5 problems

Maximal singularity conjecture. No sequence of quasimodes, that is, images of the operators $\mathcal{\hat P}_{-T,T,\phi}$, can have a more singular limit measure than the singular…

Limiting-distribution conjecture. As $N\to\infty$ through primes, the limiting distribution of the normalized matrix elements $F_j^{(N)}$ is that of the random variable

Let ${\mathsf{X}}$ be a generic solution of the coupled cat maps lattice equation, with symbolic representation ${\mathsf{M}}$, and let ${\mathcal{S}}$ and ${\mathcal{T}}$ denote t…

Entropy threshold conjecture. The entropy of $\mu$ satisfies

Let the generalized cat map have dimension $n$, and let its dominant eigenvalue mean the eigenvalue of greatest absolute value of the map's defining matrix. Dominant-eigenvalue gro…