2 problems

Uniform spectral gap conjecture. For any $\varepsilon>0$, with probability tending to $1$ as $n\to +\infty$, the cover $M_n\to M$ has no new resonance in the half-space

Let $M$ be a compact $(2n+1)$-dimensional manifold and let $\alpha$ be a contact $1$-form on $M$ whose corresponding flow is Anosov with orientable stable and unstable bundles. Let…