2
votes
0answers
68 views

Update on list of open problems for Cherednik/Symplectic Reflection Algebras

Background: There are two lists of open problems about Cherednik or Symplectic Reflection Algebras from 2007: Ian Gordon's Problems, Chapter 9 in Symplectic Reflection Algebras, and Ginzburg & ...
2
votes
1answer
92 views

References for the Keisler Order

Are there any good/modern references on the Keisler order. I have been reading Keisler's original paper, "Ultraproducts which are not Saturated", which introduces the order. However it is somewhat ...
3
votes
1answer
59 views

$C^\infty$-vectors in general representations of Lie groups on locally convex spaces

This question is related to this one. Let $G$ be a real Lie group (I should emphasize I only care about ordinary Lie groups, not Lie groups modeled on locally convex spaces or anything like that). In ...
8
votes
0answers
113 views
+50

Newton polygons of modular polynomials

This is pretty much straightforward curiosity. Is there anything known about Newton polygons of classical modular polynomials (polynomial relations between $j(\tau)$ and $j(n\tau)$)? I understand that ...
-1
votes
0answers
43 views

Question about lim and sup of a function [on hold]

Let f(t,d) be a continuous function in t. Prove that: $\lim\limits_{m\to \infty}\sup\limits_{t\in[t_1,t_2]}f(t,d_m)=\sup\limits_{t\in[t_1,t_2]}\lim\limits_{m\to \infty}f(t,d_m)$ Does anyone have any ...
3
votes
1answer
142 views

Topology on the dual of a Frechet space

If $F$ is a Frechet space, is there any locally convex space topology on the dual $F'$, such that for each local diffeomorphism $f$ from an open subset $U$ of $F$ to $F$, the map $U \times F' ...
2
votes
1answer
102 views

Interpretation of Hochschild Homology groups

In all the literature I've come across there are many concrete interpretations of the first few Hochschild Cohomology groups. For example $HH^1(A,M)\cong Derivation/Inner Derivations$ etc.... In ...
7
votes
1answer
106 views

Multiplicative domains and conditional expectations

Let $M$ be an injective von Neumann subalgebra of $B(H)$. For a completely positive map $\phi:B(H)\to B(H)$, let $Mult(\phi)$ denote be the multiplicative domain of $\phi$. For any conditional ...
0
votes
1answer
79 views

Maximize combinatorial sum for boolean function

I am trying to maximize the function $$ S(f)=\sum_{j=0}^{n-\frac{n-1}{t}}(-1)^j{n-\frac{n-1}{t}\choose{j}}\sum_{i=0}^{\frac{n-1}{t}}(-1)^{f(i-j)}(t-1)^i{\frac{n-1}{t}\choose{i}} $$ for a function ...
-6
votes
0answers
44 views

solve for three unknowns. [on hold]

Apple cost 97 dollars. Orange cost 56 and lemon cost 3. The total amount spent is 16047 dollars and total fruits bought is 240 and each one is bought atleast one. Calculate how many of each have been ...
0
votes
0answers
75 views

Rationally building bridges from Jacquet-Langlands to Langlands functoriality conjectures

For now I mainly worked on very classical proofs (viz. Bolte & Johansson, Bergeron) of the Jacquet-Langlands correspondence, but I hope to be able to understand in what this special case lead ...
4
votes
0answers
91 views

The (global) theory of Borel equivalence relations

What do we know about the complexity of the theory of Borel equivalence relations, with the Borel reducibility order $\leq_B$? That is, let $\mathcal{B}$ be the set of all Borel equivalence ...
7
votes
1answer
193 views

If $G$ is compact, $H \leq G$ open, $V$ an irreducible $H$-rep, is $\text{Ind}_H^G$ semisimple?

Let $G$ be a compact group, $H$ a normal open subgroup, and $K$ a $p$-adic field (so that not all $G$-reps with coefficients in $K$ are semisimple). Let $V$ be a finite-dimensional topological ...
4
votes
1answer
107 views

Graphs where each edge belongs to the same number of 1-factors

Let $G$ be a simple connected graph that has at least one 1-factor. We'll define: $G$ has property A iff it is edge-transitive. $G$ has property B iff each edge belongs to the same number of ...
1
vote
2answers
80 views

Estimate maximal coefficient of a polynomial from a circle containing all roots

Suppose I have a polynomial $$ p(x)=\sum_{i=0}^n p_ix^i. $$ For simplicity furthermore assume $p_n=1$. As it is well known we may use Gershgorin circles to give an upper bound for the absolute ...
1
vote
0answers
58 views

On existence of right units with control of their norms

Does, there exist a Banach algebra with a family of right units with norms converging to 1, but without right unit of norm 1?
-2
votes
2answers
91 views

Lack of parabolicity of PDE due to invariancy under diffeomorphisms? [on hold]

Let a nonlinear differential equation is invariant under all diffeomorphisms, then we get lack of parabolicity?
3
votes
1answer
151 views

Ergodic theory reference for converging sequences of matrices

I have been told that the following is a well known theorem in ergodic theory & have been given the book by Furstenberg as a reference. However, I cannot find such a statement in it. Would anyone ...
5
votes
1answer
184 views

Is the Tate conjecture known for etale covers of products of curves

Let $X$ be a (smooth projective geometrically connected) surface over a finitely generated field $k$. The Tate conjecture predicts that, for $l$ a prime number invertible in $k$, the Chern class map ...
-2
votes
0answers
60 views

Property of $\limsup$ in $\ell_1$ [on hold]

Let $w$ be any element in $\ell_1$, and $(w_n)$ be a bounded sequence in $\ell_1$ that converge to 0 pointwise. I want to prove ...
3
votes
1answer
234 views

Lower bound for a prime gap occurring infinitely often

In his striking paper of may 2013, Zhang showed the existence of an even integer $g\lt 70,000,000$ such that $g$ is a prime gap occurring infinitely often. What is the best unconditional lower bound ...
5
votes
1answer
57 views

In the definition of the Heegard Floer surgery exact triangle, what exactly is the correspondence between Whitney triangles and periodic domains?

I'm reading Osváth-Szabó's notes on Heegard Floer homology, in particular about the surgery exact triangle. On page 14 (numbered 42 on the document), they describe an isomorphism between the space of ...
9
votes
1answer
472 views

Tight prime bounds

This is a cross-post of this question on MSE. I would not usually do this, but have decided to in this case since it has had no responses having been posted as a bounty question. I did not delete the ...
1
vote
0answers
43 views

Tensor product of commutators vs. commutator in a tensor product

Let $R$ be a (noetherian) commutative ring, and let $V$ and $W$ be finitely generated free $R$-modules. Let $X \subseteq \mathrm{End}_R(V)$ and $Y \subseteq \mathrm{End}_R(W)$ be finite subsets, and ...
1
vote
1answer
174 views

Integer points on $y^2=x^2-x^3+x^4$

Does the Diophantine equation $y^2=x^2-x^3+x^4$ have solutions other than $x=1,y=1$? Interestingly, the Diophantine equation $y^2=x^2-x^3+x^5$ has such solutions: $x=3,y=15$, $x=5,y=55$, ...
12
votes
2answers
457 views

History of the connection between Riemann surfaces and complex algebraic curves

As noted in the question "Links between Riemann surfaces and algebraic geometry", there are strong connections between Riemann surfaces and algebraic geometry - for example, compact Riemann surfaces ...
2
votes
0answers
46 views

Cusp points in Alexandrov spaces

Given a space of bounded integral curvature (by which I mean a topological surface with an intrinsic metric, such that the sum of excesses of any finite collection of non-overlapping simple triangles ...
2
votes
0answers
33 views

Looking for N-dimensional spheres in the configuration space of the colorful Tverberg problem

Here we use standard notation for Tverberg's theorem: Dimension $d$, number of partition blocks $r$, and $N=(r-1)(d+1)$. The configuration space of Tverberg's theorem is the simplicial complex ...
3
votes
1answer
46 views

Are lightface \Delta-1-1 classes of reals describable with hyperarthmetic formulae?

I'd appreciate if someone could check my reasoning. Suppose $S$ is a lightface $\Delta^1_1$ class of reals. I want to argue that there is a computable $\Delta^0_\alpha$ formula $\phi(Y)$, for ...
-1
votes
0answers
55 views

Basis for the rational functions [on hold]

The rational functions $f(x)$ are given by $f(x) = \frac{P(x)}{Q(x)}$ where $P(x)$ and $Q(x)$ are polynomials. What bases for the rational functions are generally used in numerical analysis?
0
votes
1answer
50 views

Topology : Study on Separation Properties [on hold]

I want an example of a completely regular space which is not a normal space. I have tried a lot but am unable to construct any example
9
votes
1answer
169 views

Borel-Serre compactification of $\mathbb{H}^3 / SL_2(\mathcal{O}_K)$

Let $\mathbb{H}^3$ be the three-dimensional hyperbolic space. Let $K$ be an imaginary quadratic number field and $\mathcal{O}_K$ its ring of integers. Then $SL_2(\mathcal{O}_K)$ acts on $\mathbb{H}^3$ ...
1
vote
0answers
92 views

Modular form, number of divisors [duplicate]

The Fourier expansion of Eisenstein series $E_k$ $(k \ge 4)$, which are modular forms, as well as the quasimodular $E_2$, involves powers-of-divisors $\sigma_{k-1}(n) = \sum_{d|n} d^{k-1}$. Is there ...
2
votes
3answers
228 views

Cardinality of $C^*([0,1])$ [on hold]

What is the cardinality of the continuous dual of $C([0,1])$ (the set of continuous functions from $[0,1]\to \mathbb{R}$)?
-2
votes
0answers
78 views

k to 12 philippines [on hold]

i just want to ask this question, hope you will answer..what will happen to students who didn't undergo the senior high school in k to 12, students who graduated in the old curriculum in ched the not ...
-1
votes
1answer
40 views

NonLinear Maps and homogeneity [on hold]

An example of a function $\phi : R^2 \to R$ such that $\phi(av) = a \phi(v)$ but $\phi$ is not linear. So I know that I need to find a function that has linear homogeneity but doesn't have the ...
2
votes
0answers
71 views

$G$-invariant part of products of determinants of minors

Let $G = SL_n$; then for any tuple $\lambda$ such that $\sum \lambda_i = n$, define $f_\lambda(g)$ as the product of the determinants of successive minors of lengths $\lambda_i$ of $g$ (e.g. for ...
5
votes
0answers
170 views

Factors of the polynomial $X^n-a$

I am interested in the polynomial $X^n-a$ in $\mathbb{Q}[X]$, for some $a\in \mathbb{Q}^*$, and would like to know the irreducible factors of it. Is there something in the literature which gives a ...
-3
votes
0answers
70 views

Is there a group-theoretic proof of the Riemann rearrangement theorem? [on hold]

The analytic proofs are easy to understand but they don't explain why commutativity breaks down when you go from finite sums to infinite sums of real numbers. I suspect that this involves the action ...
2
votes
0answers
31 views

Generators for lattice polytopes

Let $V$ be a finite set of integral vectors in $\mathbb{R}_n$. Consider the real (positive) convex cone $\mathbb{R}^+V$ spanned by $V$. We can assume that all vectors in $V$ are extremal in ...
12
votes
3answers
829 views

Not-lonely runners

The lonely runner conjecture has several formulations. They all involve a number $n$ runners running on a circular track, each with a different speeds, and the conjecture is that each runner is ...
2
votes
1answer
33 views

Compact imbedding - reference request

I am looking for reference to the following imbedding theorem Theorem For any $s>1/2$ fractional Sobolev space $W^{s}_2(0,1)$ imbeds compactly into $C([0,1])$. I know how to prove it but I need ...
-3
votes
0answers
72 views

How subset is a set is proved in ZF system? [on hold]

I guess that all subset is a set is guaranteed by the axiom of separation in ZF system. Otherwise the notion of power-set will not make sense. But I wander how it's proved. I guess that the prove ...
1
vote
0answers
102 views

Number of faces of a polytopal subdivision

Let $\mathcal{P}$ be a (bounded) polytope in $\mathbb{R}^d$ and let $\mathcal{C}$ be a polytopal subdivision of $\mathcal{P}$ [1]. Is there a known tight upper bound in the number of polytopes in ...
8
votes
1answer
651 views

Removing an article from arxiv [on hold]

I put up my paper on arxiv before sending it for submission. But now the journal I wish to submit it to is not accepting it since its already been published (or because its publicly available). Is ...
4
votes
1answer
199 views

The embeddings $S^{6} \to S^{7}$ and $S^{7}\to S^{8}$

Is the standard smooth structure of $S^{7}$ the only structure for which each of the following canonical embedding is an smooth embedding?: 1)$S^{6}\to S^{7}$ 2)$S^{7}\to S^{8}$
2
votes
0answers
124 views

Universal cover of elliptic curve without a point

This is something that I perhaps would be expected to know, but don't. Let $E_\tau$ be the elliptic curve ${\mathbb C}/({\mathbb Z +\mathbb Z} \tau)$. Consider the complement of a point in $E_\tau$, ...
2
votes
0answers
65 views

Degree of join of two varieties‏

Let $X\subset\mathbb{P}^n$ be an irreducible variety of degree $d$ and dimension $n-4$. Let $L\subset X$ be a line of mulitplicity $m$ in $X$. Assume that $m+1\leq d$ so that the general line spanned ...
5
votes
1answer
242 views

Serious introduction to the Langlands program for nonspecialist

I recently became interested in the Langlands program and hope to learn more. For context, I am an analytic number theorist but have some light background in algebraic number theory and modular ...
0
votes
0answers
29 views

Any software that can symmetrize input sets?

Is there any software that contains symmetrization techniques ex. polarization, Steiner Symmetrization etc. I suppose not. Which software would you suggest for rigid transformations? Thank you

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