All Questions
152,870
questions
6
votes
0
answers
359
views
Tensor product of dual groups
Let $G,H$ be compact abelian groups, $G^*,H^*$ be their Pontryagin duals, $G^*\otimes H^*$ the tensor product of $G^*,H^*$ and $K=(G^*\otimes H^*)^*$. Does the group $K$ have a special name? What is ...
2
votes
1
answer
572
views
Rational normal curves as set-theoretic complete intersections
Let $C\subset\mathbb{P}^n$ be a rational normal curve of degree $n$. It is know that $C$ is a set-theoretic complete intersection and that, if $n\geq 3$, is a not a scheme-theoretic complete ...
2
votes
1
answer
526
views
Is there an english translation of Delignes "La conjecture de Weil pour les surfaces K3."?
The title is pretty self explanatory: I'm looking for an english translation of Delignes inventiones paper "La conjecture de Weil pour les surfaces K3."
Anyone know if such a thing exists?
Thanks!
2
votes
1
answer
114
views
mean length of the non-crossing graphs on n points
My original question is rather vague so I'll start with a precise example and then indicate possible generalisations.
Given a n-tuple $x=(x_1,\dots,x_n)$ in, say, a square with side-length $1$ in the ...
11
votes
5
answers
2k
views
Are all almost regular graphs obvious?
Let the maximum and minimum degress of a graph be denoted (as usual) by $\Delta$ and $\delta$ respectively.
A graph is almost regular if $\Delta-\delta=1$.
Now, here is a simple way to generate ...
2
votes
1
answer
121
views
Growth of the truncation of the integral multiples of an irrational number
Let $[a]$ denote the integral part of a real number $a$.
Let $a$ be an irrational number and $b$ a real number greater than $1$.
Consider the sequence $(b^n(na-[na]))$ with $n$ running on the ...
0
votes
1
answer
265
views
determinant of integrals of forms
Let $A$ be a complex abelian variety of dimension $d$. Let $\omega_1, \ldots, \omega_j \in H^0(A, \Omega^1_A)$ be linearly independent (so $j \leq d$) and consider $\gamma_1, \ldots, \gamma_j \in H_1(...
0
votes
1
answer
196
views
A very natural question in weak* topology [closed]
Can you provide me a counter example for this.
Suppose that I have a sequence of probability measures
$(\mu_{r,t})_{r,t>0}$ on a compact space metric $X.$
Suppose additionally that:
there exists ...
1
vote
0
answers
89
views
Commutative algebraic groups endowed with a ring action
Let $k$ be an arbitrary closed field (of arbitrary characteristic). Assume that we have a short exact sequence of k-algebraic abelian connected groups
$$
1\rightarrow K\rightarrow G \rightarrow H\...
0
votes
0
answers
145
views
"Multiplying" Clebsch-Gordan series
Assume you have a Lie algebra $G$ and a Clebsch-Gordan series $A\bigotimes{B}=C\bigoplus{D}\bigoplus...$
Assume you have a Lie algebra $g$ and a Clebsch-Gordan series $a\bigotimes{b}=c\bigoplus{d}\...
8
votes
1
answer
446
views
Closure of $L(\ell^2,\ell^2)$ in $L(\ell^2,\ell^\infty)$
Let $\ell^2$, $\ell^\infty$ denote the usual sequence spaces and let $L(\ell^2,\ell^2)$ the Banach space of bounded linear operators from $\ell^2$ to $\ell^2$ as well as $L(\ell^2,\ell^\infty)$ the ...
6
votes
2
answers
513
views
Existence of an integral equation (Faedo-Galerkin, Banach fixed point, Picard-Lindelof)
This question is concerning the paper, particularly the proof of Lemma 2.1 in Section 2.1:
Matas, A., Merker, J. Existence of weak solutions to doubly degenerate diffusion equations, Appl Math 57 (...
9
votes
4
answers
1k
views
Action of a Lie group with finitely many orbits
EDIT: Let a real Lie group $G$ act on a smooth manifold $M$ with finitely many orbits such that each orbit is locally closed ($M$, but not $G$, may be assumed to be compact in my case). Let $\mathcal{...
6
votes
1
answer
594
views
Construction of a Bott manifold
I have been searching the literature for a construction of a simply connected spin manifold of dimension 8 with A-genus 1. I am not sure, but I think this is called a Bott manifold.
Can anybody help ...
6
votes
1
answer
291
views
Characterization of intermediate submodels of generic extensions
Question 1: Suppose that $V[G]$ is a set generic extension of $V$ by some forcing notion $P\in V,$ and suppose that $W$ is a model of $ZFC, V \subset W \subset V[G].$ Can we find a forcing notion $Q\...
13
votes
1
answer
464
views
A cdga for compactly supported cohomology (à la Sullivan's algebra of polynomial forms)
Let $M$ be a smooth manifold, and let $\Omega^\bullet(M)$ be the commutative dg-algebra of differential forms on $M$. It is quasi-isomorphic to the dg-algebra of singular cochains on $M$. If $M$ is no ...
8
votes
2
answers
2k
views
Maximal order of finite subgroups of $GL(n,Z)$
I am interested in the finite subgroups of $GL(n,Z)$ of maximal order.
Except for the dimensions $n = 2,4,6,7,8,9,10$ they are -- up to conjugacy in $GL(n,Q)$ -- in each dimension the group of signed ...
4
votes
1
answer
431
views
Circulant matrix with integer entries and determinant 1 or -1
CONJECTURE
Let $A= (c_0,c_1,\ldots,c_n)$ be a circulant matrix, i.e if $(c_0,c_1,\ldots,c_n)$ is the first column of $A$ then the $i$th column of $A$ is obtained by applying the permutation $(1,2,..,n)...
21
votes
2
answers
2k
views
Is there any research on set theory without extensionality axiom?
In practice (say, in computer science), collections with many "labels" ("identities"), or collections which occur in many copies, are more frequently used than sets. Such collections do not satisfy ...
9
votes
1
answer
545
views
What is the total polarization of the determinant?
Let $A\in\mathfrak{gl}(\mathbb{R},n)$ be an endomorphism, and think up to conformal factors (in particular, $\Lambda^n\mathbb{R}^n$ will be the same as $\mathbb{R}$). By the total polarization $\...
7
votes
1
answer
259
views
Problem with Eisenbud's Lemma "Symmetry of Diagonalization"?
This question was first asked on MathSE but nobody answered.
In his proof of Lemma A2.5 in his book Commutative Algebra with a View towards Algebraic Geometry, Prof. Eisenbud writes something like ...
1
vote
1
answer
264
views
Natural bundle, g-natural metric, meaning
I am trying to understand meaning and importance of a g-natural metric. Since I do pure differential geometry for my research, I am not familiar with many notions which are needed for understanding a ...
10
votes
1
answer
306
views
What sort of W-types follow from existence of an NNO?
A W-type is an initial algebra for a polynomial endofunctor $P$ on a category $C$. A well-known example is that of a natural numbers object (NNO). Usually it is assumed that $C$ is locally cartesian ...
9
votes
1
answer
760
views
Variant of Hilbert 90 for Galois extensions
Let $K/\mathbb F_q(x)$ be a finite Galois extension with Galois group $G$. Let $Aut(K)$ be the group of $\mathbb F_q$-automorphisms of $K$.
Obviously, $G\subseteq Aut(K)$. It is well known that
$H^1(G,...
3
votes
1
answer
128
views
Polygonal Venn diagrams
Suppose that the interiors of $n$ $m$-sided planar simple closed polygons generate a $\sigma$-algebra $A$.
How many atoms can $A$ possess, at the most?
Failing an exact answer, how about good bounds?...
9
votes
1
answer
390
views
Shriek push-forward for parameterized spectra
In May and Sigurdsson's Parameterized Homotopy Theory, Proposition 2.2.11, four isomorphisms of functors are given. For a pullback square of base spaces $C=holim(A\overset{f}\to B\overset{j}\leftarrow ...
4
votes
2
answers
389
views
Is there a purely module theoretic characterization of semiprimitive rings?
A ring (say unital for simplicity) is semiprimitive (or Jacobson semisimple) if its Jacobson radical is trivial, or equivalently it has faithful semisimple module. Semiprimitivity is a Morita ...
2
votes
0
answers
120
views
Linear dynamical system with discontinuous coefficients
I am solving a linear dynamical system $X'=A(t) X$, where $t$ is the independent variable and $A(t)$ is a square matrix. Some of the coefficients of $A(t)$ have a discontinuity at a certain value of $...
15
votes
2
answers
2k
views
4d Constructive Quantum Field Theory
As a follow up to my previous question (How does Constructive Quantum Field Theory work?), I was wondering what difficulties physicists have had constructing 4d axiomatic qfts. Why has CQFT's success ...
0
votes
2
answers
929
views
Guidelines for writing proofs in math papers [closed]
In the light of the recent "proof wars" in symplectic geometry (in which some groups contend that proofs given by some other groups are wrong, see here, here and here) I thought it would be good to ...
2
votes
1
answer
126
views
the lower bounded of metrics on a group
Let $G$ be a finitely generated group, S is a set of generators. If $\forall s\in S, n\in \mathbb{Z}$, $\exists C>0$ such that $|s^n|_S\ge C|n|$, does it imply $\forall$ infinite order element $g\...
2
votes
1
answer
584
views
Is this system incomplete?
Let $\mathbf{SBM}$ be the normal modal logic system defined as $\mathbf{T}$ plus the following two axioms:
$$\mathrm{SB}: \Box(\Diamond p \rightarrow p)\rightarrow (p \rightarrow \Box p)$$
$$\mathrm{...
2
votes
0
answers
335
views
Enumerating certain types of permutation polynomials
Given a prime power $q$, I would like to enumerate (preferably up to isomorphism*) all the permutation polynomials $f(x)$ on $K = GF(q^3)$ satisfying the following conditions:
$f(ax) = af(x)$ for all ...
22
votes
2
answers
4k
views
2d Ising model in conformal fields theory and statistical mechanics
I am not completely sure that this question is appropriate for this mathematical site. But since in the past I did get on MO couple of times nice answers to rather physical questions, I will try. ...
3
votes
2
answers
547
views
Recommended textbooks for Hamiltonian group actions?
I am doing a project on Hamiltonian group actions on symplectic manifolds, and my supervisor was able to list several good books on Riemannian geometry to start me off, but he didn't know of any ...
4
votes
1
answer
119
views
Counterexample for closedness under union of $\prec_{\infty,\kappa}$ chains
Assume $\kappa$ is uncountable and $\phi$ is an $L_{\infty,\kappa}$ sentence. Let $K$ be the collection of models of $\phi$ partially ordered by $\prec_{\infty,\kappa}$. It is well-known that $K$ is ...
0
votes
1
answer
164
views
Uniform boundedness in $L^1[0,1]$ implies finite $\limsup$ almost everywhere for a subsequence? [closed]
Given a sequence of functions $f_k \in L^1([0,1])$ such that $||f_k||_{L^1(0,1)}\leq C$.
Is there a subsequence $\{k_l\,|\,l\in \mathbb N\}\subseteq \mathbb{N}$ such that for $\mathcal{L}^1$-almost ...
1
vote
1
answer
243
views
Ample divisors on $\mathbb{P}^n$ blown-up at $k$ general points
Let $X$ be the blow-up of $\mathbb{P}^n$ at $k$ general points. We can assume $k\leq n+4$. Let
$$D = aH-b_1E_1-...-b_kE_k$$
be a divisor on $X$. Are there conditions on $a,b_1,...,b_k$ ensuring that $...
2
votes
2
answers
130
views
formula for repeated finite differences
I am looking for a proof of a well-known fact, whose proof must be very easy, though I've been struggling to find it. Let $\Delta$ be the map from real-valued functions of a real variable, given by $(\...
0
votes
0
answers
70
views
Is it true that the set of points minimizing their distance to a multiset of intervals from a distributive lattice is an interval?
Let $(E, \preceq)$ be a finite distributive lattice, $H_E$ be the Hasse diagram of $E$ and $d$ be the distance on $E \times E$ defined as the length of the shortest path in $H_E$ between any pair of ...
1
vote
0
answers
89
views
Does the set of points minimizing their distance to a multiset of convex polytopes result in a polytope?
Let $\mathbb{R}^n$ be a normed affine space of finite dimension $n$, and $d : \mathbb{R}^n \times \mathbb{R}^n \mapsto \mathbb{R}^+$ be the distance derived from the norm under consideration. A convex ...
1
vote
0
answers
416
views
Application of conformal normal coordinates for higher order elliptic operator
Let $n>2$ be even. Consider a compact Riemannian manifold $(M^n,g)$ and denote with $P_g$ the critical GJMS operator.
Recall that $P_g$ is conformally invariant, i.e.
$$P_{\tilde g}=e^{-nu}P_g$$ ...
4
votes
0
answers
185
views
Has Quine's set theory NF been proved consistent (relative to ZF) [duplicate]
This question is an updated repetition of mathoverflow.net question The status of 'the consistency of NF relative to ZF' which I asked about a year ago. At that time the answer was that "the ...
0
votes
1
answer
282
views
Amenability of the Koopman representation
Let $G$ be a locally compact group which acts non-singularly on a standard probability space $(X,\mu)$. Consider the Koopman representation $\pi_X:G\rightarrow U(L^2(X,\mu))$ defined by
$(\pi_X(g)\xi)(...
3
votes
1
answer
317
views
A question about kawamata's proof of vanishing for big and nef $\mathbb{Q}$ divisors
Theorem 2 [1, p.46] Let $X$ be a non-singular projective algebraic variety of dimension $n$, and $D$ a numerically effective $\mathbb{Q}$-divisor such that $(D^n)>0$. We assume that the support of ...
3
votes
0
answers
746
views
New proofs of Euclid's theorem of the infinitude of primes?
Playing around with elementary inclusion-exclusion, I arrived at two simple variations of proofs of Euclid's theorem that I thought would be long known in the literature. So far I haven't been able to ...
1
vote
1
answer
231
views
Link between integral points on varieties and solutions to Diophantine equations
Let $k$ be a number field, $S$ a finite set of places of $k$ including the infinite ones and $F(X_1,\dots,X_n)$ a polynomial in $k[X_1,\dots,X_n]$.
I am looking for notes, books or surveys detailing ...
13
votes
3
answers
943
views
Dimensions of self-affine sets
Let $A$ be a $2\times 2$ matrix which we assume to be contracting, i.e., the exists $\alpha\in(0,1)$ such that
$$
\|A {\mathbf x}\|_2\le \alpha\|{\mathbf x}\|_2,\quad \forall {\mathbf x}\in\mathbb R^...
4
votes
0
answers
632
views
Define the space of distributions with algebraic decay?
A tempered distribution $u\in \mathcal{S}'(\mathbb{R})$ is said to be rapidly decreasing if for every $f \in \mathcal{S}(\mathbb{R})$, $u*f \in \mathcal{S}(\mathbb{R})$.
One rough way to motivate ...
4
votes
1
answer
134
views
Results where complexity bounds implies finite number of test cases
We have all been there, when a formula works for the first 30 parameters,
but it is not sufficient for a proof. My question is where one can actually just check a finite number of cases, to conclude ...