2
votes
0answers
19 views

Generalized Hurwitz Spaces

In this question all the varieties are over $\mathbb{C}$. Classic Hurwitz spaces $\mathcal{H}_{g,r}$ are moduli spaces of simple branched coverings $f \colon X \to \mathbb{P}^1$ of degree $d$, where ...
2
votes
0answers
24 views

Does the property of being a local homeomorphism descend through split surjections?

Let $f : X \to Y$ and $g : Y \to Z$ be continuous maps (between topological spaces). Assume these hypotheses: $f : X \to Y$ is a split surjection, i.e. has a section. $g \circ f : X \to Z$ is a ...
-4
votes
0answers
18 views

system of linear equations [on hold]

These are the two known equations (I2+I3)-(I1+I4)/(I1+I2+I3+I4) = 2x/L (I2+I4)-(I1+I3)/(I1+I2+I3+I4) = 2y/L where I know x,y,L values. How can I find the values of I1,I2,I3,I4?
0
votes
1answer
19 views

Hadamard Product and Eigendecomposition

I just found this related question in here Q1. Given a positive definite matrix $\mathbf{A}$, consider its eigendecomposition $(\mathbf{A}\mathbf{V} = \mathbf{V}\mathbf{D})$. Consider an arbitrary ...
0
votes
0answers
7 views

Oscillating Markovprocess Transition Probabilities

Suppose we have an irreducible positive-recurrent Markov process $\{X(t), t\geq0\}$ with generator $G$. Let $P(t)$ be its transition probability matrix and $\pi$ its stationary distribution. Then we ...
0
votes
0answers
7 views

Pseudo-braided fusion categories

A few definitions first, please replace with the standard terminology (and correct me if I confuse all the by-names of fusion categories :-) I call a complex number $z$ pseudo-cyclotomic if $|z|=1$. I ...
4
votes
0answers
55 views

How many Fréchet manifolds are there?

Clearly the title needs clarifying. Allow me to let "how many" to mean a set larger than a skeleton of the category of Fréchet manifolds and smooth maps, if this category is indeed essentially small. ...
1
vote
0answers
50 views

Two questions about Whittaker functions

I am watching the video: Modeling p-adic Whittaker functions, Part I. I have two questions about Whittaker functions in the video. From 33:00 to 37:00, it is said that after changing of variables, ...
1
vote
0answers
37 views

Analytic continuation of intertwining operator

I was trying to understand the paper "Form of GL(2) from analaytic point of view", by Gelbart and Jacquet. On Page 226 in Remark (4.13) they mention that the kernel of the local intertwining operator ...
0
votes
0answers
38 views

canonical divisors of a resolution of a normal surface singularity

Let $(0\in X)$ be the germ of a normal surface singularity and let $f: Y \to X$ be the minimal resolution. Questions> (1) How can I define a map $f_*\mathcal{O}_Y(K_Y)\hookrightarrow ...
9
votes
1answer
152 views

Are symplectic methods used in (classical) Economics?

The tl;dr question is this: are economists using coordinate-free formulations in studying theory? Borrowing from classical mechanics, the framework I have in mind for classical economics--involving ...
2
votes
2answers
62 views

If $X$ is compact, is $[X]^2$ compact, too?

Let $(X,\tau)$ be a Hausdorff space. Let $[X]^2 = \big\{\{x,y\}: x,y\in X \land x\neq y\big\}$. For $U,V\in \tau$ with $U\cap V = \emptyset$ we set $[U,V] = \big\{\{x,y\} \in [X]^2: x\in U\land y\in ...
2
votes
0answers
61 views

Are genus zero Gromov Witten Invariants on Del-Pezzo surfaces enumerative?

Let $X_k$ be $\mathbb{P}^2$ blown up at $k$ points (where $k$ is $0$ to $8$). Let $\beta \in H_2(X_k, \mathbb{Z})$ be the homology class given by $$ \beta := n L + m_1 E_1 + \ldots + m_k E_k $$ ...
-4
votes
0answers
17 views

log in calculating depreciation rate [on hold]

I can't understand log160=log2000+10log(1-r); 2.2041=3.3010+10log(1-r); 10log(1-r)=2.2041-3.3010; 10log(1-r)=-1.10969; ...
3
votes
0answers
78 views

Where can I find a proof of this result?

Here is an excerpt from the paper "The Hexagon Theorem" by Donald J.Newman Does anyone know where I can find a proof of the underlined statement? Newman states it without a proof, and I could get ...
4
votes
0answers
73 views

Map between homotopy groups of O, related to J-homomorphism and K-theory of Z

Let $s \geq 0$ be fixed. The $J$-homomorphism includes $\pi_{8s+1}(SO) = \mathbb Z/2$ in $\pi_{8s+1}^s$, the $(8s+1)$-th stable homotopy group of spheres. Now regard $\pi_{8s+1}^s = \pi_{8s+1} ...
1
vote
0answers
24 views

Examples of non-extremal subfactors

Every subfactor $(N \subset M)$ in this post are supposed to be finite index inclusion of ${\rm II}_1$ factors. Definition (here p64): Such a subfactor is called extremal if $tr_{N'} = tr_M$ on ...
1
vote
1answer
50 views

finite generation of a certain type of subring

Let $k$ be a field, and let $R$ be a finitely generated $k$-algebra. (If it helps, you may assume $R$ is an integral domain.) Let $I$ be an ideal of finite colength. Note that $A:=k+I$ is a subring ...
0
votes
0answers
16 views

Which properties determine the uniqueness of the local Artin map?

Any abelian extension of local fields can be realized as the completion of a global abelian extension. So let $L/K$ be abelian, $w/v$ an extension of places. From the global Artin map on ideles we ...
17
votes
0answers
230 views

What can topological modular forms do for number theory?

Topological modular forms ($TMF$) have in the recent years made an impact in algebraic topology. Roughly, the spectrum $tmf$ is the (derived) global sections of the sheaf of $E_\infty$ ring spectra ...
1
vote
1answer
42 views

Suggestions for dealing with the “timed” balls-into-bins model

Definitions: Let $T$ (for "time") be a random variable $T \sim \text{Exp}(\lambda)$ and $\Delta t$ is a realization (or called an observed value) of $T$. Let $D$ (for "delay") be a random variable $D ...
-7
votes
1answer
107 views

IMPA (Brazil) vs Iowa State University (USA) [on hold]

I was recently offered admission to Iowa State for a math PhD. I thought they were to deny me admission since they had not answer me until now (I spected an answer in March). Since I had not had a ...
-1
votes
0answers
18 views

associated prime of a module under a ring homomorphism [on hold]

Let $f: A\rightarrow B$ be a homomorphism of Noetherian rings, and $M$ a $B$-module(not necessarily finitely generated). Question: Is $^af(Ass_B(M))=Ass_A(M)$? If $q$ is an associated prime of the ...
0
votes
0answers
26 views

Prove the isomorphism of categories $Fun(\mathcal{A}\times\mathcal{B},\mathcal{C})\cong Fun(\mathcal{A},Fun(\mathcal{B},\mathcal{C})),$ [migrated]

I'm a computational engineer starting with a course of Introduction to Category Theory, and perhaps is extremely basic what I'm asking but I'm trying to learn how to make proofs in category theory ...
3
votes
2answers
103 views

Acyclic complexes for extraordinary cohomology theories

Let $X$ be a CW complex such that for all extraordinary homology theories, if you plug $X$ into them you get the same value as plugging in a point. Must $X$ be contractible?
0
votes
0answers
34 views

When can two Cauchy transforms intersect?

Given two polynomials $p$ and $q$ over reals and being guaranteed that both have all roots real I want to know if there is any characterization of the solutions of the equation $\frac{p'}{p} = ...
1
vote
0answers
60 views

Hyperplane sections of algebraic groups

Let $P_i$ denote the $i-th$ vertex in the Dynkin diagramm of an algebraic group. It symbolizes a parabolic subgroup of $G$ corresponding to the other vertices, meaning $G/P_i$ is a smooth, projective, ...
1
vote
1answer
164 views

How does the solenoid structure of $\mathbb{A}/\mathbb{Q}$ lift to $PGL(2, \mathbb{A})/ PGL(2, \mathbb{Q})$?

Some papers I am reading talk about an "adelic" object $PGL(2, \mathbb{Q}) \backslash PGL(2, \mathbb{A})$ . This has sparked a lot of confusion since I don't know what such a quotient could mean. A ...
5
votes
1answer
60 views

Penrose tiling substitution is bijective

Let $\mathcal{P}$ a Penrose tiling built by a substitution $\omega$ with two triangles. It is claimed, for instance, in the article of Anderson and Putnam "Topological invariants for substitution ...
0
votes
0answers
113 views

Soft Question: Relationships Between Moduli Space and Objects They Parametrize

Apologies in advance if this question is not suitable for MO. My friend and I were wondering recently what, if any, are the relationships between the geometric properties of a moduli space and the ...
2
votes
0answers
20 views

Dual cone of 'positive' Bochner integrable functions

If we consider the space of integrable functions $L^1([0,1];\mathbb{R})$, it can be ordered by the convex cone of positive integrable functions $L^1([0,1];\mathbb{R}_+)$. It is known that the ...
1
vote
0answers
34 views

Quantum dimension in SU(N) level k Kac-Moody algebra

The CFT of the SU(N) level k Kac-Moody current algebra has many Kac-Moody primary fields. I wonder if any one has calculated the quantum dimensions of those Kac-Moody primary fields. I know that, ...
0
votes
0answers
29 views

Singularities of the product of a $(\mathbb{C}^*)$-surface with $\mathbb{C}$

Recall that any normal $\mathbb{C}^*$-surface is Cohen-Macaulay and there exists normal $\mathbb{C}^*$-surfaces whose singularities are not rational. Does anyone know an example of a normal ...
1
vote
1answer
141 views

Ask the name of a combinatorial theorem

It is a classical theorem. For given integer $n \ge 1$, among ${n\choose{n/2}} = 2^{(1-o(1)n)}$ strings in the cube $\{0, 1\}^n$ with weights $n/2$, i.e., $n/2$ indices are 1, there are at least ...
0
votes
0answers
39 views

Schubert Polynomials for Complex Projective Space

The Borel picture of the cohomology ring of a flag variety gives a description as a coset space, without identifying any representatives for the classes. Lascaux and Sch\"utzenberger gave specific ...
8
votes
2answers
215 views

Sumsets and dilates: does $|A+\lambda A|<|A+A|$ ever hold?

The following problem is somehow hidden in this recently asked question, but I believe that it deserves to be asked explicitly. Is it true that for any finite set $A$ of real numbers, and any real ...
6
votes
3answers
344 views

Helly's theorem in other areas of mathematics

Are there some outstanding results using some version of Helly's theorem in a totally different area (whatever that means) than convex geometry?
1
vote
0answers
66 views

Injectivity of the Dehn-Nielsen-Baer map?

If $S$ is a closed hyperbolic surface, is there an easy proof of the injectivity of the Dehn-Nielsen-Baer map from $\mathrm{Mod}(S)$ to $\mathrm{Out}(\pi_1(S))$, taking an element of the mapping class ...
14
votes
1answer
193 views

What are applications of commutativity theorems for rings?

Herstein's little book "Noncommutative Rings" has a chapter called Commutativity Theorems in which he proves results like Jacobson's theorem: if a ring (associative with identity, please) has the ...
5
votes
0answers
91 views

Free actions of non-amenable groups

Let $G$ be a locally compact, second countable, non-amenable group, let $X$ be a Haudorff space that is not necessarily compact, and let $G \curvearrowright X$ be a topological action that is free ...
0
votes
0answers
31 views

A question on an set of 8 matrices related to the SU(3) generators

SU(2) and SU(3) differ quite a bit. The Lie algebra of SU(2) formed by the three generators g_n is the same as the algebra formed by the SU(2) matrices/elements F_n=exp (pi * i * g_n / 2). In fact, ...
0
votes
0answers
90 views

How to give a $\Delta$-complex structure?

The quotient space of a finite collection of disjoint 2-simplices obtained by identifying pairs of edges is always a surface,locally homeomorphic with $\mathbb{R^2}$. But I am not able to prove , ...
7
votes
0answers
77 views

One identity in Lie algebras

Let $L$ be a (non-restricted) Lie algebra over a field of prime characteristic $p,$ $UL$ be its universal enveloping algebra and $a_1,\dots, a_p \in L$ (the number of elements is equal to the ...
4
votes
0answers
63 views

$H^s$ norm of a solution of a nonlinear Schrödinger equation

I'm reading the paper "Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on $\mathbb{R}^3$ by Colliander, Keel, Staffilani, Takaoka and Tao. They study the ...
7
votes
0answers
55 views

A family of posets

Consider the family of all (finite) posets that can be obtained by repeatedly applying one of the following three operations (starting e.g. with the empty poset): (O1) Disjoint union of one or more ...
1
vote
0answers
36 views

Bounds on the spherical measure of sub-level sets of quadratic forms

I'm wondering if there are any bounds on the spherical measure of sets of the form $$ \mu_n\left(\{y\in S^{n-1} : \frac{y_1^2}{y_2^2} < \alpha\}\right) \leq f(\alpha) $$ where $\alpha$ is some ...
1
vote
0answers
67 views

On the compactification of moduli space of vector bundles

Let $X$ be an irreducible, nodal curve over an algebraically closed field of genus at least $2$. Denote by $U(r,d)$ (resp. $U^0(r,d)$) the moduli space of torsion-free (resp. locally free) sheaves of ...
7
votes
1answer
84 views

Does the Tutte polynomial of iterated cone graphs detect isomorphism?

Let $T_G(x,y)$ denote the Tutte polynomial of a graph. Of course we may have $T_G(x,y) = T_H(x,y)$ for $G$ and $H$ non-isomorphic graphs. Now let $c(G)$ denote the cone graph of $G$, i.e., the graph ...
1
vote
0answers
32 views

Dense subgroups in subgroups of profinite groups

Let $G$ be a finitely generated residually finite group and $\hat G$ its profinite completion. Then for all $g\in \hat G$ we have $gGg^{-1}\leq \hat G$ is dense. Suppose that $H\leq \hat G$ is a ...
1
vote
0answers
27 views

Perturbation of a Fredholm sections which preserves compactness of 0-set

I am learning Morse-Bott-Floer theory and found the following cool paper http://de.arxiv.org/abs/1310.5080 by P. Albers and D Hein. In order to prove a cup-length estimate on the number of critical ...

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