2 problems

Let $\Gamma$ be an infinite sofic group, let $\Sigma$ be a sofic approximation, and let $V$ be a finite-dimensional representation of $\Gamma$. The finite-dimensional vanishing con…

Let $\Gamma$ be a sofic group, let $\sigma\colon \Gamma\to S_{d_i}$ be a sofic approximation, let $2<p<\infty$, and let $V$ be a finite-dimensional normed vector space. The full…