2
votes
0answers
83 views
+50

Codimension of the set of topologically singular points of an Alexandrov space.

I am reading Burago, Burago and Ivanov's book A course in metric geometry. In chapter 10 the mention that Alexandrov spaces of curvature bounded below have a stratification into topological manifolds. ...
5
votes
0answers
276 views
+150

Neveu-Schwarz and Ramond sector in the free fermion CFT

My question is about the Neveu-Schwarz and the Ramond sector in the free fermion CFT. The setup is as follows. We consider two dimensional Minkowski space with a point removed $M = \mathbb{R}^{1, ...
1
vote
2answers
362 views
+50

orbits of linear algebraic group $G({\Bbb Q}_p)$ acting on subgroups of ${\Bbb Q}_p^n$

Let $G\subseteq GL(n)$ be a linear algebraic group, and let $G({\Bbb Q}_p)\subseteq GL(V)$ act on a ${\Bbb Q}_p$-vector space V of finite dimension. Consider the action of $G$ on abelian subgroups ...
5
votes
1answer
256 views
+50

Why are pushouts the right tool in these setups

$\newcommand{\cat}[1]{\mathcal{#1}}$ $\newcommand{\cod}{\operatorname{cod}}$ $\DeclareMathOperator{\dom}{dom}$ $\DeclareMathOperator{\colim}{colim}$ The question is about two pushout constructions ...
2
votes
1answer
156 views
+50

Generators vs minimal degree polynomials of ideals

Given an ideal $I$ of $\mathbb{R}[X_1,X_2,X_3,X_4,X_5]$ generated by two unknown polynomials. I know two homogenous polynomials $p_1 \in I$ and $p_2 \in I$ such that $p_1$ is of degree 2 and up to a ...
1
vote
0answers
109 views
+50

PRNG and coding theory

Let $k, n \in \mathbb{N}$, $k = (1 - \epsilon)n$ where $1 >\epsilon > 0$. I want to find $f: \{0,1\}^k \to \{0, 1\}^n$ such that: 1) $f(a) \not= f(b)$ if $a \not=b $ 2) for any $x \in ...
14
votes
0answers
311 views
+50

Why would the roots of the generating functions of the number of k-almost primes less than x have negative real parts?

There is a 50 point bounty on this question. Specifically, I find it appealing to count only squarefree numbers having $k$ prime factors, so I define $$\pi_k(x)=\#\{n\leq x: ...