2
votes
0answers
52 views

Does the invariant from resolution of singularities provide a Whitney stratification?

The topic of Whitney stratifications came up in a lecture, and the general procedure in the examples was to decompose the singular locus of the variety into the strata starting with the "worst" ones. ...
1
vote
0answers
27 views

Discrete J-method of interpolation

The discrete $J$ method is, given Banach spaces $A_0$ and $A_1$: The interpolationn space $[A_0, A_1]_\theta$ is defined by: $a \in [A_0, A_1]_\theta$ if and only if $a$ can be written as ...
0
votes
0answers
57 views

Shifting a function with non-simple root creates complex roots [on hold]

Hello friendly people, I have seen a vague statement in an article that i couldn't prove: that if a function has a root with multiplicity greater than 1, by shifting the function (adding a small ...
2
votes
2answers
505 views

Has this formula about prime gaps already been conjectured and/or proven?

While playing around with prime gaps, I found out that the following formula seems to be a rather good approximation of the ratio $\dfrac{p_{b}-p_{a}}{b-a}$ where $a<b$ are positive integers: ...
-3
votes
0answers
20 views

multi-variate closed form solution [on hold]

I have a loss function with two paramters. I found that when I fix one I can obtain the closed form solution of the other. In that case how can I optimize to learn those two parameters. Lets my ...
3
votes
1answer
200 views
+50

Tannakian fundamental group of two explicit tensor categories

Let $K/k$ is a field extension and $G$ an affine group scheme over $K$. What are the Tannakian fundamental groups of these two $k$-tensor categories (with trivial fiber functors over $k$): 1. The ...
8
votes
0answers
199 views

Transcendence of products of certain real algebraic numbers

Let \begin{equation} z := \prod_p p^{1/p^2}, \end{equation} where the product is over all prime numbers $p$, and we always take the positive real root. Is $z$ transcendental or algebraic, or (as I ...
2
votes
1answer
100 views

Braid wiring diagrams and matroids

recently I started reading some articles about the presentation of the fundamental group of lines arrangements in $\mathbb{C}^{2}$ via Wiring diagrams. I also found some relation with matroid theory. ...
0
votes
1answer
92 views

Fixed field of the Nebentypus of a newform for $\Gamma_1(N)$

Let $f=\sum_{n\geq 1}\in S_2(\Gamma_1(N),\varepsilon)$ be a normalized newform without CM and with Nebentypus $\varepsilon$. Let $L=\mathbb Q(a_n\colon n\in \mathbb N)$ be the number field generated ...
2
votes
1answer
82 views

The rigid-analytic open disk

Let $K$ be a local field and $D_K$ the open unit disk, considered as a rigid space or adic space over $K$. What is the algebra of analytic functions on $D_K$? Proposition 1.1 of this article describes ...
0
votes
0answers
77 views

Coordinate charts on converging Riemann surfaces

Let $S$ be a $2-$dim manifold and $q \in S$. Furthermore, let $j_{n}$ be a sequence of complex structures on $S$ converging in $C^{\infty}_{\text{loc}}$ to a complex structure $j$ on $S$ as ...
-1
votes
0answers
50 views

How do I solve this differential equation by differentiation? [on hold]

How do I solve this equation $$ f(x) = \int_{y=0}^{1-x}f(x+y)\, dy + \int_{y=1-x}^1 y\, dy $$ by differentiation?
0
votes
0answers
32 views

Definition of mth order stationarity

in the definition of the weak GARCH processes they use the terminology of the 4th-order stationarity of the process $(X_t)$. I know the definition of 2n-order stationarity, but I'm not exactly sure, ...
9
votes
0answers
119 views

Elements of order 3 normalizing no non-identity 2-subgroups in Almost Simple Groups

This question is partly motivated by a situation which arises in modular representation theory. A finite group $G$ is said to be almost simple if $G$ has a unique minimal normal subgroup which is a ...
0
votes
0answers
129 views

What is a Beilinson spectral sequence?

I'm writing to ask just a question. I would like to understand better what is the Beilinson's spectral sequence and how it can be used. Is there any useful and clear reference you advice to someone ...
6
votes
2answers
133 views

How are the Walker-Wang TQFT and the Crane-Yetter TQFT related?

Mathematical physicists in solid state physics and topological insulators talk a lot about Walker-Wang models, which are a family of Hamiltonians defined on a 3d lattice. Unfortunately, the original ...
3
votes
0answers
48 views

Induced subgraphs of small strongly regular graphs

Consider a strongly regular graph $G$ with parameters $(76,30,8,14).$ Hoffman's bound tells us that $\overline{G}$ has an independent set of size at most $4$ and its not hard to see there are indeed ...
0
votes
0answers
80 views

undergraduate research [on hold]

I am a undergraduate student from Sri Lanka.I'm following a maths special degree programme.I have to submit a research project.I chose the area,Linear programming/Differential equation.So can you ...
0
votes
0answers
33 views

Generating alternating cycles on a perfect matching

Given a perfect matching $M$ in a regular bipartite graph $G$, is there an efficient algorithm to randomly generate self-avoiding alternating cycles with uniform distribution? Ideally, such an ...
0
votes
0answers
54 views

Restriction of derivations on $C^\infty(X)$

In 'Kriegl, Michor - A convenient setting for global infintite-dimensional analysis', they say that for an element $x$ in a convenient (i.e. Mackey-complete locally convex) space $X$, a bounded ...
-8
votes
1answer
144 views

Proof of a cubic equation problem [on hold]

Well I was doing some questions and i found something. This equation $x^3+y^3+z^3=w^3$ has only one solution which is $x=3,y=4,z=5,w=6$. And what I have have proposed is that there is not other ...
0
votes
0answers
52 views

What does deg=0 imply for the gauss map?

I am facing the following problem. I have a Riemannian manifold $(M,g)$ with gauss curvature zero, an isometric immersion $v:M\rightarrow \mathbb{R}^3$ that is $C^{1,\alpha}$ and I consider the Gauss ...
0
votes
0answers
128 views

A (possible) equivalent relation on the space of vector bundles

Edit: According to the essential comment of Alex Degtyarev, we revise the question as follows; Assume that $\alpha$ and $\beta$ are two oriention preserving automorphism of Lie groups $O(n)$ and ...
2
votes
1answer
316 views

Do hom-sets really live in the category Set?

This isn't really a research-level question (sorry!), but I asked on math.se (link), and though the question was upvoted a few times, I didn't get any answers. So since there may well be more ...
0
votes
0answers
32 views

Integral over a point process. Asymptotic of the dispersion

I consider an integral (or a sum with random index) $$ M(t) =\int\limits_0^t f(t-u)dX(u), $$ where $$ X(u) = \sum\limits_{i=1}^{N(u)} \xi_i,\qquad N(u)=\max\{k: \tau_1+\,\dots,\,\tau_k\, <\, u\}, ...
0
votes
0answers
84 views

A linear operator on $M_{n}(\mathbb{R})$ [on hold]

In this question $O(n)$ is the orthonormal group which is equpied with a unique Haar meaure. We define a linear map $T$ on $M_{n}(\mathbb{R})$ with $$T(A)=\int_{O(n)} (g^{-1}Ag)dg$$ What is the ...
1
vote
0answers
54 views

A reasonable framework to study properties of operator $A \mapsto KAK$ on Banach space

Let $K$ be a continuous linear operator on $C[0,1]$ (more, precisely, it is a linear integral operator). Then $K$ defines a continous linear operator $\widehat K$ on $\mathcal L(C[0,1])$ by the rule ...
-3
votes
0answers
48 views

Radius of convergence of power series [on hold]

Suppose that $f(z)=\sum_{k=0}^{\infty}c_{k}z^{k}$ is a power series with complex coefficients, such that there exists $M>0$ and $A\in (0, 1)$ with the property that $|c_{k}|\le M\cdot ...
1
vote
0answers
59 views

continuous homomorphism with open image in a product topological space

I originally posted the problem below in MathSE, but I deleted it since it is not receiving any attention. So I decided to transfer the question here instead. Let $G$ be a profinite group and $I$ ...
1
vote
0answers
49 views

Invariance of the Noether charge

The paper http://epubs.siam.org/doi/abs/10.1137/1023098 (Generalizations of Noether’s Theorem in Classical Mechanics, by Willy Sarlet and Frans Cantrijn) mentions "an interesting property of the ...
2
votes
1answer
86 views

Matching power series to infinity

As pointed out by Makoto, on this question about power series rings and the axiom of choice, an idea I had needed the axiom of dependent choice to work. However, the construction raises another ...
4
votes
0answers
265 views

Consequences of ZF+“all subsets of reals are Lebesgue measurable”

(I'm not sure if this is entirely suitable here so feel free to close it if it's not.) The statement "there is a Lebesgue measure on $\mathbb{R}$($2^\omega$)" means: there is a total $\sigma$-additive ...
-3
votes
0answers
47 views

Increasing order [on hold]

It's been a long time (20 years) since I took any math class. In High School I made it as far as Algebra II with Basic Trig I'm currently taking an online algorithm course. I have reasoned that the ...
-4
votes
0answers
48 views

Notation in groups/rings/fields [on hold]

I'm reading about Imaginary Quadratic Fields, and I came across this notation Z/nZ, but i don't know what it means. What does \mathbb{Z}/n\mathbb{Z} mean?
3
votes
0answers
96 views

a game with generic filters

The present question is a follow-up to this one. Assume GCH holds in $V$ and suppose $G \subseteq Add(\omega_1,\omega_2)$ is generic over $V$. For any $g \subseteq Add(\omega_1,\alpha)$ in $V[G]$ ...
12
votes
7answers
545 views

Examples of categorical adjunctions in analysis, Lie theory, and differential geometry?

In introductory texts on category theory, it seems like the majority of examples come from algebraic topology, algebra, and logic. Are there any good examples of adjunctions in analysis, Lie theory, ...
1
vote
1answer
271 views

Isomorphism between a mapping class group and the fundamental group of a moduli space

For some fixed integer $d \geq 3$, let $M(0, d)$ be the mapping class group of self-homeomorphisms of the Riemann sphere which fix each of the $d$ points $0, 1, ... , d-2, \infty$. Let $X$ be the ...
0
votes
1answer
81 views

Graph lifts and representation theory

Is there any connection known between the two? One can naturally define lifts of graphs by groups like $\mathbb{Z}_k$ and hence I wonder if representation theoretic properties can be used to say ...
2
votes
1answer
29 views

Sampling point uniformly at random satisfying equality constraints

First of all, I apologize in advance if the question has already been asked in some way on this site and/or if there is a widely known solution to this problem. The description of my problem is ...
0
votes
0answers
16 views

Column Subset Selection implementations

Are there readily available implementations of algorithms for the CSSP - Column Subset Selection Problem?
3
votes
0answers
39 views

Highest (short) roots and commutation relations in (twisted) DAHA

I am trying to understand, explicitly, the commutation relation between $X_\vartheta$ and $Y_\vartheta = T_0T_{s_\vartheta}$ in the (twisted) DAHA for a root system $R$, where $\vartheta$ is the ...
2
votes
1answer
77 views

Proper domain for operators

in this paper on arxiv in equation 27, two operators $$A_m^* = (1-x^2)^{\frac{1}{2}} \frac{d}{dx} + \frac{mx}{\sqrt{1-x^2}}$$ and $$A_m = - \frac{d}{dx}(1-x^2)^{\frac{1}{2}} + ...
0
votes
0answers
19 views

Moments in the Quantile Process

Let $q_{n}(t)$ be the $nth$ quantile processes ($t\in (0,1)$) based on the distribution F: $$q_{n}(t) = \{\sqrt{n}[F^{-1}_{n}(t)-F^{-1}(t)]\}.$$ In this case, $F^{-1}$ is the (generalized) inverse of ...
0
votes
0answers
66 views

Discrete measures and discrete kernels

This is a cross-post from math.stack. Let $d\in\mathbb N$ and $\mu$ be the probability measure on $\mathbb R^d$ defined by $\mu=\sum_{k=1}^\infty 2^{-k}\delta_{x_k}$ for some sequence ...
1
vote
0answers
54 views

About Theorem $3.1.3$ in Kubota's book: Elementary theory of eisenstein series

My question is about the proof of Theorem $3.1.3$ given in kubota's book, which shows how the function $\varphi(s)$ appearing in the Fourier expansion of eisenstein series can be continued ...
3
votes
1answer
138 views

Verlinde Formula and Theta Function Identities

The paper Fusion rules and modular transformations in 2D conformal field theory by Erik Verlinde mentions a simple case of rational conformal field theory, where the fusion algebra is just ...
1
vote
1answer
132 views

rational point of a curve [on hold]

Let $X$ be a smooth projective curve over $\mathbb{Q}$. I heard (if I did not misunderstood) that the geometry of the complex points $X(\mathbb{C})$ (flat, hyperbolic case) dicts the shape (group ...
10
votes
1answer
214 views
+300

Does the Legendre-Hadamard condition imply a generalized Gårding inequality?

For simplicity, we restrict to constant coefficients. Let $A^{ij}_{ab} \in \mathbb{R}$, $1 \le i, j \le n$ and $1 \le a, b\le m$, satisfy the Legendre-Hadamard condition: $$ ...
1
vote
0answers
110 views

Integration in C^* algebra

Let $\mathfrak{A}$ be a C${}^*$ algebra and $\mathbb{R}\ni s \mapsto \alpha_s$ a continuous family of its automorphisms. Is it true that $$ \int d s \, f(s)\, \alpha_s(A) $$ is well defined as a ...
6
votes
2answers
166 views

Decidability of diophantine equation in a theory

Given a theory $T \subseteq \operatorname{Th}(\mathbb{N})$, define the decision problem $D_T$ as follows: Given a polynomial $p$ with integer coefficients and variables $\bar{x}$, decide whether ...

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