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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 ...
William of Baskerville's user avatar
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 ...
user avatar
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!
jacob's user avatar
  • 2,814
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 ...
kaleidoscop's user avatar
  • 1,268
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 ...
Felix Goldberg's user avatar
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 ...
Ángel del Río's user avatar
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(...
detted92's user avatar
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 ...
user39115's user avatar
  • 1,785
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\...
Hugo Chapdelaine's user avatar
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}\...
Hauke Reddmann's user avatar
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 ...
Winfried's user avatar
  • 261
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 (...
riem's user avatar
  • 256
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{...
user51305's user avatar
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 ...
user36924's user avatar
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\...
Mohammad Golshani's user avatar
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 ...
Dan Petersen's user avatar
  • 39.2k
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 ...
eins6180's user avatar
  • 1,302
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)...
Fabienne's user avatar
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 ...
Ioachim Drugus's user avatar
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 $\...
Giovanni Moreno's user avatar
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 ...
brunoh's user avatar
  • 1,136
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 ...
Novak Djokovic's user avatar
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 ...
David Roberts's user avatar
  • 33.8k
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,...
joaopa's user avatar
  • 3,655
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?...
David Feldman's user avatar
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 ...
Jonathan Beardsley's user avatar
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 ...
Benjamin Steinberg's user avatar
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 $...
Gateau au fromage's user avatar
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 ...
Jimbo's user avatar
  • 225
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\...
user50402's user avatar
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{...
JuneA's user avatar
  • 343
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 ...
Anurag's user avatar
  • 1,157
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. ...
asv's user avatar
  • 21.1k
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 ...
user109527's user avatar
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 ...
Ioannis Souldatos's user avatar
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 ...
Jdr's user avatar
  • 11
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 $...
user avatar
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 $(\...
David Epstein's user avatar
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 ...
user109711's user avatar
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 ...
user109711's user avatar
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. $$P_{\tilde g}=e^{-nu}P_g$$ ...
gin111's user avatar
  • 327
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 ...
Garabed Gulbenkian's user avatar
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)(...
m07kl's user avatar
  • 1,672
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 ...
user avatar
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 ...
user45947's user avatar
  • 955
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 ...
Wesley Barnard's user avatar
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^...
Nikita Sidorov's user avatar
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 ...
Goulifet's user avatar
  • 2,174
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 ...
Per Alexandersson's user avatar

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