Suppose we have $\theta=(\theta_1,\ldots,\theta_n)$, with $v_i:\mathbb{R}\times\mathbb{R}\to\mathbb{R}$ being a continuous, differentiable, concave function. Now I want to solve the following maximization problem: $$ \max_{\theta} \sum_{i=1}^{n} v_i(\theta_i,a_i) $$ subject to $$ \theta_i\geq 0,\...

Moduli spaces are spaces of solutions of geometric classification problems. That is, the points of a moduli space correspond to solutions of geometric problems. Moduli spaces can be thought of as giving a universal space of parameters for the problem. Q1: Is $\zeta_{\Bbb R^n}$ a space of modu...

In trying to answer this question on MSE, I got stuck. This taunts me because I think I should be able to do it. The Question: Let $\phi : G\twoheadrightarrow H$ be an epimorphism of groups. Suppose $W$ and $K$ are conjugate in $H$. Show that $\phi^{-1}(W)$ and $\phi^{-1}(K)$ are conjugate i...