2 problems

Let $G$ be a semisimple Lie group and let $V$ be a uniformly bounded representation of $G$ on a Hilbert space. The uniformly bounded cohomology conjecture. The cohomology with coef…

Spectral conjecture. There exists such a function $f$ and such representations and vectors for every compact $K\subset\Gamma$ and every $\varepsilon>0$. This would yield, by a limi…