comes with a generous start up funds for "office supplies", which I must use or lose. What does a pure mathematician need? I have good computers already. I ...
2
votes
0answers
52 views

Infinite series of determinants

I am interested in what is known about the following class of sums. For a sequence of matrices $A_i$ (which possibly have different size), I am wondering about examples and methods for evaluating sums ...
2
votes
2answers
73 views

Bounds for the fat tail after trimming the mean?

I am interested in the quantity $$f(X,t) = \int_t^\infty\negthinspace x\ p(x)\ dx,$$ where $p$ is a probability distribution for a positive variable $X$. 1) Does this quantity $f(X,t)$ have a name? ...
3
votes
1answer
38 views

submatrix of a given size with maximum frobenius norm

Let $I\subset \{1,2,\ldots,n\}$, and let $|I|$ denote its cardinality. Now given a Hermitian matrix $\mathbf{A}\in\mathbf{C}^{n\times n}$. I am interested in finding the subset $I$ that maximizes the ...
2
votes
1answer
307 views

On quantities with no very small odd prime factors; a response to Wlodzimierz Holsztynski

In response to a comment posted under Powers of $2$ and the products of initial odd primes , I shall raise some questions about quantities near $O_n= P_{n+1}/2$, the product of the first $n$ odd ...
6
votes
4answers
426 views

Conjugation Quandles and… “Quandle-Groups”? From quandles to Groups

This question is already asked MathSE A quandle $(Q,*,/ )$ is a idempotent right-distributive and right invertible structure. 1) $a*a=a$ 2) $(a*b)*c=(a*c)*(b*c)$ 3) $(a*b) ...
5
votes
2answers
178 views

How to define the square root of $1-\Delta $?

If $M$ is a Riemannian manifold with $\Delta $ its Laplacian, how can we define $(1-\Delta)^{1/2}$? The book I am reading says that $(1-\Delta)^{1/2}$ is an invertible first-order pseudo-differential ...
2
votes
0answers
35 views

$p$-groups with $\Omega_1(G)\leq\Phi(G)$

Let $G$ be a finite $p$-group with $\Omega_1(G)\leq\Phi(G)$. What do we have information about this group?
2
votes
0answers
31 views

Reference for Frobenius’s proof of Schur’s finite version of the Rogers - Ramanujan identities

In his paper “Ein Beitrag zur additiven Zahlentheorie und zur Theorie der Kettenbrüche” I. Schur has stated that Frobenius has communicated to him a simple direct proof of his finite version of the ...
1
vote
1answer
97 views

What are finite groups $H$ such that $H^n(H,\mathbb{Q/Z}) \cong H_n(G,\mathbb{Z})$?

Let $G$ be a finite group and $G^{\prime}$ be its commutator subgroup. Let $\mathbb{Z}$ and $\mathbb{Q}$ denote the integers and rationals. $\mathbb{Z}$ and $\mathbb{Q/Z}$ treated as trivial ...
0
votes
0answers
24 views

First-countable topological monoids without local absorbing elements whose topology is induced by a semimetric

This is a follow up of Question 163246. For the reader's convenience, let me first copy&paste some basic definitions. We let a semimetric on a set $X$ be a function $d: X \times X \to [0,\infty]$ ...
-5
votes
1answer
49 views

An elementary question in abstract algebra [on hold]

Let K be a field and A be a K-algebra, then how can we show that $\lambda1_A=\lambda$ for $\lambda\in$K and $1_A$ is the identity of A?
-2
votes
1answer
32 views

How to find a matrix by its characteristic value and characteristic vectors? [on hold]

Now I am studying linear algebra course, In that for a given matrix we are finding the characteristic values (eigen vlaues) and characteristic vectors (eigen vectors). But my qustion is why cant we ...
2
votes
2answers
114 views

Interpolation of periods for a Hida family of modular forms

Let $\mathbf{f}$ be a Hida family of ordinary $p$-adic modular forms, and let $V(\mathbf{f})$ be the corresponding $\Lambda$-adic Galois representation (a quotient of the inverse limit $$ ...
1
vote
0answers
65 views

Estimate infinity norm with Lp and W1p norm

Let $p \in [1,\infty)$. Does there exist $C>0$ such that for every $f \in W^{1,p}([0,1],\mathbb{R})$ we have $$\|f\|_{L^\infty}\leq C\|f\|_{L^p}^{1-\frac{1}{p}}\|f\|_{W^{1,p}}^{\frac{1}{p}}?$$ My ...
6
votes
2answers
374 views

Translation length functions of non-simplicial trees

Let $G$ be a finitely generated group. By a theorem of Culler and Morgan, the set of non-abelian (not necessarily simplicial) minimal $\mathbb{R}$-trees with isometric $G$-action injects into the ...
14
votes
2answers
930 views

What is a Gaussian measure?

Let $X$ be a topological affine space. A Gaussian measure on $X$ is characterized by the property that its finite-dimensional projections are multivariate Gaussian distributions. Is there a direct ...
1
vote
1answer
65 views

Equivalence of star products on two differents Poisson algebras?

Let $A$, $B$ be two commutative and associative $\mathbb k$-algebras and let $A_\hbar:=A[[\hbar]]$, $B_\hbar:=B[[\hbar]]$ be the corresponding ring of formal series. Of sense [Deformation theory and ...
1
vote
0answers
29 views

A counterpart of Karhunen theorem

According to the Karhunen theorem, if the correlation function of a process $X(t)$ can be represented as $$ R(t,s)= \int_{\Lambda} f(t, \lambda) \overline{f(s, \lambda)}d\nu(\lambda) $$ then the ...
-1
votes
0answers
22 views

departure time/overlap algorithm [on hold]

i'm looking for "departure time/overlap algorithm" or any other idea. Suppose you have n trains and each one has a performance profile(how much electricity they need at the current time while driving ...
1
vote
2answers
46 views

Approximating Probability Distribution by Sampling

Consider a discrete probability distribution over $n$ events. Assume that the probabilistic kernel is a black box, that is, we can only sample from it without knowing anything about the type or ...
4
votes
1answer
688 views

Goin' with the flow with Kummer and Pascal: Combinatorics and geometry underlying the logarithm of the derivative operator

In a MO-Q111165 and associated MSE-Q125343, I present a pair of raising / lowering (creation / annihilation) operators $R_x = log(D)$ and $L_x = -x·D$ with $D=d/dx$ (for a sequence of functions ...

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