MathOverflow

The classical development of class field theory makes heavy use of the Brauer group $Br(K)$ of a (local or global) number field $K$. One modern point of view on Brauer groups is as follows: we have an $\infty$-category $D(K)$ which is a commutative ring...

There are two sets of nodes $S$ and $V$. Each element $s\in S$ has value $\pi_s\geq 0$ and a parameter $\alpha_s\in [0,1]$. There is a bipartite graph $G=(S,V,E)$, in which an edge $(s,v)\in E$ indicates that $v$ node allocates some value $\sigma_v^s...

Remark: This is a cross-post of MSE5124853. I was told to ask here again.
Let $O$ be a 1-colored $\mathsf{Set}$-operad with $O(0)=\{0\}$, $O(1)=\{1\}$. It comes with multiplication maps of the form$$\mu:O(m) \times O(k_1) \times \dots \times O(k_m) \longrightarrow O(k_1+...+k_m).$$...

I have a question concerning the paper by Yuan-Wei Qi,The critical exponents of parabolic equations and blow-up in $\mathbb{R}^n$.
The author studies the Cauchy problem$$u_t = \Delta(u^m) + t^s|x|^\sigma u^p\qquad \text{in } \mathbb{R}^n,$$with $m>1$, and analyzes both finite-time blow-up (subcritical case) and globalexistence (supercritical case), where the critical exponent...